Grade 2 Curriculum Notebook

Instructional Strategies Used
Resources Used
Using a hundreds chart students will model skip counting patterns starting at either 0 or another given number by coloring the multiples of 5 and 10 using different colors.
Teach students that counting backwards (inverse) is the same as repeated subtraction and still follows a similar counting pattern (ex: 50, 45, 40, 35, 30, etc.) Skip count orally together while raising hand in the air for each number Stop on a given number and skip count backward together while moving hand down for each number (e.g., 15 - hand up each time, 25, 35, 45, 55, Stop, 45 – hand down each time, 35, 25, etc).
Students will complete the pattern (500, ____, _____, 800, ____, 1000
Pop game: Students will stand in a circle; decide what
number you are skip counting by and what number
you are stopping at (such as skip count by 5s, and stop Company 2.pdf at 35). Students take turns going around the circle
counting by the pattern, when it gets to the student
with the chosen stopping number, instead of saying
35, they say POP and sit down. Play continues with
the next student starting again at 5, (still using 35)...
each time a child gets to the number 35 they say POP
and sit down. Keep playing until every child has sat
down. After students understand how to play POP,
they can play in teams and race to be the first team
with everyone sitting down.
Skip Counting with a calculator:
Students enter 0 + 5 and press equals (or enter), and continue to press equal repeatedly, watching the calculator skip count. Students record answers on the hundreds chart as they press enter each time. (can be repeated with other numbers or other starting points).
Ready or Not, Here I Come byTeddy Slater
512 Ants on Sullivan Street by Carol A. Losi
One Hundred Ways to get to One Hundred by Jerry Pallotta
One Hundred Hungry Ants by Elinor J. Pinczes
The Father Who had 10 Children
by Benedicte Guettier
Mental Math in the Primary Grades by Hope, Leutzinger, Reys, Reys
Composite Cookie Company Activity 2
(Skip or stress
counting): Composite Cookie
Composite Cookie Company Activity 3
(In numbers I can't
see): Composite Cookie Company 3.pdf
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Assessment Tasks Used
Skill-based Task:
Problem Task:
Chris skip counts by 5’s. Ryan skip counts by 10’s. If both boys start at zero and count 8 times what number will they end at? Will it be the same number? If both boys
Give students a blank hundred chart
and have them skip count and write
the numbers in starting at a given
number (such as 415 and skip count bycontinue their skip counting pattern 4 more times, what
5 or 780 and skip count by 10)
This can be done multiple times as an ongoing assessment. Start at a different number each time and use different skip counting patterns each time.
number will each boy reach? Show your thinking using words, pictures or numbers?
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Number and Operations in Base Ten 2NBT3
Core Content
Cluster Title: Understand place value.
Standard :3. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand that there are multiple ways to express a given number (base ten, number name, expanded form)
• Understand what expanded form is and how to compose and decompose numbers between standard and expanded form
Procedural:
• Express the same number in multiple ways: o 671
o Six hundred seventy-one
o 6 hundreds, 7 tens, and 1 one
o 600 + 70 + 1 (six hundred plus seventy plus one)
Representational:
• In addition to the procedural process, students will show the number 671 pictorially with base 10 blocks or drawing:
Students will write the related expanded form problem for a given pictorial representation
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand that numbers can be represented as words
• Understand that the two digits of a two-digit number represent amounts of tens
and ones.
Procedural:
• Represent one number in multiple ways Representational:
• Use base ten blocks, straws, beans or virtual manipulatives to demonstrate the connection between the written form and the pictorial representation.
