Math Grade 4

2016 – 2017

Fourth Grade

MATHEMATICS

Curriculum Map

Volusia County Schools

Mathematics Florida Standards

0 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Table of Contents

I. Critical Area for Mathematics in Grade 4……………….…………..…2
II. Mathematics Florida Standards: Grade 4 Overview……….……..…3
III. Standards for Mathematical Practice………………………….…….....4
IV. Common Addition and Subtraction Situations……………….….......5
V. Common Multiplication and Division Situations………………….....6
VI. Common Strategies…………………………………………………...…..7
VII. 5E Learning Cycle: An Instructional Model………………………...11
VIII. Instructional Math Block……………………………………………..…12

IX. Units
A. Unit 1..………………………………..……………………………………13
B. Unit 2…………………………..…………………………………………..24
C. Unit 3………………………………………………………………………37
D. Unit 4……………………………………….………………………...……49

X. Appendices
Appendix A: Formative Assessment Strategies………………………..64
Appendix B: Intervention / Remediation Guide………………………...74

XI. Glossary of Terms for the Mathematics Curriculum Map………...75

1 Volusia County Schools Grade 4 Math Curriculum Map
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Mathematics Department

Critical Areas for Mathematics in Grade 4

In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-
digit multiplication, and developing understanding of division to find quotients involving multi-digit dividends; (2)
developing understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and
multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified
based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and
symmetry.

(1) Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place.
They apply their understanding of models for multiplication (e.g., equal-sized groups, arrays, area models), place value, and
properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and
generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select
and accurately apply appropriate methods to estimate or mentally calculate products. They develop fluency with efficient procedures
for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations;
and use them to solve problems. Students apply their understanding of models for division, place value, properties of operations,
and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures
to find quotients involving multi-digit dividends. They select and accurately apply appropriate methods to estimate and mentally
calculate quotients, and interpret remainders based upon the context.

(2) Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions
can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions. Students extend
previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing
fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole
number.

(3) Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-
dimensional shapes, students deepen their understanding of properties of two-dimensional objects and the use of them to solve
problems involving symmetry.

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Mathematics Department

Grade 4 Overview

Domain: Operations and Algebraic Thinking
Cluster 1: Use the four operations with whole numbers to solve problems.
Cluster 2: Gain familiarity with factors and multiples.
Cluster 3: Generate and analyze patterns.

Domain: Number and Operations in Base Ten
Cluster 1: Generalize place value understanding for multi-digit whole numbers.
Cluster 2: Use place value understanding and properties of operations to perform multi-digit arithmetic.

Domain: Number and Operations—Fractions
Cluster 1: Extend understanding of fraction equivalence and ordering.
Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on
whole numbers.
Cluster 3: Understand decimal notation for fractions, and compare decimal fractions.

Domain: Measurement and Data
Cluster 1: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller
unit.
Cluster 2: Represent and interpret data.
Cluster 3: Geometric measurement: understand concepts of angle and measure angles.

Domain: Geometry
Cluster 1: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

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Mathematics Department

Standards for Mathematical Practice

Students will:

1. Make sense of problems and persevere in solving them. (SMP.1)

Mathematically proficient students in Grade 4 know that doing mathematics involves solving problems and discussing how they solved them. Students explain to
themselves the meaning of a problem and look for ways to solve it. Fourth graders may use concrete objects or pictures to help them conceptualize and solve problems.
They may check their thinking by asking themselves, “Does this make sense?” They listen to the strategies of others and will try different approaches. They often will use
another method to check their answers.

2. Reason abstractly and quantitatively. (SMP.2)
Mathematically proficient students in Grade 4 recognize that a number represents a specific quantity. They extend this understanding from whole numbers to their work
with fractions and decimals. This involves two processes- decontexualizing and contextualizing. Grade 4 students decontextualize by taking a real-world problem and
writing and solving equations based on the word problem. For example, consider the task, “If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5
people at the party, how many pounds of roast beef will be needed? Students will decontextualize by writing the equation 3/8 × 5 or repeatedly add 3/8 5 times. While
students are working they will contextualize their work- knowing that the answer 15/8 or 1 7/8 represents the total number of pounds of roast beef that will be needed.
Further, Grade 4 students write simple expressions, record calculations with numbers, and represent or round numbers using place value concepts.

3. Construct viable arguments and critique the reasoning of others. (SMP.3)
Mathematically proficient students in Grade 4 construct arguments using concrete representations, such as objects, pictures, and drawings. They explain their thinking and
make connections between models and equations. Students refine their mathematical communication skills as they participate in mathematical discussions involving
questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking through discussions and written
responses.

4. Model with mathematics. (SMP.4)
Mathematically proficient students in Grade 4 represent problem situations in various ways, including writing an equation to describe the problem. Students need
opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Grade 4 students
should evaluate their results in the context of the situation and reflect on whether the results make sense.

5. Use appropriate tools strategically. (SMP.5)
Mathematically proficient students in Grade 4 consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might
be helpful. For instance, they may use graph paper or a number line to represent and compare decimals and protractors to measure angles. They use other measurement
tools to understand the relative size of units within a system and express measurements given in larger units in terms of smaller units.

6. Attend to precision. (SMP.6)
Mathematically proficient students in Grade 4 develop their mathematical communication skills, they try to use clear and precise language in their discussions with others
and in their own reasoning. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, they use appropriate
labels when creating a line plot.

7. Look for and make use of structure. (SMP.7)
Mathematically proficient students in Grade 4 closely examine numbers to discover a pattern or structure. For instance, students use properties of operations to explain
calculations (area model). They relate representations of counting problems such as arrays to the multiplication principal of counting. They generate number and shape
patterns that follow a given rule.

8. Look for and express regularity in repeated reasoning. (SMP.8)
Mathematically proficient students in Grade 4 notice repetitive actions in computation to make generalizations. Students use models to explain calculations and understand
how algorithms work. They also use models to examine patterns and generate their own algorithms. For example, students use visual fraction models to write equivalent
fractions.

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Mathematics Department

Common Addition and Subtraction Situations

Add to Result Unknown Change Unknown Start Unknown
Take from
Two bunnies sat on the grass. Three more Two bunnies were sitting on the grass. Some bunnies were sitting on the grass.
bunnies hopped there. How many bunnies Some more bunnies hopped there. Then Three more bunnies hopped there. Then
are on the grass now? there were five bunnies. How many bunnies there were five bunnies. How many bunnies
hopped over to the first two? were on the grass before?

2+3=? 2+?=5 ?+3=5
Five apples were on the table. I ate two
apples. How many apples are on the table Five apples were on the table. I ate some Some apples were on the table. I ate two
now? apples. Then there were three apples. How apples. Then there were three apples. How
many apples did I eat? many apples were on the table before?

5–2=? 5-?=3 ?–2=3

Put Total Unknown Addend Unknown Both Addends Unknown1

Together/ Three red apples and two green apples are Five apples are on the table. Three are red Grandma has five flowers. How many can
Take Apart2 on the table. How many apples are on the and the rest are green. How many apples she put in her red vase and how many in
table? are green? her blue vase?

3+2=? 3 + ? = 5, 5 – 3 = ? 5 = 0 + 5, 5 = 5 + 0
5 = 1 + 4, 5 + 4 + 1
Compare3 Difference Unknown Bigger Unknown 5 = 2 + 3, 5 = 3 + 2

(“How many more?” version): (Version with “more”): Smaller Unknown

Lucy has two apples. Julie has five apples. Julie has 3 more apples than Lucy. Lucy (Version with “more”):
How many more apples does Julie have has two apples. How many apples does
than Lucy? Julie have? Julie has three more apples than Lucy. Julie
has five apples. How many apples does
(“How many fewer?” version): (Version with “fewer”): Lucy have?

Lucy has two apples. Julie has five apples. Lucy has three fewer apples than Julie. (Version with “fewer”):
How may fewer apples does Lucy have than Lucy has two apples. How many apples
Julie? does Julie have? Lucy has three fewer apples than Julie. Julie
has five apples. How many apples does
2 + ? = 5, 5 – 2 = ? 2 + 3 = ?, 3 + 2 = ? Lucy have?

5 – 3 = ?, ? + 3 = 5

1 These take apart situations can be used to show all the decompositions of a given number. The associated equations, which have the total on the left of the equal sign, help children understand that

the = sign does not always mean makes or results in, but always does mean is the same number as.
2 Either addend can be unknown, so there are three variations of these problem situations. Both Addends Unknown is a productive extension of this basic situation, especially for small numbers less
than or equal to 10.
3 For the Bigger Unknown or Smaller Unknown situations, one version directs the correct operation (the version using more for the bigger unknown and using less for the smaller unknown). The other

versions are more difficult.

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Mathematics Department

Common Multiplication and Division Situations4

Unknown Product Group Size Unknown Number of Groups Unknown
3×6=? (“How many in each group?” Division) (“How many groups?” Division)

3 × ? = 18 and 18 ÷ 3 = ? ? × 6 = 18 and 18 ÷ 6 = ?

There are 3 bags with 6 plums in If 18 plums are shared equally into 3 If 18 plums are to be packed 6 to
each bag. How many plums are bags, then how many plums will be in a bag, then how many bags are
there in all? each bag? needed?

Equal Groups Measurement example. You Measurement example. You have 18 Measurement example. You have
Arrays5, Area6 need 3 lengths of string, each 6 inches of string, which you will cut into 18 inches of string, which you will
inches long. How much string 3 equal pieces. How long will each cut into pieces that are 6 inches
Compare will you need altogether? piece of string be? long. How many pieces of string
General will you have?
There are 3 rows of apples with 6 If 18 apples are arranged into 3 equal If 18 apples are arranged into
apples in each row. How many rows, how many apples will be in each equal rows of 6 apples, how many
apples are there? row? rows will there be?

Area example. What is the area Area example. A rectangle has area Area example. A rectangle has
of a 3 cm by 6 cm rectangle? 18 square centimeters. If one side is area 18 square centimeters. If
3 cm long, how long is a side next to one side is 6 cm long, how long is
A blue hat costs $6. A red hat it? a side next to it?
cost 3 times as much as the blue A red hat costs $18 and that is 3 times A red hat costs $18 and a blue hat
hat. How much does the red hat as much as a blue hat costs. How costs $6. How many times as
cost? much does the blue hat cost? much does the red hat cost as the
blue hat?