Academic Vocabulary and Notation
thousands, hundreds, tens, ones, standard form: 726, word form: seven hundred twenty-six expanded form: 700 + 20 + 6, base ten language: seven hundreds, two tens, and six ones models: (flat, bar, cube)
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Instructional Strategies Used
1. Teacher and students will create place value cards (5 index cards per number with each of the 5 expanded form models shown:
2. Students can then use the place value cards for multiple learning activities (differentiate as needed based on readiness and learning levels):
• Memory game: use 2 of the cards for each number and have students make matches (example: sets of standard and expanded form cards placed face up or down depending on challenge level)
• I have / Who has? – distribute all of the cards to students and play I have, who has?... Students will find the rest of their number forms and get into groups together
• Play “Scoot” – each student has one card on their desk and they “scoot” from desk to desk. Children have a recording sheet and write down the number at each desk as well as one other way that the number can be represented
• Stack-A-Value Cards from 2004 Core Academy web site
Resources Used
100 Hungry Ants by Elinor J. Pinczes 2. Place Value Dice (available from
www.etacuisenaire.com item # IN46464
3. Stack-A-Value Cards
http://coreacademy.usu.edu/Materials/20 04/Handbooks/SecondGrade.pdf
pages 162-165
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Assessment Tasks Used
Skill-based Task:
Students will complete the following assessment on 3 given numbers of teacher’s choice (or teacher can use place value dice)
Problem Task:
Suzie went trick-or-treating and collected 238 pieces of candy. Show 3 different examples of how Suzie could represent how much candy she collected using examples of standard form, word form, or expanded form. Place value (hundreds, tens, and ones) and pictorial models can also be used).
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Number and Operations in Base Ten 2NBT4
Core Content
Cluster Title: Understand place value.
Standard :4. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand that when comparing two numbers, one is looking at the whole number, not just individual digits.
• Understand that when comparing two numbers if the number of hundreds is the same than one should look at and compare the number of tens.
Procedural:
• Use the vocabulary words (greater than, less than, equal to) to compare two 3-digit numbers in terms of value
• Use the vocabulary words and >, <, = symbols together to compare two 3-digit numbers in terms of value
• Use only symbols to compare two 3-digit numbers in terms of value
• Understand that two 3-digit numbers can have equal value are represented by the =
sign
Representational:
• Model greater than, less than and equal to using sets of money
• Model each number with base ten blocks(straws, beans, or place value drawings, etc.)
attending to precision in the placement of hundreds with hundreds, tens with tens, and ones with ones. After they have created the model, they will write the comparison in 2 ways (symbol and words): (see example below)
(ex: 452 > 438, 452 is greater than 438)
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Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand how to compare two-digit numbers using the words greater than, less than, and equal to.
Procedural:
• Solve problems using only the vocabulary words.
• Solve problems using >, =, and < symbols. Representational:
• Compare sets of objects using vocabulary.
• Compare two-digit numbers using >, =, and < symbols. Academic Vocabulary and Notation
Greater than, less than, more, fewer, compare, equal to, < , > , =
Instructional Strategies Used Resources Used
Before introducing the symbols teach the vocabulary and More or Less by Stuart J. Murphy review the concept of comparing two 2-digit numbers using Just Enough Carrots by Stuart J.
the words greater than, less than, and equal to.
Play “Guess my number” using a number line in the classroom. Teacher picks a number then children ask questions in terms of greater than or less than (such as the teacher chooses a number between 10 and 80; students begin guessing numbers and the teacher offers clues such as “My number is less than Billy’s guess of 45”; “My number is more than Jamie’s guess of 21” etc.) Teacher writes the clues on the board using the < and > symbols. Later, the students can choose the numbers and give the clues (to help them practice the vocabulary).
“Fruit Basket”: give every student an index card and have them create their own 3-digit number. Once everyone has chosen a number, they quickly find a partner and compare their numbers to decide who has the greater number. The teacher calls “fruit basket” and all students pick a new partner. The teacher can choose each time if they are identifying the number that is “greater than” or “less than”. Play continues for 5 – 8 rounds.
Murphy
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Assessment Tasks Used
Skill-based Task:
Students will compare sets of numbers using symbols (see sample below)
Problem Task:
Determine which number is greater: 426 or
419? Draw a picture or write a sentence explaining which number is greater.
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Number and Operations in Base Ten 2NBT5
Core Content
Cluster Title: Use place value understanding and properties of operations to add and subtract.
Standard :5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. MASTERY Patterns of Reasoning:
Conceptual:
• Understand a variety of computation strategies for addition and subtraction
• Understand related addition and subtraction facts and how to use addition to solve for
subtraction (and vice versa)
• Understand the commutative property, associative property of addition, and identity
property of 0
• Understand that in adding or subtracting three-digit numbers, one adds or subtracts
hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to
compose or decompose tens or hundreds.
Procedural:
• Solve single and double digit addition and subtraction problems in both vertical and horizontal form using a variety of strategies
• Use more than one strategy to solve a given equation
o Adding by place value 58+34 (50+30=80 8+4=12 80+12=92)
o Properties of operation-commutative (7+8=15 8+7=15) associative
property (3+8)+1=12 3+(8+1)=12 identity property of 0 (9+0=9) o Compensation (48+22 22-2=20 48+2=50 50+20=70)
o Incremental 58+34 58+10 68+10 78+10 88+4=92
• Demonstrate the relationship between addition and subtraction Example: fact family (25+12=37 12+25=37 37-12=25 37-25=12)
Representational:
• Represent addition and subtraction strategies in oral and written form
• Model addition and subtraction problems and their relationship using manipulatives
such as base ten blocks, straws, beans, or place value drawings.
• Use the number line to model addition and subtraction situations.
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Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand mental math strategies to solve all one digit plus one digit addition and subtraction facts from “Operations and Algebraic Thinking” (2.0A2) (doubles, doubles plus / minus one, ways to make 10, counting on, compensation, incremental adding or subtracting)
• Understand the relationship between addition and subtraction problems.
• Understand that in adding or subtracting two-digit numbers, one adds or subtracts tens
and tens, ones and ones; and sometimes it is necessary to compose a ten.
Procedural:
• Solve addition and subtraction problems within 100 using a variety of strategies
• Solve addition and subtraction problems using multiples of 10 Representational:
• Model addition and subtraction problems within 100 using a variety of models
Academic Vocabulary and Notation
commutative property, associative property, identity property, sum, difference, fact family, related facts, vertical and horizontal format, addition, subtraction, place value
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Instructional Strategies Used
Resources Used
1. Have the class play “Race to 100” – each pair of students needs a die, base ten blocks, place value work mat, and a hundred chart. Player one rolls the die, takes the given number of ones cubes to put on their place value mat, and marks that many spaces on their hundred chart. Play continues with player two, and player one and two alternate taking
turns. Whenever a 10 can be made, students will trade their 10 ones for a 10 rod, (showing regrouping) and eventually trade their 10 sets of 10 rods for a 100 flat, and is the winner.
To relate this game to subtraction, play “Race to Zero”: Each player starts at 100 and subtracts the number they roll as they try to clear their mat and make it down to zero.
2. Using two colors of linking cubes each student creates a two digit number (example 30 blue cubes 4 red cubes equals 34) then two students join their cubes to find the sum of the 2 digit numbers manipulating cubes to show relationship between addition and subtraction.
3. Separate the class into groups. Give each group a domino. Working together, the group must create a fact family for the given domino. Groups then pass the domino to another group and create a fact family for the new domino. Passing continues until each group has made a fact family for all of the dominos. When students are more proficient in creating fact families, have students work individually to make the fact families.
The Mission of Addition by Brian P. Cleary
The Action of Subtraction by Brian P. Cleary
Understanding Numbers: Place Value
By Kathy Richardson
Assessment Tasks Used
Skill-based Task:
Solve 58+34= 76-47=
Problem Task:
Mr. James’ class collected 22 books for the book drive. Mrs. Kim’s class collected 59 books for the book drive. How many books did the two classes collect all together? How many more books did Mrs. Kim’s class collect than Mr. James’ class? Solve using at least two different strategies. Show your work.
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Number and Operations in Base Ten 2NBT6
Core Content
Cluster Title: Use place value understanding and properties of operations to add and subtract.
Standard :6. Add up to four two-digit numbers using strategies based on place value and properties of operations.
MASTERY Patterns of Reasoning:
Conceptual:
• Recognize that adding with more than two addends follows the same process as adding with two addends.
• Understand the commutative property (23+15 = 15+23) and associative property ( {13 + 2} +57 = 13 + {2 + 57} ) of addition.
• Understand that “regrouping” may be necessary when adding up to four 2-digit numbers. Procedural:
• Model addition of 2-digit numbers up to 4 addends with base ten blocks.