Measurement example. A rubber Measurement example. A rubber Measurement example. A rubber
band is 6 cm long. How long will band is stretched to be 18 cm long band was 6 cm long at first. Now
the rubber band be when it is and that is 3 times as longs as it was it is stretched to be 18 cm long.
stretched to be 3 times as long? at first. How long was the rubber band How many times as long is the
at first? rubber band now as it was at first?
a×b=?
a × ? = p and p ÷ a = ? ? × b = p and p ÷ b = ?

4The first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples.
5The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3

rows and 6 columns. How m any apples are in there? Both forms are valuable.
6Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement

situations.

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Mathematics Department

Name Addition Strategies Student Work Sample

Counting All Clarification 8+9
Counting On
Doubles/Near Doubles  student counts every number 1,2,3,4,5,6,7,8,9,10,11,12,13,
 students are not yet able to add on from either addend, they must mentally build every 14,15,16,17
8+9
number
 transitional strategy 8…9,10,11,12,13,14,15,16,17
 student starts with 1 number and counts on from this point
 student recalls sums for many doubles 8+9

 student uses fluency with ten to add quickly 8 + (8 + 1)
(8 + 8) + 1
16 + 1= 17
8+9

Making Tens (7 +1) + 9
7 + (1 + 9)
Making Friendly Numbers/  friendly numbers are numbers that are easy to use in mental computation 7 + 10 = 17
Landmark Numbers  student adjusts one or all addends by adding or subtracting to make friendly numbers 23 + 48
 student then adjusts the answer to compensate
23 + (48 + 2)
Compensation  student manipulates the numbers to make them easier to add 23 + 50= 73
 student removes a specific amount from one addend and gives that exact amount to the 73 – 2 = 71
Breaking Each Number into its 8+6
Place Value other addend
8-1=7 6+1=7
 strategy used as soon as students understand place value 7+7=14
 student breaks each addend into its place value (expanded notation) and like place value 24 + 38

amounts are combined (20 + 4) + (30 + 8)
 student works left to right to maintain the magnitude of the numbers 20 + 30 = 50
4 + 8 = 12

50 + 12 = 62

 follows place value strategy 45 + 28

Adding Up in Chunks  student keeps one addend whole and adds the second addend in easy-to-use chunks 45 + (20 + 8)

 more efficient than place value strategy because student is only breaking apart one addend 45 + 20 = 65

65 + 8 = 73

Children do not have to be taught a particular strategy. Strategies for computation come naturally to young children. With opportunity and encouragement, children invent

strategies for themselves.

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Mathematics Department

Name Subtraction Strategies Student Work Sample

Adding Up Clarification 14 – 7
7… 8,9,10,11,12,13,14 (+1 each jump)
 student adds up from the number being subtracted (subtrahend) to the whole
(minuend)

 the larger the jumps, the more efficient the strategy
 student uses knowledge of basic facts, doubles, making ten, and counting on

Counting Back/Removal  strategy used by students who primarily view subtraction as taking away 7 + 3= 10
 student starts with the whole and removes the subtrahend in parts 10 + 4= 14
 student needs the ability to decompose numbers in easy-to-remove parts 3 + 4= 7
65 – 32
 student breaks each number into its place value (expanded notation)
 student groups like place values and subtracts 65 – (10 + 10 + 10 + 2)
65, 55, 45, 35, 33
Place Value
65 – (30 + 2)
65 – 30 = 35
35 – 2 = 33
999 – 345

(900 + 90 + 9) – (300 + 40 + 5)
900 – 300 = 600
90 – 40 = 50
9–5=4

600 + 50 + 4 = 654

 student understands that adding or subtracting the same amount from both 123 – 59

Keeping a Constant numbers maintains the distance between the numbers 123 + 1 = 124
Difference  student manipulates the numbers to create friendlier numbers 59 + 1 = 60

124 – 60 = 64

 strategy requires students to adjust only one of the numbers in a subtraction 123 – 59

Adjusting to Create an problem 59 + 1 = 60
Easier Number  student chooses a number to adjust, subtracts, then adjusts the final answer to 123 – 60 = 63
I added 1 to make an easier number.
compensate 63 + 1 = 64
 students must understand part/whole relationships to reason through this strategy

I have to add 1 to my final answer

because I took away 1 too many.

Children do not have to be taught a particular strategy. Strategies for computation come naturally to young children. With opportunity and encouragement, children invent strategies for themselves.

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Name Multiplication Strategies Student Work Sample

Clarification 6 × 15

 beginning strategy for students who are just learning multiplication 15+15+15+15+15+15 = 90
 connection to an array model provides an essential visual model
2 × 15 = 30
Repeated Addition/Skip 2 × 15 = 30
Counting 2 × 15 = 30
30 + 30 + 30 = 90

 students who are comfortable multiplying by multiples of 10 9 × 15

Friendly Numbers/ Add 1 group of 15
Landmark Numbers 10 × 15 = 150
We must now take off 1 group of 15.

150 – 15 = 135

 strategy based on the distributive property and is the precursor for our 12 × 15

Partial Products standard U.S. algorithm 12 × (10 + 5)
 student must understand that the factors in a multiplication problem can 12 × 10 = 120
12 × 5 = 60
be broken into addends 120 + 60 =180
 student can then use friendlier numbers to solve more difficult problems

 strategy relies on students’ understanding of breaking factors into 12 × 25

Breaking Factors into Smaller smaller factors (3 × 4) × 25
Factors  associative property 3 × (4 × 25)

(4 × 25) + (4 × 25) + (4 × 25) = 300

 used by students who have an understanding of the concept of arrays 8 × 25

Doubling & Halving with different dimensions but the same area 8÷2 = 4
 student can double and halve numbers with ease 25 × 2 = 50
 student doubles one factor and halves the other factor 4 × 50 = 200

Children do not have to be taught a particular strategy. Building a conceptual understanding before procedural knowledge helps students navigate and explore different
approaches to computation. Children’s invented algorithms for multiplication and division generally build on their procedures for adding and subtracting multi-digit numbers.

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Division Strategies

Name Clarification Student Work Sample

Repeated Subtraction/Sharing  early strategy students use when they are developing multiplicative 30 ÷ 5
reasoning
Multiplying Up 30 – 5 = 25
 repeated subtraction is one of the least efficient division strategies 25 – 5 = 20
 presents opportunities to make connections to multiplication 20 = 5 = 15
15 – 5 = 10
 strategy is a natural progression from repeated subtraction 10 – 5 = 5
 student uses strength in multiplication to multiply up to reach the dividend 5–5=0
 students relying on smaller factors and multiples will benefit from discussions I took out 6 groups of 5
30 ÷ 5 = 6
related to choosing more efficient factors 384 ÷ 16

10 × 16 = 160 384 – 160 = 224
10 × 16 = 160 224 – 160 = 64
2 × 16 = 32
2 × 16 = 32 64 – 32 = 32
32 – 32 = 0

 maintains place value 10 + 10 + 2 + 2 = 24
 allows students to work their way toward the quotient by using friendly 384 ÷ 16

Partial Quotients numbers such as ten, five, and two 16 384 ×10 24
Proportional Reasoning  as the student chooses larger numbers, the strategy becomes more efficient -160 ×10
224 ×2
 students who have a strong understanding of factors, multiples, and -160 ×2
fractional reasoning 64
-32
 students’ experiences with doubling and halving to solve multiplication 32
problems can launch an investigation leading to the idea that you can divide -32
the dividend and the divisor by the same number to create a friendlier 0
problem
384 ÷ 16

384 ÷ 16
÷2 ÷2
192 ÷ 8
÷2 ÷2
96 ÷ 4
÷2 ÷2
48 ÷ 2 = 24

384 ÷ 16 = 24

Children do not have to be taught a particular strategy. Building a conceptual understanding before procedural knowledge helps students navigate and explore different approaches to computation. Children’s

invented algorithms for multiplication and division generally build on their procedures for adding and subtracting multi-digit numbers.

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Mathematics Department

5E Learning Cycle: An Instructional Model

ENGAGEMENT EXPLORATION EXPLANATION ELABORATION EVALUATION

The engagement phase of the model The exploration phase of the model is The explanation phase of the model is The elaboration phase of the model is The evaluation phase of the model is
is intended to capture students’ intended to provide students with a intended to grow students’ intended to construct a deeper intended to be used during all phases
interest and focus their thinking common set of experiences from understanding of the concept,
on the concept, process, or skill which to make sense of the concept, understanding of the concept, process, or skill through the of the learning cycle driving the
that is to be learned. process or skill that is to be learned. process, or skill and its associated exploration of related ideas. decision-making process and

During this engagement phase, During the exploration phase, academic language. During the elaboration phase, informing next steps.
the teacher is on center stage. the students come to center stage. the teacher and students
During the explanation phase, share center stage. During the evaluation phase,
What does the teacher do? What does the teacher do? the teacher and students the teacher and students
 create interest/curiosity  provide necessary materials/tools share center stage. What does the teacher do? share center stage.
 raise questions  pose a hands-on/minds-on  provide new information that
 elicit responses that uncover What does the teacher do? What does the teacher do?
problem for students to explore  ask for justification/clarification of extends what has been learned  observe students during all
student thinking/prior knowledge  provide time for students to  provide related ideas to explore
(preview/process) newly acquired understanding  pose opportunities (examples and phases of the learning cycle
 remind students of previously “puzzle” through the problem  use a variety of instructional  assess students’ knowledge and
taught concepts that will play a  encourage students to work non-examples) to apply the
role in new learning strategies concept in unique situations skills
 familiarize students with the unit together  use common student experiences  remind students of alternate ways  look for evidence that students
 observe students while working to solve problems
What does the student do?  ask probing questions to redirect to:  encourage students to persevere are challenging their own thinking
 show interest in the topic o develop academic language in solving problems  present opportunities for students
 reflect and respond to questions student thinking as needed o explain the concept
 ask self-reflection questions:  use a variety of instructional What does the student do? to assess their learning
What does the student do? strategies to grow understanding  generate interest in new learning  ask open-ended questions:
o What do I already know?  manipulate materials/tools to  use a variety of assessment  explore related concepts
o What do I want to know? strategies to gage understanding  apply thinking from previous o What do you think?
o How will I know I have learned explore a problem What does the student do? o What evidence do you have?
 work with peers to make sense of  record procedures taken towards learning and experiences o How would you explain it?
the concept, process, or skill? the solution to the problem  interact with peers to broaden What does the student do?
 make connections to past the problem  explain the solution to a problem  participate actively in all phases
 articulate understanding of the  communicate understanding of a one’s thinking of the learning cycle
learning experiences concept orally and in writing  explain using information and  demonstrate an understanding of
problem to peers  critique the solution of others the concept
Evaluation of Engagement  discuss procedures for finding a  comprehend academic language experiences accumulated so far  solve problems
The role of evaluation during the and explanations of the concept  evaluate own progress
engagement phase is to gain access solution to the problem provided by the teacher Evaluation of Elaboration  answer open-ended questions
to students’ thinking during the  listen to the viewpoint of others  assess own understanding The role of evaluation during the with precision
through the practice of self- elaboration phase is to determine the  ask questions
pre-assessment event/activity. Evaluation of Exploration reflection
The role of evaluation during the Evaluation of Explanation degree of learning that occurs
Conceptions and misconceptions exploration phase is to gather an The role of evaluation during the following a differentiated approach to
currently held by students are understanding of how students are explanation phase is to determine the
uncovered during this phase. progressing towards making sense of students’ degree of fluency (accuracy meeting the needs of all learners.
a problem and finding a solution. and efficiency) when solving
These outcomes determine the Application of new knowledge in
concept, process, or skill to be Strategies and procedures used by problems. unique problem solving situations
students during this phase are during this phase constructs a deeper
explored in the next phase Conceptual understanding, skill
of the learning cycle. highlighted during explicit instruction refinement, and vocabulary and broader understanding.
in the next phase.
acquisition during this phase are The concept, process, or skill has
The concept, process, or skill is enhanced through new explorations. been and will be evaluated as part
formally explained in the next phase of all phases of the learning cycle.
The concept, process, or skill is
of the learning cycle. elaborated in the next phase
of the learning cycle.

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Mathematics Department

Elementary Instructional Math Block

Time Components Description
5
minutes Opening: Teachers will engage students to create interest for the whole group mini
Hook/Warm-up lesson or to review previous learning targets by posing a hands-on minds-
15 (engage/explore) on problem for students to explore.
minutes
Whole Group: During this time, the learning target will be introduced through explicit
Mini Lesson & Guided instruction by the teacher or through exploration/discovery by the
Practice students. Teachers model their thinking and teach or reinforce
(explore/explain/evaluate) vocabulary in context. Teacher leads students to participate in guided
practice of the new learning target.

Students will explore using manipulatives and having conversations about
their new learning. Students and teachers explain and justify what they
are doing. Teachers are using probing questions to redirect student
thinking during guided practice. Teachers provide explicit instruction to
scaffold the learning if the majority of the students are struggling.

Formative techniques are used to evaluate which students will need
interventions and which students will need enrichment.

35-45 Small Group: The teacher will work with identified, homogeneous groups to provide
minutes Guided Practice & intervention or enrichment. The students will explain their thinking
Collaborative/ through the use of a variety of instructional strategies. The teacher will
Independent Practice evaluate student understanding and address misconceptions that still
(explain/evaluate/ exist.
explore/ elaborate)
Students will work in groups using cooperative structures or engaging in
mathematical tasks. These activities are related to the mini lesson,
previously taught learning targets, or upcoming standards. Students will
continue to explore the learning targets by communicating with peers.

All students will elaborate to construct a deeper understanding while
engaging in collaborative and independent practices. Students will
evaluate their own understanding through the practice of self-reflection.

5 Closure: The teacher will revisit the learning target and any student discoveries.
minutes Summarize Students will explain and evaluate their understanding of the learning
(explain/evaluate) target through a variety of techniques. The teacher will evaluate
students’ depth of understanding to drive future instruction.

Formative techniques occur throughout each piece of the framework.

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Mathematics Department

Standards for Mathematical Practice

Students will: (to be embedded throughout instruction as appropriate)
Make sense of
problems and Reason abstractly Construct viable Model with Use appropriate Attend to precision. Look for and make Look for and express
and quantitatively. arguments and mathematics. tools strategically. use of structure. regularity in repeated
persevere in solving reasoning.
them. SMP.2 critique the
reasoning of others.
SMP.1
SMP.3 SMP.4 SMP.5 SMP.6 SMP.7 SMP.8

MAFS Domains: Number and Operations in Base Ten Pacing: Weeks 1- 8

Operations and Algebraic Thinking August 15-October 7

Learning Targets Standards Vocabulary

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on MAFS.NBT.1.2 base-ten numeral
meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
(standard form)
Students will:
compare
HINT: Third grade teaches whole numbers through 999. digit
equal (=)
 identify the digits and periods in multi-digit whole numbers up to 1,000,000. expanded form
greater than (>)
I.e., hundred thousands
hundreds
Millions Period Thousands Period Ones Period less than (<)
Millions millions
Hundred Ten Thousands Hundreds Tens Ones millions period
Thousands Thousands multi-digit
number names
 read and write multi-digit numbers through one million in base-ten numerals (standard form), number names (word form), and
expanded form. (word form)

HINT: Expanded form of 285 can be 200 + 80 + 5. However, students should have opportunities to explore the idea that ones period
285 could also be 28 tens plus 5 ones or 1 hundred, 18 tens and 5 ones (necessary for fluent regrouping using the ten thousands
standard algorithm). tens
E.g., How can you show 285 with base ten blocks? thousands
285= (2 × 100) + (8 × 10) + (5 × 1) thousands period
value

 show place value understanding for multi-digit whole numbers by naming the meaning of a given digit in whole numbers to
1,000,000 (e.g., What is the meaning of the 6 in 3,652? Answer: 600 or 6 hundreds).

 read, write, and compare multi-digit whole numbers to 1,000,000 in multiple formats (i.e. base-ten numerals, number names,
and expanded form).

 compare two multi-digit numbers to 1,000,000 using place value and record the comparison numerically using the following
symbols: <, >, or =.

 write and compare whole numbers in expanded form in multiple formats (i.e. base-ten numerals, number names, and expanded
form).

13 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, MAFS.4.NBT.1.1 digit
recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. multi-digit
ten times
Students will: value

 demonstrate with models that in a multi-digit whole number, a digit in one place represents ten times the value of the place to its
right.

E.g.,

Thousands , Hundreds Tens Ones
300 30 3
3,000

 explain that a digit in one place is worth ten times the value of the place to its right.

E.g., 10 × 540 = 5,400; the 5 in 5,400 represents 5 thousands which is 10 times as much as the 5 hundreds in 540.
HINT: While students may be able to easily see the pattern of adding a “0” at the end of a number when multiplying by 10, they

need to be able to justify why this works. When you multiply a number by 10, you increase the value 10 times; you
change the value by one place.

14 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Use place value understanding to round multi-digit whole numbers to any place. MAFS.4.NBT.1.3 digit
round
Students will: place value

 recognize that the digit to the right of an identified place value will determine how to round a number.
 use a number line as a tool to support work with rounding.

E.g., vertical number line

Represent the number 38,450 on a number line.

30,000

Possible student response: 20,000
On the number line, 38,450 is between 30,000 and 40,000.
The number 38,450 is closer to 40,000 than to 30,000. Grade 4 Math Curriculum Map
So, 38,450 rounded to its nearest ten thousands is 40,000. May 2016

 write a multi-digit number (between 1,000 and 1,000,000) rounded to any given place.
 justify the reasonableness of a response.

E.g., Round 76,398 to the nearest 1000.
Step 1: I need to round to the nearest 1000, so the answer is either 76,000 or 77,000.
Step 2: I know that the halfway point between these two numbers is 76,500.
Step 3: I see that 76,398 is between 76,000 and 76,500.
Step 4: Therefore, the rounded number would be 76,000.

 determine a number that falls between two numbers of different place values.
 determine possible starting numbers when given a rounded number.

E.g.,

Possible Rounded to the Rounded to the
Starting Nearest Nearest
Number Hundred
Thousand
13,600
2,400 14,000
2,000

15 Volusia County Schools

Mathematics Department

Fluently add and subtract multi-digit whole numbers using the standard algorithm. MAFS.4.NBT.2.4 algorithm
calculate
Students will: difference
regroup
 apply an understanding of addition and subtraction, place value, and flexibility with multiple strategies to use the standard sum
algorithms for addition and subtraction fluently.

HINT: Fluently means accurately, efficiently, and strategically. 4th grade is the first grade level in which students are expected to
be fluent with the standard algorithm to add and subtract.

 determine the missing digit that makes a statement true.
E.g.

 analyze and describe an error in a strategy and show the correct solution.
 describe and justify the processes used to add and subtract using the standard algorithm by using place value understanding.

E.g.,
3546
-928

Possible student response:
1. There are not enough ones to take 8 ones from 6 ones so I have to use one ten as 10 ones. Now I

have 3 tens and 16 ones. (Student marks through the 4 and notates with a 3 above the 4 and
writes a 1 above the ones column to represent 16 ones.)
2. Sixteen ones minus 8 ones is 8 ones. (Student writes an 8 in the ones column of answer.)
3. Three tens minus 2 tens is one ten. (Student writes a 1 in the tens column of answer.)
4. There are not enough hundreds to take 9 hundreds from 5 hundreds so I have to use one
thousand as 10 hundreds. (Student marks through the 3 and notates with a 2 above it. Then
writes a 1 above the hundreds column.) Now I have 2 thousands and 15 hundreds.
5. Fifteen hundreds minus 9 hundreds is 6 hundreds. (Student writes a 6 in the hundreds column of
the answer).
6. I have 2 thousands left since I did not have to take away any thousands. (Student writes a 2 in the
thousands place of answer.)
7. My answer is 2,618.

HINT: Addition expressions may contain up to three addends.

16 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as MAFS.4.OA.1.1 additive comparison
5. Represent verbal statements of multiplicative comparisons as multiplication equations. equation

Students will: expression

 read a basic multiplication equation as a comparison (e.g., a is n times as much as b). group size unknown
 identify and verbalize which quantity is being multiplied and which number tells how many times. multiplicative
 represent statements of multiplicative comparisons as multiplication equations.
comparison
number of groups

HINT: Statements for comparative language: as tall as, as long as, as fast as, as many as, as much as, etc. unknown

quantity

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown MAFS.4.OA.1.2 symbol

number to represent the problem, distinguishing multiplicative comparison from additive comparison. times as many

Students will: times as much

 distinguish multiplicative comparison (e.g., Tonya has 3 times as many cousins as Matthew) from additive comparison (e.g., twice
Tonya has 3 more cousins than Matthew). unknown number
unknown product

HINT: In an additive comparison, the underlying question is what amount would be added to one quantity in order to result in the variable

other. In a multiplicative comparison, the underlying question is what factor would multiply one quantity in order to result in

the other.

 solve word problems involving multiplicative comparison (situations may include 2-digit by 1-digit expressions or a multiple of 10
by a 1-digit expression).