• Solve double digit addition problems in both vertical and horizontal form
• Use more than one strategy to solve a given equation
Representational:
• Draw a model of what happens when we have more than two addends.
• Represent sums and differences in oral and written form
• Demonstrate with manipulatives or writing how they grouped the order of addends while
solving the problem
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand how to add more than 2 single-digit addends
• Understand computation strategies (doubles and doubles plus / minus one, making 10,
counting on, compensation, incremental adding)
• Understand how to properly line numbers up in the correct place value column when
writing addition problems in vertical form
• Understand “regrouping” process of 2-digit addition
Procedural:
• Model 2-digit addition with two addends.
• Add two 2-digit numbers with or without regrouping. Representational:
• Show how to solve two 2-digit numbers.
• Draw a model of what happens when numbers require regrouping Academic Vocabulary and Notation
Add, sum, place value, addend, regrouping, digit
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Instructional Strategies Used
Resources Used
Have students work in pairs; each player will roll a number cube 4 (6 or 8) times and record each roll in their math journal. Using the 4 digits rolled, each child will create two 2-digit numbers and add them together to find the sum. Then they will compare the sums at the end of each round. Play continues for a total a 5 rounds; the player who rolled the highest sum the most times is the winner.
** Ideas for differentiation--after students have mastery with adding two 2-digit numbers, they will play again and create three 2-digit numbers, and eventually four 2-digit numbers. Teacher can use blank number cubes to make numbers easier or harder to work with (based on students’ individual needs)
Sea Sums – Joy N. Hulme Mall Mania – Stuart Murphy
Assessment Tasks Used
Skill-based Task:
24+36+18+32=
Problem Task:
The second grade classes are going on a field trip to the dinosaur museum. There are 24 students in Mrs. Carter’s class, 28 in Mr. Hall’s class and 27 in Mr. Smith’s class. How many students are going on the field trip? If there are 12 adults going how many people are going on the fieldtrip altogether? Show your thinking.
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Number and Operations in Base Ten 2NBT7
Core Content
Cluster Title: Use place value understanding and properties of operations to add and subtract.
Standard :7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens
and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand computation strategies relating to place value (hundreds and hundreds, tens and tens, ones and ones)
• Understand how to compose and decompose large numbers in addition and subtraction
• Understand that 10 ones can be regrouped into the ten’s place. Similarly, 10 tens can be
regrouped into the hundreds place.
• Understand the regrouping principle with relation to subtraction (decomposing the
number)
• Understand how to strategically use compensation to make friendly numbers
• Understand how to use incremental adding (breaking one number into 10s and 1s)
Procedural:
• Solve addition and subtraction problems (up to 1,000) in both vertical and horizontal form
• Use more than one strategy to solve a given equation
• Demonstrate the relationship between addition and subtraction Representational:
• Represent sums and differences in oral and written form
• Model addition and subtraction problems and their relationship using manipulatives
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Concepts taught in Standard 5 must be mastered prior to teaching this standard
• Students should already have a solid understanding of place value terms and meanings, and be able to add and subtract fluently within 100 before moving onto larger numbers.
Procedural:
• Show how to properly line numbers up in the correct place value column when writing addition and subtraction problems in vertical form
• Use a variety of strategies when adding and subtracting 1- and 2-digit numbers. Representational:
• Model 2-digit addition and subtraction with or without regrouping.
• Show a solution for a 2-digit problem. Academic Vocabulary and Notation
Compose, decompose, compensation, incremental adding / subtracting, regrouping
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Instructional Strategies Used
• Use manipulatives to model addition and subtraction problems.
• Students will use a deck of number cards (0 – 9). Playing with partners, each student will draw 3 cards and create a number of their choice. Partners then add their 2 numbers together and record the problem and answer in their math journal or response sheet. After students record the answer in their journal, they will model the numbers using base-10 blocks to self-check for the correct answer.
Similarly with subtraction, students will play the game again but with the consideration of place value and understanding that in subtraction, the number with the greater value is placed in the top position.