E.g., A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat?

blue hat $6

red hat $6 $6 $6
$18

The red hat costs 3 times as much as the blue hat.

 translate a word problem involving multiplicative comparison into an expression or equation involving a symbol for the unknown
number.
HINT: Notation for an unknown
number may include, but is not
limited to, the following:

? , m, _, ᴥ, □

17 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Investigate factors and multiples. MAFS.4.OA.2.4 composite
a. Find all factor pairs for a whole number in the range 1–100. even
b. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a factor
multiple
multiple of a given one-digit number. odd
c. Determine whether a given whole number in the range 1–100 is prime or composite. prime
product
Students will: rectangular arrays

 determine factors of whole numbers in the range 1-100 using manipulatives.

HINT: Provide students with counters to find the factors of a number. Have them find ways to separate the counters into equal
subsets (groups) and write multiplication expressions for the numbers.

E.g., Use manipulatives to find the factors of six. ◊◊◊◊◊◊ one group of six 1x6
◊◊◊ ◊◊◊ two groups of three 2x3
 recognize that a whole number is a multiple of its factors. ◊◊ ◊◊ ◊◊ three groups of two 3x2
◊◊◊
E.g., six groups of one 6x1
The factors of 8 are 1, 2, 4, and 8. ◊◊◊
Multiples of 1 – 1, 2, 3, 4, 5, 6, 7, 8
Multiples of 2 – 2, 4, 6, 8, 10, 12
Multiples of 4 – 4, 8, 12, 16, 20
Multiples of 8 – 8, 16, 24, 32

 determine whether a whole number is a multiple of a given one-digit number.

 investigate whether numbers in the range 1-100 are prime or composite by building rectangles (arrays) with the given area and
finding which numbers have more than two rectangles.

 determine if a number in the range 1-100 is prime or composite. Grade 4 Math Curriculum Map
 apply the concepts of factors, multiples, and prime and composite numbers in problem-solving contexts. May 2016

18 Volusia County Schools

Mathematics Department

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value MAFS.4.NBT.2.5 area model
and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. decomposition
equation
Students will: factor
multiply
 use manipulatives or drawings of a model to solve multi-digit multiplication problems that extend to 2-digit by 2-digit product
or up to 4-digit by 1-digit. rectangular array
E.g., strategy

 solve multi-digit multiplication problems that extend to 2-digit by 2-digit or up to 4-digit by 1-digit using a variety of strategies.
E.g.,

 explain and justify a chosen strategy and make connections between different multiplication strategies.
 analyze and describe an error in a strategy and show the correct solution.

HINT: Use of the standard algorithm for multiplication is a 5th grade learning target.
Refer to page 9 in the Fourth Grade Mathematics Curriculum Map for clarification of Multiplication Strategies.

19 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Unit 1 Suggested Instructional Resources

MAFS AIMS Lakeshore MFAS Internet enVision

Modeling A Teacher Guide Reading Greater Numbers www.k- www.IXL.com/signin/volusia 1-2 SE, A&R
Million pp. 7-8 5mathteachingresources.com A.1, A.3, A.9 1-4 SE
Using Word and Expanded NBT.2
I’m The Reproducibles Form https://learnzillion.com/
Greatest p. 3 www.cpalms.org Unit 4
Writing Number Names to a Place Value Made Simple Lesson 3: Sorting numbers by
Place Value Daily Math Journal Million Numbers In Expanded Form type and by equivalence
Patterns pp. 16, 18, 20, 21, 22, Using Word and Expanded Lesson 4: Representing
NBT.1.2 24, 27, 28, 30, 32 Collections Form numbers in different ways
My Digit is Bigger than Your
Pick A Problem Numbers in Expanded Digit! http://achievethecore.org
#21, 22, 23 Form The Street Where Place Value
Lives
Whole Number Place
Value Magnets hcpss.instructure.com/cours
es/107
How Did You Solve It? NBT.2 Lessons
#21, 22 NBT.2 Formatives

Modeling A Teacher Guide Base Ten Place Value www.k- www.IXL.com/signin/volusia 1-1 SE, A&R
Million pp. 6-7 5mathteachingresources.com A.2, A.1
Family Vacations NBT.1
NBT.1.1 Reproducibles https://learnzillion.com/
pp. 3, 5 Seven Hundred Seventy www.cpalms.org Unit 4
Seven Terrific Tim's Ten Tiny Toes Lesson 1: Understand Place
Daily Math Journal 10X Bigger! Value: the power of 10
pp. 16, 22, 24, 26, 28, Comparing Amounts of Count on Math: Making Your Lesson 2: Place Value-
30 Baseball Cards First Million Compare values of digits
What's My Value?
Whole Number Place The Right Rental http://achievethecore.org
Value Magnets
hcpss.instructure.com/cours
How Did You Solve It? es/107
#19, 20 NBT.1 Lessons
NBT.1 Formatives

enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook

20 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Unit 1 Suggested Instructional Resources

MAFS AIMS Lakeshore MFAS Internet enVision

Making The Teacher Guide Rounding Numbers www.k- www.IXL.com/signin/volusia 1-5 SE,
Rounds pp. 8-9 5mathteachingresources.com A.6 RMC, A&R
Rounding to the Thousands NBT.3
NBT.1.3 Reproducibles Place https://learnzillion.com/
pp. 3 www.cpalms.org Unit 4
Rounding to the Ten Just Hanging A-Round Lesson 6: Rounding to
Daily Math Journal Thousands Place Locate Benchmark Numbers on multiple places
pp. 16, 19, 20, 24, 26, a Number line
29, 30, 33 Rounding to the Hundred Round Me! http://achievethecore.org
Thousand Place
Pick A Problem
#24, 25, 26 hcpss.instructure.com/cours
es/107
How Did You Solve It? NBT.3 Lessons
#23, 24 NBT.3 Formatives

Palindromic Teacher Guide Find the Error www.k- www.IXL.com/signin/volusia 1-7A
Ponderings p. 9 Fill in the Missing Number 5mathteachingresources.com B.1, B.2, B.3, C.1, C.2, C.3 1-7B
NBT.4
Subtraction Reproducibles Addition Using the https://learnzillion.com/
Palindromes p. 3 Standard Algorithm www.cpalms.org Unit 4
Let’s Make a Movie Lesson 11: Adding numbers
NBT.2.4 Two-Digit Daily Math Journal Subtraction Using the Subtraction Attraction that involve regrouping
Turn Around pp. 17, 19, 21, 23, 25, Standard Algorithm Subtraction with Regrouping Lesson 13: Subtracting
28, 31, 32 Subtracting: Regrouping Twice numbers that involve
regrouping
Pick A Problem hcpss.instructure.com/cours
#27, 28, 29 es/107 http://achievethecore.org
NBT.4 Lessons
How Did You Solve It? NBT.4 Formatives
#25, 26

enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook

21 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Unit 1 Suggested Instructional Resources

MAFS AIMS Lakeshore MFAS Internet enVision

Estimating Teacher Guide Pet Snakes www.k- www.IXL.com/signin/volusia 2-6 RMC,
Everything p. 3 5mathteachingresources.com D.2, D.1 A&R
Kate and Her Doll OA.1 3-8 A&R
Reproducibles https://learnzillion.com/
OA.1.1 p. 3 Animal Photographs www.cpalms.org Unit 4
Bar Model Math – Twice as Video: See multiplication as a
Daily Math Journal Writing an Equation to Nice comparison using number
pp. 2, 4, 6, 8, 11, 12, 14 Match a Word Problem Great Estimation sentences
(Resources-Performance
How Did You Solve It? hcpss.instructure.com/cours Task)
#1, 2, 3 es/107
OA.1 Lessons http://achievethecore.org
Zoo Books Teacher Guide Books and Yarn OA.1 Formatives
p. 3 Throwing Footballs www.k- www.IXL.com/signin/volusia
Making Necklaces 5mathteachingresources.com E.2, E.1
Reproducibles Dogs as Pets OA.2
p. 3 https://learnzillion.com/
OA.1.2 www.cpalms.org Unit 7
Daily Math Journal Comparing Growth, Variation 1 Lesson 1: Extend
pp. 2, 4, 6, 8, 10, 12, 14 Comparing Money Raised understanding of multiplicative
comparisons in different types
Pick A Problem hcpss.instructure.com/cours of problems
#9, 10 es/107 Lesson 2: Extend
OA.2 Lessons understanding of multiplicative
How Did You Solve It? OA.2 Formatives comparisons in different types
#4, 5, 6 of problems

http://achievethecore.org

enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook

22 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Unit 1 Suggested Instructional Resources

MAFS AIMS Lakeshore MFAS Internet enVision

One Number Teacher Guide Find All the Factor Pairs www.k- www.IXL.com/signin/volusia 13-2 SE,
Indivisible p. 5 Multiples of Six 5mathteachingresources.com D.3, D.4, A.5 A&R, RMC
Factor Pairs OA.4 13-3 SE,
Reproducibles Prime or Composite https://learnzillion.com/ A&R, RMC
p. 3 www.cpalms.org Unit 1
OA.2.4 Factor Pair Trees Lesson 2: Use an area model
Daily Math Journal Prime Factorization-From and t-chart to determine
pp. 2, 4, 7, 8, 10, 13, 14 Fingerprint to Factorprint factors
Factor Game Lesson 3: Use skip counting
Pick A Problem Searching for the Primes to find multiples
#12, 13, 14, 15, 16, 17, Lesson 5: Use an area model
18 hcpss.instructure.com/cours to determine if a number is
es/107 prime or composite
How Did You Solve It? OA.4 Lessons
#11, 12, 13, 14 OA.4 Formatives http://achievethecore.org

Factor Triangles

Frame Filling Teacher Guide Reading Challenge www.k- www.IXL.com/signin/volusia 4-1 SE
p. 10 5mathteachingresources.com D.5, D.6, D.8, D.18, D.19 4-2 SE
Multiplication Partial Products NBT.5 4-3 SE
Stretch Reproducibles https://learnzillion.com/ 6-1 SE, A&R
p. 3 Multiplying Using an Array www.cpalms.org Unit 2 7-1 SE, A&R
Picturing or Area Model Model Multiplication Lesson 1: Penguin Array: 7-3 SE, A&R
Rectangles Daily Math Journal 2-digit Array Multiplication Using arrays and base ten
pp. 17, 20, 27, 31, 33 The Produce Shop Amazing Arrays 2 × 1 blocks in larger multiplication
Writing Chance Product problems
NBT.2.5 Rectangles Pick A Problem Boxing Math-Using the Area Lesson 3: Using place value
#30, 31, 37, 38, 39 Model strategies to multiply two
Quick Sticks double digit numbers
and Lattice How Did You Solve It? hcpss.instructure.com/cours http://achievethecore.org
Multiplication #27, 28, 29 es/107
NBT.5 Lessons
NBT.5 Formatives

enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook

23 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Students will: Standards for Mathematical Practice
(to be embedded throughout instruction as appropriate)
Make sense of problems
and persevere in solving Reason abstractly and Construct viable arguments Model with mathematics. Use appropriate tools Attend to precision. Look for and make use of Look for and express
quantitatively. and critique the reasoning strategically. structure. regularity in repeated
them.
of others. reasoning.

SMP.1 SMP.2 SMP.3 SMP.4 SMP.5 SMP.6 SMP.7 SMP.8

MAFS Domains: Number and Operations in Base Ten Pacing: Weeks 9-18
Operations in Algebraic Thinking October 10-December 16
Number and Operations - Fractions

Learning Targets Standards Vocabulary

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the MAFS.4.NBT.2.6 area model
properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, decomposition
rectangular arrays, and/or area models. digit
dividend
Students will: divisor

HINT: Refer to page 10 in the Fourth Grade Mathematics Curriculum Map for clarification of Division Strategies.

 demonstrate division of a multi-digit dividend (with up to four digits) by a one-digit divisor using manipulatives, place value, equation

rectangular arrays, and area models. factor

E.g., What is 260 divided by 4? OR What is the quotient of 260 and 4? inverse
product
o Using Base 10 Blocks: Students build 260 with base 10 blocks and distribute them into 4 equal groups. Some students quotient
may need to trade the 2 hundreds for tens but others may easily recognize that 200 divided by 4 is 50. rectangular array
remainder
o Using Place Value (decomposition): 260 ÷ 4 = (200 ÷ 4) + (60 ÷ 4) strategies
o Using Multiplication: whole number

4 x 50 = 200, 4 x 10 = 40, 4 x 5 = 20; 50 + 10 + 5 = 65; so 260 ÷ 4 = 65
o Area Model: 966 ÷ 7 = ? Area Model Demonstration Video

http://www.youtube.com/watch?v=N7boECP9BAE&safe=active

 solve division of a multi-digit number by a one-digit number using strategies, explain a chosen strategy, and
make connections between different division strategies.

 recognize a remainder as what is left over after dividing equally. (Interpreting remainders will be taught in 4.OA.1.3).
 use the relationship between multiplication and division to check the quotient.
 analyze and describe an error in a strategy and show the correct solution.

24 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which MAFS.4.OA.1.3 equation
remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the estimation
reasonableness of answers using mental computation and estimation strategies including rounding. mental computation
operation
Students will: reasonableness
remainder
 choose the correct operation to perform at each step of a multi-step word problem with whole-number answers. round
strategies
 solve multi-step word problems (i.e., up to 3 steps) that involve any of the four operations using various strategies. unknown quantity
variable
 explain the strategies used to solve multi-step word problems.

 represent a multi-step word problem using equations involving a variable represented by a letter for the unknown number.

 interpret remainders that result from multi-step word problems.

 assess the reasonableness of answers to multi-step word problems using The context of a word problem must

estimation strategies and mental computation. be considered when interpreting

E.g., Your class is collecting bottled water for a service project. The goal is to collect 300 remainders. Here are some ways
bottles of water. On the first day, Max brings in 3 packs with 6 bottles in each remainders can be addressed:
container. Sarah wheels in 6 packs with 6 bottles in each container.  remainder as a leftover
About how many bottles of water still need to be collected?  discard leaving only the whole

number answer

Student 1: Student 2:  increase the whole number
First, I multiplied 3 and 6 which answer by one
First, I multiplied 3 and 6 which equals 18. Then I multiplied 6 and 6
which is 36. I know 18 is about 20  round to the nearest whole
equals 18. Then I multiplied 6 and 6 and 36 is about 40 40+20=60. 300- number for an approximate
result
which is 36. I know 18 plus 36 is
about 50. I’m trying to get to 300. 50

plus another 50 is 100. Then I need 2 60=240, so we need about 240 more

more hundreds. So we need 250 bottles.

bottles.

HINT: Refer to pages 5 and 6 in the Fourth Grade Mathematics Curriculum Map for clarification of Common Addition and
Subtraction Situations and Multiplication and Division Situations. It is expected that students will become proficient with all
situations.
The expectations for multi-step word problems include multiplication of 2-digit by 1-digit or a multiple of 10 by a 1 digit and
division of 2-digit by 1-digit.

25 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Determine whether an equation is true or false by using comparative relational thinking. For example, without adding 60 and 24, determine whether MAFS.4.OA.1.a compare
the equation 60 + 24 = 57 + 27 is true or false. comparative relational
thinking
Students will: compose
decompose
 identify the equal sign as expressing equivalence or same value between numbers. equal sign
 determine if a given equation is true or false ie, by comparing, composing, and/or decomposing the numbers without solving. equation
 use a variety of strategies to justify why an equation is true or false without solving. equivalence
 interpret an unknown quantity without solving. same value

E.g.,

Teacher: Use comparative relational thinking to determine if the following equation is true or
false.
8+4=7 +5

Student: True. I saw that the 5 over here [pointing to the 5 in the number sentence] was one
more than the 4 over here [pointing to the 4 in the number sentence], since 7 is one less
than 8 the equation is true.
Teacher: Let’s try another one. How about 57 + 86 = 59 + 84?

Student: That’s easy. True. It’s just like the other one. 59 is two more than 57, and 84 is
two less than 86.

HINT: Equations may include:
o Addition and subtraction with 1,000.
o Multiplication of 2-digit by 1-digit, or a multiple of 10 by 1-digit.
o Division of 2-digit by 1-digit or a multiple of 10 by 1-digit.

Determine the unknown whole number in an equation relating four whole numbers using comparative relational thinking. For example, solve 76 + 9 = MAFS.4.OA.1.b balanced equation
n + 5 for n by arguing that nine is four more than five, so the unknown number must be four greater than 76. comparative relational
thinking
Students will: same value
unknown value
 identify the equal sign as expressing equivalence or same value between numbers. 27 + n 25 + 42
 explain how two or more numbers relate to each other within an equation.
 create a balanced equation by comparing the two sides of an equation.
 determine the unknown value to create a balanced equation.

E.g., 25 + 42 = 27 + n

HINT: Equations may include:
o Addition and subtraction with 1,000.
o Multiplication of 2-digit by 1-digit, or a multiple of 10 by 1-digit.
o Division of 2-digit by 1-digit or a multiple of 10 by 1-digit.

26 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Explain why a fraction a/b is equivalent to a fraction (n x a)/ (n x b) by using visual fraction models, with attention to how the number and size of the MAFS.4.NF.1.1 denominator
parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. equivalence
equivalent fractions
Students will: fractions
numerator
 generate equivalent fractions by partitioning number lines, rectangles, squares, and circles using visual models.

HINT: Denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, 100.
E.g.,

1/2 2/4 4/8
Half of each area model is shaded.

 recognize how to display 1 in the form of a fraction (e.g., 3/3, 5/5, 8/8).
 apply the identity property of multiplication (you can multiply any number by 1 and it keeps its identity; the number stays the

same) to generate equivalent fractions numerically.

E.g., 1 1
3 3
Start with . Multiply by 1 in the form of a fraction as shown below.

× = × =
× ×

 explain, using visual representation, how and why fractions can be equivalent even though the numbers are not the same.

27 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing MAFS.4.NF.1.2 benchmark fraction
to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of common
comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. compare
denominator
Students will: equal to (=)
fraction greater than 1
 explain that fractions can only be compared when they refer to the same whole (e.g., 1/2 of a small pizza is very different from greater than (>)
1/2 of a large pizza). less than (<)
numerator
HINT: Denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, 100. whole

 compare two fractions visually (e.g., using an array, area, or linear model).
 determine whether a fraction is closest to zero (0), to one whole (1), or to a benchmark fraction (such as ¼ , ½ or ¾ ).

E.g.,

There are two cakes on the counter that are the same size. The first cake has 1/2 of it left. The second cake has 5/12 left. Which
cake has more left? Student: “I know that 6/12 equals 1/2. Therefore, the second cake which has 5/12 left is less than 1/2”.

 compare two fractions with different numerators and different denominators by:
o reasoning about their size or location on a number line.
o multiplying by one in the form of a fraction to create common numerators.
o multiplying by one in the form of a fraction to create common denominators.

 record the results of comparisons with the symbols <, > or = .
 justify the conclusions by using visual model.

HINT: Fractions may be greater than 1 (e.g., 6/5).
Student need to be able to recognize equivalent fractions, but will NOT use the language, “simplify or find the lowest term”.

28 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Understand a fraction a/b with a > 1 as a sum of fractions 1/b. MAFS.4.NF.2.3 decomposition
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. denominator
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an difference
equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 equivalent fraction
= 8/8 + 8/8 + 1/8. fraction greater than 1
c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using mixed number
properties of operations and the relationship between addition and subtraction. model
d. Solve word problems involving the addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by numerator
using visual fraction models and equations to represent the problem. product
sum
Students will: unit fraction
whole number
 demonstrate with visual models (i.e., number lines, rectangles, squares, and circles) that adding fractions within the same
whole (i.e., fractions with the same denominator) is joining parts of that whole.

 demonstrate with visual models (i.e., number lines, rectangles, squares, and circles) that subtracting fractions within the same
whole (i.e., fractions with the same denominator) is separating parts of that whole.

HINT: Denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, 100.

 decompose a fraction in more than one way using visual models (i.e., number lines, rectangles, squares, and circles), including
decomposing a fraction into a combination of several unit fractions (i.e., fractions with a numerator of one).

 record the decomposition of a fraction in an equation.
E.g.,

HINT: Student need to be able to recognize equivalent fractions, but will NOT use the language, “simplify or find the lowest term”.
…continued…

29 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

 decompose a mixed number into fractions equal to one and unit fractions to find the fraction greater than one. decomposition
E.g., denominator
difference
2 1/8 equivalent fraction
fraction greater than 1
2 1/8 mixed number
/\ | model
1 + 1 + 1/8 numerator
||| product
8/8 + 8/8 + 1/8 sum
unit fraction
17/8 whole number

 convert fractions greater than one to mixed numbers by decomposing the fraction into a sum of fractions equal to one and
fractions less than one.