Resources Used
The 329th Friend – Marjorie W. Sharmat
Animal Giants – Sara Louise Cats Add Up – Diane Ochitree
Assessment Tasks Used
Skill-based Task:
Give students an addition and subtraction problem (such as 482 + 326 = )
Students will choose their preferred strategy and solve; they will also relate the strategy to a written method and explain the steps taken to solve the problem
Problem Task:
The second grade collected 235 cans for the food drive. The third grade collected 137 cans. How many cans did the second and third grades collect all together? How many more cans did the second grade class collect than the third grade?
How many more cans do they need to get to 500? Explain your thinking.
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Number and Operations in Base Ten 2NBT8
Core Content
Cluster Title: Use place value understanding and properties of operations to add and subtract.
Standard :8. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand that adding 10 or 100 to any number only changes the digit in the 10s or 100s place (same goes for subtracting 10 or 100)
Procedural:
• Add or subtract 10 or 100 mentally Representational:
• Drawing a picture of the number in base-10 format (or use base-10 blocks), and demonstrate the change being made (i.e. cross out a set of 10 or 100, or draw another set of 10 or 100).
• After children have a solid understanding of how to relate the drawing to adding / subtracting 10 or 100, demonstrate proficiency in being able to mentally add or subtract 10 or 100 from a given number.
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand that counting patterns can start from any number.
• Understands how to use a hundreds chart
• Understands skip counting patterns (ie. 10, 20, 30, etc.)
Procedural:
• Count on and back by 1.
• Skip counting by 10s and 100s and discuss how the number in the 10s place changes
when skip counting by 10s and how the number in the hundreds place changes when skip
counting by 100s
• Add or subtract 10 or 100 to ANY starting number and extend the counting pattern (ex:
28: 38, 48, 58, etc.)
Representational:
• Model using base-ten blocks addition or subtraction of 10 or 100.
• Show the relationship between skip-counting by 10s and mentally adding 10 to a given
number (such as with the number 64, the related skip counting pattern is 60, 70, so to mentally add 10 to 64, the answer would be 74). Apply the same concept when adding or subtracting hundreds.
Academic Vocabulary and Notation
Increase, decrease, skip count, mental math
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Instructional Strategies Used
Resources Used
Hundreds chart Base-ten blocks Place value dice Numeral cards
• Roll the place value dice and build the number using base 10 blocks; draw a “change” card and follow the directions on the card to change the number. Make the change with the blocks and record both number and answer in math journal. Write down the change that was made.
• Play a game similar to “I Have, Who has...” where each child has a number and a statement such as “Who has 10 more?” and the next person has the answer and a new question.
Assessment Tasks Used
Skill-based Task:
Teacher will create an assessment using the following format (choose amount of problems and difficulty of numbers according to ability level of class):
Problem Task:
Sara reads 313 pages during the week. Mark reads 100 more pages than Sara. Gary reads 10 fewer pages than Mark.
How many pages does Gary read? Explain how you know.
- 100
- 10
Number
+ 10
+100
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Number and Operations in Base Ten 2NBT9
Core Content
Cluster Title: Use place value understanding and properties of operations to add and subtract.
Standard :9. Explain why addition and subtraction strategies work, using place value and the properties of oper Note: Explanations may be supported by drawings or objects.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand place value and the value of each digit as well as the whole number represented
• Understand the properties of operations Procedural:
• Solve the same problem in more than one way
• Clearly explain their thinking and justify their reasoning
• Connect a given addition problem to a related subtraction problem
• Connect a given subtraction problem to a related addition problem
• Connect models to written numbers in relation to addition and subtraction problems
• Connect properties of operations to addition and subtraction strategies
Representational:
• Represent the connections between strategies and identify similarities and differences of various strategie
• Use numbers, pictures, or words to explain addition and subtraction strategies.
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Prior understanding of multiple addition and subtraction strategies
• Concepts taught in Standard 2NBT must be mastered prior to assessing this standard
• Understand how to justify reasoning in math problems
• Understand how to make connections between strategies (similarities and differences)
Procedural:
• Demonstrate solving one problem with multiple strategies
• Be able to guide student thinking through higher-order questioning
• Teachers need to enable their students to explain, clarify, and justify their thinking
Representational:
• Model the process of solving a problem and explaining the steps taken to arrive at a given answer
Academic Vocabulary and Notation
Place value, properties of operations, addition, subtraction, strategy, inverse, justify, clarify, reasoning, explain
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Instructional Strategies Used
Resources Used
Use a variety of types of problem solving activities with differentiated numbers
Various Manipulatives
• Give students a problem
• Allow time to explore problem
• Have students solve the problem in more than
one way (using multiple strategies)
• Ask students to explain why they chose the
strategy they used
• Have students share their answers
• Guide discussion: Explain your thinking. Why
do you know that your answer is right? How do you know that it will work every time? How are your two strategies different from each other and how are they the same? How do the numbers relate to your picture?
Assessment Tasks Used
Skill-based Task:
Problem Task:
Sarah as 33 marbles in a bag. Jeff has 29 marbles in a bag. How many marbles do they have if they put them all together?
Solve the following problem in 2 different ways:
Show both strategies
• Explain all of your thinking and why you know
that your answer is right.
• How are your 2 strategies different from each
other and how are they the same? How do the numbers say the same thing as your picture
Have students create a story problem and solve; justify their answer
Have children solve a few 2- and 3-
digit addition and subtraction problems using two different strategies and
explain their process in solving the • problem •
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Measurement and Data 2MD1
Core Content
Cluster Title: Measure and estimate lengths in standard units.
Standard :1. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
MASTERY Patterns of Reasoning:
Conceptual:
• Identify & understand the difference between the standard tools for linear measurement
• Understand longer units of measure take fewer repetitions to measure objects
• Understand shorter units of measure take more repetitions to measure objects
• Understand that they will typically use tools closest to the size of the measured object for
efficiency (ex. Use a ruler to measure a book, not a meter stick)
• Identify and understand the beginning point of the appropriate measuring tool.
Procedural:
• Investigate and use customary and metric tools of linear measurement
• Learn tool names and linear measurement vocabulary
• Measure a variety of objects using the appropriate tools
• Measure accurately (leave no gaps, allow no overlays, and start at 0 on your measurement
tool.)
Representational:
• Identify and record the appropriate length and unit (5 inches, 2 yds, or 9 cm)
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand linear measurement (measurement of length)
• Understand repeated use of the same unit of measurement to measure one object
• Understand units of measure (paperclips, unifix cubes, inches, feet, centimeters, meters,
etc...)
Procedural:
• Measure length by comparing two (or more) objects and identify which is longer and which is shorter.
• Use multiple copies of one object or one object repeatedly end to end to measure another object (paperclips to measure a book).
Representational:
• Record length and unit of measure
Academic Vocabulary and Notation
Inch, foot, yard, yardstick, ruler, centimeter, meter, meterstick, measuring tape, length, customary, metric, measure, unit/s
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Instructional Strategies Used
Transition from nonstandard to standard units- Read 12 Snails to One Lizard.
Show standard tools together for comparison. Use inch squares and rulers to measure in inches.
Use centimeter cubes and centimeter rulers to measure in centimeters.
Measure irregular objects with a soft tape measure.
Go outside and measure longer objects with a measuring tape.
Resources Used
12 Snails to One Lizard by Susan Hightower How Big is a Foot by Rolf Myller (another transition book)
Jim and the Beanstalk by Raymond Briggs http://www.k- 5mathteachingresources.com/measurement-and- data-activities.html
Assessment Tasks Used
Skill-based Task:
Measure the length of the door; include length and unit. Measure the length of your partner’s arm.
Measure the length of your classroom.
Measure the crayon box, length of your pencil, etc.
When shown several pictures of different sized items students determine which measurement tool would be more appropriate for measuring each item.
Problem Task:
We need to decorate for our party. How much ribbon will we need to go across four desks placed side by side? Be sure to include your tool and unit of measure. Why did you use that unit?
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Measurement and Data 2MD2
Core Content
Cluster Title: Measure and estimate lengths in standard units.
Standard:2. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
MASTERY Patterns of Reasoning:
Conceptual:
• Identify & understand the difference between the standard tools for linear measurement
• Understand longer units of measure take fewer repetitions to measure objects
• Understand shorter units of measure take more repetitions to measure objects
• Understand the difference between the size of units (ex. centimeters/inches,
meters/yards, inches/feet, feet/yards)
Procedural:
• Measure the same object with two different measurement tools; compare the difference in units used.