E.g.,

17/6

/\
6/6 + 11/6

| /\
6/6 + 6/6 + 5/6

|||
1 + 1 + 5/6

2 5/6

 add mixed numbers with like denominators using equivalent fractions and the properties of operations.
E.g., 3 ¾ + 2 ¼

Student 1: Student 2: Student 3:
3+2=5 and ¾ + ¼ = 1 3¾+2=5¾+¼= 3 ¾ = 15/4 and 2 ¼ = 9/4,
so 5 + 1 = 6 5 + 4/4 = 5 + 1 = 6 so 15/4 + 9/4 = 24/4 = 6

 subtract mixed numbers with like denominators using equivalent fractions and the properties of operations.

…continued…

30 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

 add or subtract mixed numbers with like denominators using the relationship between addition and subtraction. decomposition

denominator

E.g., Students use their knowledge of decomposition (17/6 = 12/6 + 5/6) to calculate 17/6 – 5/6 = 12/6. difference

equivalent fraction

 solve word problems involving addition of fractions with like denominators using models, drawings, pictures, and equations. fraction greater than 1

mixed number

E.g., Lindsey and Brooke need 3 3/8 feet of ribbon to design costumes for a performance. Lindsey has 11/8 and Brooke has 2 5/8 model

feet of ribbon. If they combine what they have, will that be enough for the project? Explain why or why not. numerator

product

sum

unit fraction

whole number

Ribbon needed for the project 33/8 ft. = 8/8 ft. + 8/8 ft. + 8/8 ft.+ 3/8 ft.= 27/8 ft.
Lindsey’s 9/8 ft. + Brooke’s 21/8 ft. = 30/8 ft.
30/8 ft. is greater than 27/8 ft. So they have enough ribbon for the costumes.

 solve word problems involving subtraction of fractions with like denominators using models, drawings, pictures, and equations.

31 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. MAFS.4.NF.2.4 decomposition
a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording denominator
the conclusion by the equation 5/4 = 5 x (1/4). equivalent fraction
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a fraction greater than 1
visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b). mixed number
c. Solve word problems involving multiplication of a fraction by a whole number, e.g. by using visual fraction models and equations to model
represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, numerator
how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? product
sum
Students will: unit fraction
whole number
 decompose a fraction into a representation of a multiple of unit fractions (i.e., fractions with a numerator of one).

E.g., ¾ = ¼ + ¼ + ¼ = 3 x (¼)
5/4 = ¼ + ¼ + ¼ + ¼ + ¼ = 5 x (¼)

 understand that a fraction can be represented as the numerator times the unit fraction with the same denominator.

E.g., 7/5 = 7 x 1/5 5/9 = 5 x 1/9

 multiply a fraction by a whole number.

E.g.,

 solve word problems that involve multiplying a whole number and fraction using visual models and equations.

E.g., If each person at a 5 x 3/8 = ?
party eats 3/8 of a pound of
roast beef, and there are 5
people at the party, how
many pounds of roast beef
are needed?

HINT: Denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, 100. Grade 4 Math Curriculum Map
May 2016
32 Volusia County Schools

Mathematics Department

Unit 2 Suggested Instructional Resources

MAFS AIMS Lakeshore MFAS Internet enVision

Pack 10 Teacher Guide Dividing Using an Area www.k- www.IXL.com/signin/volusia 9-7A
Trading p. 10 Model 5mathteachingresources.com E.4, E.5, E.8 9-7B
Center Book Drive NBT.6 9-7C
Reproducibles Interpreting Division https://learnzillion.com/ 9-7D
Candy p. 3 www.cpalms.org Unit 2
Factory Dividing Using Place Value I see! Division with the Lesson 6: Elephant and Food-
Daily Math Journal Distributive Prop. Using arrays and base 10
NBT.2.6 pp. 18, 22, 23, 25, 26, Problem Solving and blocks to solve division
29, 32, 40 Interpreting Remainders problems
Share and Share Alike Lesson 7: Using arrays and
Pick A Problem partial quotients to solve
#33, 34, 35, 36 hcpss.instructure.com/cours division problems
es/107 Lesson 9: Interpreting
How Did You Solve It? NBT.6 Lessons remainders
#30, 31, 32 NBT.6 Formatives
http://achievethecore.org

Picturing Teacher Guide Picking Strawberries www.k- www.IXL.com/signin/volusia 1-6 SE
Clues p. 4 Estimating the Solution 5mathteachingresources.com E.7, E.11, F.4 1-7 SE, RMC
Roller Coaster Rides OA.3 4-6 SE
Party Reproducibles Juice Boxes https://learnzillion.com/ 5-4 SE, A&R
Planning p. 3 www.cpalms.org Unit 14
Express Yourself! With Math Lesson 1: Add and subtract
Hall Of Daily Math Journal Story Chains multi-digit numbers using
Mirrors pp. 3, 5, 7, 9, 11, 13, 15 Birthday Balloon Planner various strategies
Gimme Two Steps! Lesson 4: Multiply whole
OA.1.3 Pick A Problem Travel and More numbers using various
#1, 2, 32 I Love Leftovers strategies
One Step at a Time: Word Lesson 5: Solve multi-step
How Did You Solve It? Problems multiplication problems
#7, 8, 9, 10 Lesson 8: Solve multi-step
hcpss.instructure.com/cours division problems
es/107
OA.3 Lessons http://achievethecore.org
OA.3 Formatives

enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook

33 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Unit 2 Suggested Instructional Resources

MAFS AIMS Lakeshore MFAS Internet enVision

Teacher Guide Are the Equations True? www.cpalms.org www.IXL.com/signin/volusia 11-1 SE,
p. 4 Can You Compare and Find the D.28, E.25, F.10 RMC, A&R
Determining If an Equation Missing Numbers in an
OA.1.a Problem Solving is True? Equation? https://learnzillion.com/
Strategy Puzzles
True and False Division
Equations Is My Equation True or False? http://achievethecore.org

True and False
Multiplication Equations

Zoo Books Teacher Guide Comparative Relationship www.cpalms.org www.IXL.com/signin/volusia 11-2 SE,
A&R
p. 4 In a Division Equation Can You Compare and Find the https://learnzillion.com/
Missing Numbers in an Unit 8 13-4 SE,
Reproducibles Comparative Relationship Equation? Lesson 1: Using equations A&R
p. 4 In a Multiplication Equation with letters standing for the
OA.1.b unknown quantity
Pick A Problem Comparative Relationship Lesson 2: Representing
#3, 4, 5, 6 In a Subtraction Equation unknowns

Comparative Relationship

In a Addition Equation http://achievethecore.org

NF.1.1 Fraction Teacher Guide Eating Cake www.k- www.IXL.com/signin/volusia
Fringe: On pp. 11-12 5mathteachingresources.com Q.6, Q.8
the Cutting Are the Fractions NF.1
Edge Reproducibles Equivalent https://learnzillion.com/
pp. 3, 6 www.cpalms.org Unit 5
Same Name Equivalence Using a Chocolate Fractions Lesson 2: Compare and order
Frame Daily Math Journal Number Line The Brownie Breakdown fraction using models
pp. 35, 37, 39, 40, 42, Equivalent Fractions Dominoes Lesson 7: Generate
Shady 44, 46, 50 Equivalence Fractions on a Fraction Land equivalent fractions
Fractions Number Line Create a Quilt-Equivalent Lesson 8: Generate
Pick A Problem Fractions equivalent fractions using
#41, 42, 43 models
hcpss.instructure.com/cours
How Did You Solve It? es/107 http://achievethecore.org
#33, 34 NF.1 Lessons
NF.1 Formatives
Daily Dose of Fractions
& Decimals #1-120

Giant Magnetic Fraction
Circles and Bars

enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook

34 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Unit 2 Suggested Instructional Resources

MAFS AIMS Lakeshore MFAS Internet enVision

Ordering Up Teacher Guide Comparing Four-Fifths and www.k- www.IXL.com/signin/volusia 13-7A
Fractions pp. 12-13 Three-Fourths 5mathteachingresources.com Q.10, Q.11, Q.15, Q.16
NF.1.2 Half Track Compare Fractions NF.2
Between Reproducibles Comparing Fractions Using https://learnzillion.com/
Zero and pp. 3, 6, 8, 9, 10 Benchmark Fractions www.cpalms.org Unit 5
One Corn Farms Comparing Fractions with Lesson 1: Compare fractions
Daily Math Journal Cupcakes with unlike numerators and
Shady pp. 34, 36, 38, 40, 44, Decomposing Three-Fifths Fraction Line Up! denominators
Fractions 46, 48, 54 Anna Marie and the Pizza Fraction War Lesson 5: Compare fractions
Cindy’s Fraction Word Problems Fractions: Let’s Compare with common benchmarks- 0,
Carpet Pick A Problem Adding and Subtracting 1/2, 1.
Emporium #44, 45, Mixed Numbers hcpss.instructure.com/cours Lesson 6: Compare fractions
es/107 using various benchmarks
How Did You Solve It? NF.2 Lessons
#35, 36, 37 NF.2 Formatives http://achievethecore.org

Daily Dose of Fractions www.k- www.IXL.com/signin/volusia
& Decimals #1-120
Teacher Guide 5mathteachingresources.com R.4, R.5, R.6, R.7, R.11, R.1,
pp. 13-16
NF.3 R.2, R.3, R.12, R.9, R.10
Reproducibles
NF.2.3 pp. 3, 7, 11, 12 www.cpalms.org https://learnzillion.com/
Decomposing Fractions Unit 3
Daily Math Journal Adding and Subtracting in the Lesson 7: Add fractions with
pp. 34, 35, 36, 39, 41, Real World with Unit Fractions like denominators
43, 45, 48, 50, 53, 55 Lesson 8: Subtract fractions
hcpss.instructure.com/cours with like denominators
Pick A Problem es/107 Lesson 5: Understand
#46, 47, 48, 49, 50, 55 NF.3 Lessons fractions can be decomposed
NF.3 Formatives in multiple ways
How Did You Solve It?
#38, 39, 40, 41, 42, 43, UNIT 9
44, 45 Lesson 2: Adding and
subtracting mixed numbers
Daily Dose of Fractions using equivalent fractions
& Decimals #1-120 Lesson 8: Solving word
problems by adding and
Giant Magnetic Fraction subtracting mixed numbers
Circles and Bars

http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook

35 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Unit 2 Suggested Instructional Resources

MAFS AIMS Lakeshore MFAS Internet enVision

Teacher Guide Fractions and Multiples www.k- www.IXL.com/signin/volusia 14-1A
pp. 17-18 How Many One-Fourths?
How Much Sugar? 5mathteachingresources.com T.1, T.2, T.3, T.4, T.5, T.7, T.8, 14-1B
Reproducibles Training for a Race
pp. 3, 6 NF.4 T.10, T.6

NF.2.4 Daily Math Journal www.cpalms.org https://learnzillion.com/
pp. 37, 38, 41, 44, 47, Unit 11
49, 51, 53, 54 Modeling Multiplication with Lesson 1: Sleepover Snacks-
Fractions multiplying until fractions by
Pick A Problem whole numbers
#51, 52, 53, 54 Modeling Multiple Groups of Lesson 2: Playing Fill Three-
Fractions multiply unit fractions by whole
How Did You Solve It? Multiple Bake Sale Cookie numbers
#46, 47, 48, 49, 50, 51 Recipes in Fractional
Ingredients Part 1 http://achievethecore.org
Daily Dose of Fractions Multiple Bake Sale Cookie
& Decimals #1-120 Recipes in Fractional
Ingredients

Problem Solving hcpss.instructure.com/cours
Strategy Puzzles- Blue es/107
Set NF.4 Lessons

Giant Magnetic Fraction NF.4 Formatives

Circles and Bars

enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook

36 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Standards for Mathematical Practice

Students will: (to be embedded throughout instruction as appropriate)
Make sense of
problems and Reason abstractly Construct viable Model with Use appropriate Attend to precision. Look for and make Look for and express
and quantitatively. arguments and mathematics. tools strategically. use of structure. regularity in repeated
persevere in solving reasoning.
them. SMP.2 critique the
reasoning of others.
SMP.1
SMP.3 SMP.4 SMP.5 SMP.6 SMP.7 SMP.8

MAFS Domains: Number and Operations - Fractions Pacing: Weeks 19-26
Operations and Algebraic Thinking December 19 - February 17
Measurement and Data
Standards Vocabulary
Learning Targets
MAFS.4.NF.3.5 decimal fractions
Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this technique to add two fractions with respective denominator
denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. equivalent fraction
expanded form
Students will: hundredths
numerator
 read, write and identify decimal fractions (i.e., fractions with denominators of 10 and 100). tenths

 represent fractions with a denominator of 10 and fractions with a denominator of 100 using models

(e.g., grids, base ten blocks, and number lines).

 rewrite a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100.

E.g.,

Tenths Grid Hundredths Grid

3/10 = 30/100

HINT: While students may be able to easily see the pattern of adding a “0” at the end of a numerator when creating these

equivalent fractions, they need to be able to justify why this works.

 add two fractions with denominators 10 and/or 100 by finding equivalent fractions with like denominators.
E.g., 3/10 + 4/100 = ? 3/10 is equivalent to 30/100 so 30/100 + 4/100 = 34/100

 solve missing addend problems with denominators 10 and 100 by finding equivalent fractions with like denominators.

37 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe length as 0.62 meters; locate 0.62 on MAFS.4.NF.3.6 compare
a number line diagram. decimal
decimal notation
Students will: decimal point
digit
 identify the place value of digits to the right of the decimal point (i.e., limited to tenths and hundredths). equivalence
hundredths
Hundreds Tens Ones • Tenths Hundredths number line
place value
 demonstrate place value of decimals through the hundredths using concrete materials (e.g., decimal grids, base ten blocks, tenths
number lines).

 use different-sized grids (e.g., 10 х 10 and 100 х 100) to represent equivalency of decimals to fractions with denominators of 10
or 100.

 explain the relationship between fraction and decimal representations in graphic models (i.e., limited to tenths and hundredths).

E.g.,

This is a graphic representation
28
of 0.28 and 100 .

 read, write, and identify decimals through the hundredths place from graphic and numeric representations.
 translate the number name (word form) of a decimal into its equivalent fraction.

E.g., 0.39 reads thirty-nine hundredths and can be written 39/100.

 translate a fraction with a denominator of 10 or 100 into its equivalent decimal form.
 translate fractions greater than 1 with denominators of 10 or 100 into equivalent decimal form.
 understand the relationship between decimal values (i.e. that .3 is the same value as .30).
 represent a decimal value on a number line.

E.g.,
Represent 0.32 on a number line

Students represent values such as 0.32 or 32/100 on a number line. 32/100 is more than 30/100 (or 3/10) and less than 40/100
(or 4/10). It is closer to 30/100 so it would be placed on the number line near that value.

HINT: Students should be exposed to decimals and fractions greater than 1.

38 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the MAFS.4.NF.3.7 compare
same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. decimal grid
decimals
Students will: equal (=)
greater than (>)
 explain that decimals can only be compared when they refer to the same whole. hundredths
less than (<)
HINT: Decimals may be greater than 1. model
tenths
E.g., Each of the models below shows 0.3 (three tenths), but the whole on the right is much bigger than the whole on the left;
therefore, the model on the right is a much larger quantity than the model on the left, and these decimals cannot be compared.

0.3 0.3

 compare decimals with and without models (such as decimal grids or base ten blocks) and record the comparison numerically
using symbols: <, > or =.

 justify the comparison by reasoning about the size of the decimal or by using a visual model.
E.g., Compare 0.32 and 0.5

Students draw a model to show that 0.32 < 0.5

39 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For MAFS.4.OA.3.5 feature
example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate growing shape pattern
between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. numeric pattern
rule
Students will: term

HINT: Students should be exposed to rules containing up to two procedural operations.

 identify and demonstrate numeric and growing shape patterns.
 generate a number or shape pattern that follows a given one-step rule.

E.g.,
Rule: Multiply by 2 and then subtract 4.
The first number in the pattern is 6.
Show the next three numbers in the pattern.
Answer: 8,12, 20

 generate a number or shape pattern that follows a given two-step rule.
 identify features in patterns following a given rule.

E.g.,

Rule Pattern Feature(s)
Start with 4 and 4, 9, 14, 19, The numbers alternate ending in a 4 or 9.
add 5 24, 29, 34,
39, … After the starting number, all numbers that
Start with 1 and 1, 5, 25, 125, follow end in 5.
multiply by 5 625, 3125, … All the numbers that have resulted are odd.
The numbers alternate from even to odd.
Start with 100 100, 97, 94, All digits from 0-9 eventually end up in the
and subtract 3 91, 88, 85, ones place.
82, 79, 76,
73, …

MEASUREMENT AN DATA

40 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; L, mL; hr, min, sec. Within a single system of MAFS.4.MD.1.1 centimeter
measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For convert
example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing cup
the number pairs (1, 12), (2, 24), (3, 36), … customary units
day
Students will: equivalent
foot
HINT: Students are expected to utilize the Grade 4 FSA Mathematics Reference Sheet located on the Elementary gallon
Mathematics Intranet and on p. 50 of the Grade 4 Mathematics Item Specifications. gram
hour
 know relative size of measurement units within one system. inch
 differentiate between units of measure for length, volume, and mass/weight within one system. kilogram
kilometer
E.g., liter
measurement
CUSTOMARY LENGTH VOLUME WEIGHT TIME meter
SYSTEM MASS/ metric units
mile (mi) gallon (G) ton year mile
yard (yd) quart (qt) pound (lb) month milligram
foot (ft) pint (pt) ounce (oz) week milliliter
inch (in) cup day millimeter
ounce (oz) kilogram (kg) hour (hr) minute
gram (g) minute (min) month
liter (L) milligram (mg) second (sec) ounce
milliliter (mL) pint
METRIC kilometer (km) pound
SYSTEM meter (m) quart
centimeter (cm) second
millimeter (mm) ton
two-column table
 discover equivalent relationships in measurement using tools (e.g., there are 1000 milliliters in 1 liter; there are 16 ounces in 1
pound; there are 12 inches in 1 foot). (function table)
units
HINT: Students should be given multiple opportunities to measure the same object with different measuring units. week
E.g., Have students measure the length of the room with one-inch tiles, one-foot rulers, and with yard sticks. Students yard
should notice that it takes fewer yard sticks to measure the room than rules or tiles and explain their reasoning. year

 convert larger units of measure into smaller equivalent units.
 complete a two-column table (function table) showing measurement equivalents.

E.g.,

lb oz ft in kg g
1 16 1 12 1 1000
2 32 2 24 2 2000
3 48 3 36 3 3000

41 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Use the four operations to solve word problems1 involving distances, intervals of time, and money, including problems involving simple fractions or MAFS.4.MD.1.2 intervals of time
decimals2. Represent fractional quantities of distance and intervals of time using linear models. formerly known as
(1See Table 1 and Table 2) elapsed time
(2Computational fluency with fractions and decimals is not the goal for students at this grade level.)

Students will:

 represent fractional quantities of distance using linear models.
E.g., Billy has been training for a half-marathon. Each day he runs on the treadmill 2 2/4 miles and runs on the outdoor track for 3
1/4 miles. In all, how many miles does Billy run each day?

0 | | | 1 | | | 2 | | | 3 | | | 4 | | | 5 | | | 6 | | | 7 | | | 8 | | | 9 | | | 10
 use the four operations to solve word problems involving distances (i.e., mile, yard, foot, feet, inch; kilometer, meter, centimeter)

including problems that require expressing measurements given in a larger unit in terms of a smaller unit (converting units).

 represent intervals of time using linear models.
E.g.,

What time does Marla have to leave to be at her friend’s house by a quarter
after 3, if the trip takes 90 minutes?

 use the four operations to solve word problems involving intervals of time.
 use the four operations to solve word problems involving money including dollars and cents with decimal notation.

E.g., Helen bought popcorn at the movies. She bought 2 large bags, and each one cost $1.30.
How much change did she receive from $5?

 use the four operations to solve multistep word problems, including problems involving fractions or decimals and problems that
require expressing measurements given in a larger unit in terms of a smaller unit (converting units).

HINT: Decimal amounts should be limited to hundredths in multiples of 10 (e.g., $0.10, $0.20, $0.30, $ 0.40…) in order to relate
to fractions.
Computational fluency with fractions and decimals is not the goal for students at this grade level.
Refer to pages 5 and 6 in the Fourth Grade Mathematics Curriculum Map for clarification of Common Addition and
Subtraction Situations and Multiplication and Division Situations. It is expected that students will become proficient with
all situations.

42 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room MAFS.4.MD.1.3 area
given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. formula
length (l)
Students will: perimeter (P)
square units
HINT: It is a 3rd grade expectation that students are able to communicate their understanding of why the perimeter and area width (w)
formulas work.

 identify situations that require the use of the perimeter formula in real-world contexts. E.g., amount of fencing needed to make a
rectangular pig pen, length of ribbon needed to wrap around a box, distance around a city block.

 apply the perimeter formula (P = 2l + 2w) in real world and mathematical situations.
 identify situations that require the use of the area formula in real-world contexts (e.g., size of a carpet, area of a garden,

covering a wall with paint).
 apply the area formula (A = l × w) in real world and mathematical situations.
 write area measurements in square units (e.g., cm2, ft2, km2, etc.).
 solve for missing dimensions of rectangles when provided with the perimeter and/or area.

E.g., A rectangular garden has as an area of 80 square feet. It is 5 feet wide.
How long is the garden? 80 ft2 = 5ft x l

 apply methods of maximizing area using a given perimeter, and vice versa.
 solve problems involving area of a composite figure composed of rectangles.

43 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of MAFS.4.MD.2.4 data set
fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and fraction units
shortest specimens in an insect collection. length
line plot
Students will:

 create a line plot recording measurement data including fraction units of halves, quarters, and eighths.
E.g., Thomas’ father cuts a wooden rod into 8 smaller pieces. He records the measurements of each piece on a line plot.

Wooden Rods

Length of Rods in Inches

 use the measurement data on a line plot to solve multistep problems involving the addition and subtraction of fractions and draw
conclusions about the data.

HINT: Addition and subtraction of fractions is limited to fractions with like denominators.

E.g., A small group of students in Mr. Tordini’s class measure the antennae of different insects to the nearest eighth of an inch.
They display the measurements on the line plot shown below. Answer the following questions based on the line plot.
Insect Antennae

Length of Antennae in Inches

o What is the difference between the longest and shortest antennae of all the insects that were measured?
(Answer: 12/8 – 1/8 = 11/8 inches)

o If the antennae with the longest length were laid end to end, what would their total length be?
(Answer: 12/8 + 12/8 = 24/8 inches)

44 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Unit 3 Suggested Instructional Resources

MAFS AIMS Lakeshore MFAS Internet enVision

Teacher Guide Adding Five Tenths www.k- www.IXL.com/signin/volusia
pp. 18-19 Hundredths and Tenths 5mathteachingresources.com Q.7, U.1, U.5, S.5, U.2
Seven Tenths NF.5
Reproducible Tenths and Hundredths https://learnzillion.com/
pp. 3, 13 www.cpalms.org Unit 12
NF.3.5 Terrific Tenths Lesson 1: Model and
Daily Math Journal Happy Hundredths represent fractions as
pp. 34, 38, 42, 45, 47, Playground Picks decimals using money
48, 51, 52, 54 Dimes and Pennies Lesson 4: Use models of
Adding Tenths and Hundredths fractions and decimals to
How Did You Solve It? make comparisons
#52, 53 hcpss.instructure.com/cours
es/107 http://achievethecore.org
Daily Dose of Fractions NF.5 Lessons
& Decimals 121-150 NF.5 Formatives

What’s the Teacher Guide Using Benchmark Fractions www.k- www.IXL.com/signin/volusia 12-1 SE,
Point? p. 19 on a Number Line A&R, RMC
5mathteachingresources.com U.7, U.3, U.6, U.4, U.8 12-2 RMC
Reproducible Using Benchmark Decimals 12-3 RMC
p. 3 on a Number Line NF.6 Grade 3: AA.2 12-4 SE,
A&R, RMC
Daily Math Journal Fractions to Decimals www.cpalms.org https://learnzillion.com/
NF.3.6 pp. 46, 50, 52 Shopping with Tenths and Unit 12
Decimals to Fractions Hundredths Lesson 9: Solve word
How Did You Solve It? Fractions Undercover problems by comparing
#54, 55 Dynamic Decimals! Fractions fractions and decimals
and Money Lesson 7: Relate decimal
Daily Dose of Fractions comparison to fraction
& Decimals 121-150 hcpss.instructure.com/cours comparison
es/107
NF.6 Lessons http://achievethecore.org
NF.6 Formatives

enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook

45 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Unit 3 Suggested Instructional Resources

MAFS AIMS Lakeshore MFAS Internet enVision

Dueling Teacher Guide Compare Decimals www.k- www.IXL.com/signin/volusia
Decimals pp. 19-20
Comparing Four Tenths 5mathteachingresources.com U.14, U.13
Show Me Reproducible
The Money pp. 3, 14 Using Models to Compare NF.7 Grade 3: AA.5
Decimals
Daily Math Journal www.cpalms.org https://learnzillion.com/
pp. 40, 43, 49, 52 Comparing Decimals in Cell Phone Inquiry Unit 12
Context Comparing and Ordering Lesson 8: Compare decimals
How Did You Solve It? Decimals and fractions on a number line
NF.3.7 #56 Decimal War Lesson 10: Compare
decimals to solve word
Daily Dose of Fractions hcpss.instructure.com/cours problems
& Decimals 121-150 es/107
NF.7 Lessons http://achievethecore.org
Decimal Place Value NF.7 Formatives
Magnets

Decimal Grids

Key Codes Teacher Guide Multiply by Four www.k- www.IXL.com/signin/volusia
p. 6 Dot Patterns 5mathteachingresources.com L.1, L.2, L.3, L.4, L.5, O.9
Baseball Cards OA.5
Reproducible Shape Patterns https://learnzillion.com/
p. 3 www.cpalms.org Unit 13
OA.3.5 Chips Ahoy! Lesson 9: Understand
Daily Math Journal Pattern Fun problems that follow a
pp. 3, 5, 6, 9, 10, 12, 15 Rules, Number Patterns and rule
Tables Lesson 10: Explore patterns
Pick A Problem that follow rules
#7, 8, 11, 19, 20 hcpss.instructure.com/cours
es/107 http://achievethecore.org
How Did You Solve It? OA.5 Lessons
#15, 16, 17, 18 OA.5 Formatives

enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook

46 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Unit 3 Suggested Instructional Resources

MAFS AIMS Lakeshore MFAS Internet enVision

Measure for Reproducible Conversions in the Metric www.k- www.IXL.com/signin/volusia 12-9A
Measure p. 3 System 5mathteachingresources.com N.1, N.2, N.3, N.4, N.5, N.6, 12-9B
MD.1 N.7, N.8, N.9, N.10, N.11,
MD.1.1 Daily Math Journal Conversions in the Metric N.12, N.13, N.14
pp. 56, 58, 60, 62, 64 System Part 2 www.cpalms.org
Give an Inch, Take a Foot https://learnzillion.com/
Pick A Problem Conversions in the Jumping Rope: A Time Telling Unit 6
#59, 63, 73 Customary System Game Lesson 2: Practice converting
Let’s Think in Small Units metric units of length.
How Did You Solve It? Converting Units of Time All-Star Track Runners Lesson 3: Practice converting
#57, 58 metric units of mass and
Relative Sizes of hcpss.instructure.com/cours capacity
Measurement Units for es/107 Lesson 7: Apply conversions
Weight MD.1 Lessons of customary measurements
MD.1 Formatives Lesson 9: Practice converting
Relative Sizes of customary units of
Measurement Units for measurement with a function
Length table

http://achievethecore.org

Step by Step Reproducible Shopping List www.k- www.IXL.com/signin/volusia 12-9C
p. 3 Kesha and Juan
Mix-Ups and Remote Control Motorcycle 5mathteachingresources.com O.1, O.3, O.5, O.6, O.7, O.8
Mysteries Daily Math Journal Piano Lessons
pp. 56, 58, 61, 63, 65 MD.2 M.4, M.6, M.7

MD.1.2 Pick A Problem www.cpalms.org https://learnzillion.com/
#56, 57, 58, 60, 61, 62, Amazing Race- Elapsed Time Unit 7
64, 65, 66, 67, 68, 69, Supermarket Sweep Lesson 7: Convert
70, 71, 72 measurements in order to
hcpss.instructure.com/cours compare amounts
How Did You Solve It? es/107 Lesson 8: Practice converting
#59, 60, 61, 62, 63 MD.2 Lessons measurements in order to
MD.2 Formatives compare amounts

http://achievethecore.org
.
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook

47 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department

Unit 3 Suggested Instructional Resources

MAFS AIMS Lakeshore MFAS Internet enVision

Hall of Teacher Guide Using Area and Perimeter www.k- www.IXL.com/signin/volusia 15-3 SE,
Mirrors pp. 20-21 RMC
Fencing a Garden 5mathteachingresources.com P.19, P.20, P.21, P.22, P.24, 15-6 SE,
Hook, Line Reproducible RMC
and Sticker pp. 3, 15 What is the Perimeter of the MD.3 P.25 15-7 SE
Lettuce Section?
MD.1.3 Daily Math Journal www.cpalms.org https://learnzillion.com/
pp. 57, 58, 60, 64 Applying Area and Area Action Unit 2
Perimeter Bre and Brent the Builders Lesson 13: Applying area and
Pick A Problem Numbers Grow Here perimeter
#74, 75, 76, 77, 78 Draw a Blueprint Lesson 15: Finding area,
On the Hunt for Measurements perimeter, and missing sides
How Did You Solve It?
#64, 65, 66 hcpss.instructure.com/cours http://achievethecore.org
es/107
Area Tiles MD.3 Lessons
MD.3 Formatives
Party Math Geometry
Problem Solving Kit Race Cars Part One www.k- www.IXL.com/signin/volusia 15-9B
Activity Cards 5-6
Teacher Guide Race Cars Part Two 5mathteachingresources.com J.6, J.7, J.8
p. 21
Science Experiment Part MD.4 5th Grade: V.10, V.11, V.12
Reproducible One
MD.2.4 p. 3 www.cpalms.org https://learnzillion.com/
Science Experiment Part Marshmallow Math In search bar type: Solve
Daily Math Journal Two One Leg Up subtraction problems using
pp. 57, 61, 63, 65 data from line plots
hcpss.instructure.com/cours
Pick A Problem es/107 In search bar type: Solve
#79, 80, 81 MD.4 Lessons addition problems using data
MD.4 Formatives from line plots
How Did You Solve It?
#67, 68

http://achievethecore.org

enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook

48 Volusia County Schools Grade 4 Math Curriculum Map
May 2016
Mathematics Department