Representational:
• Record the measurements using the correct units. Record their observations with a focus on the comparison and unit difference. (centimeters vs. inches, inches vs. feet, etc.)
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand linear measurement
• Understand repeated use of the same unit of measurement to measure one object
• Understand units of measure (paperclips, unifix cubes, inches, feet, centimeters,
meters, etc...)
• Understand how to record measurement in proper units
Procedural:
• Measure length by comparing units. Identify which units are smaller and larger; compare sizes.
• Use multiple copies of one object or one object repeatedly end to end to measure another object (centimeter cubes or inches to measure a book).
• Correctly use measurement tools (ex. Start at 0, stay in a straight line). Representational:
• Record length of an object using two different units of measurement
Academic Vocabulary and Notation
Inch, foot, yard, yardstick, ruler, centimeter, meter, meterstick, measuring tape, length, customary, metric, measure, unit/s
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Instructional Strategies Used Resources Used
If You Were an Inch or a Centimeter by Marcie Use a T chart to record measurements of objects Aboff
using different units of measure. Compare
measurements. (Use one T chart for comparing How Big is a Foot by Rolf Myller inches to feet, a different one if comparing
centimeters to inches etc..) We are not asking Inch by Inch by Leo Lionni student to convert, just compare.
Assessment Tasks Used
Skill-based Task:
Measure how tall your chair is in inches, then measure how tall your chair is in centimeters. Which measurement required more units? Explain why.
http://www.k- 5mathteachingresources.com/measurement- and-data-activities.html
Problem Task:
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Measurement and Data 2MD3
Core Content
Cluster Title: Measure and estimate lengths in standard units.
Standard:3. Estimate lengths using units of inches, feet, centimeters, and meters.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand the length of inches, feet, centimeters, and meters.
• Understand the value of using a point of reference when estimating length. (i.e. The top
of your thumb is approximately an inch.)
• Understand how to check the reasonableness of an estimate and adjust as needed.
Procedural:
• Estimate a length then justify reasonableness of the estimation and the unit of measurement used.
• Estimate a length, measure only a small section, then adjust the estimation as needed. Representational:
• Record the estimation of an object’s length and specify the purpose for the unit of measurement used.
• Show justification for use of chosen unit of measurement.
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand linear measurement.
• Understand iterating (using one object, end to end, to measure another object).
• Understand units of measure (inches, feet, centimeters, meters).
• Understand the concept of measuring length by comparing units. Identify which units
are smaller and larger; compare sizes.
Procedural:
• Estimation strategies should be taught and then estimation should be incorporated into all other measurement activities for maximum learning.
• Know how to measure objects to check reasonableness of estimates.
• Use measurement tools correctly; start with 0 not 1 on your measurement tool. Representational:
• Record length and unit of measure
Academic Vocabulary and Notation
estimate, inch, foot, ruler, centimeter, meter, meterstick, measuring tape, length, customary, metric, measure, unit/s
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Instructional Strategies Used
Practice estimating and measuring often.
Use a 3-column chart to track estimates, actual measurements, and the difference.
Use part of students’ bodies to measure classroom objects and make an estimate. Then measure with a standard tool. (ex. Measure with the top of your thumb and then test with inches)
Resources Used
Assessment Tasks Used
Skill-based Task:
Estimate the length of your hand. Test your estimate.
Think about your principal’s
height. Which is the best estimate of his/her height? Will you estimate in centimeters, inches, feet, or meters and why?
Estimate the distance from your desk to the door in feet. Make the same estimate in inches. Why is the number of inches different from the number of feet?
How Tall, How Short, How Far Away? By David Adler
Betcha by Stuart Murphy (general estimation)
Counting on Frank by Rod Clement (general estimation)
How Many How Much (poem) by Shel Silverstein
You need to tell your Grandma how tall you are. You don’t have anything to measure yourself with. Tell how tall you think you are using inches, feet, centimeters, or meters. What unit of measurement did you use and explain why.
Problem Task:
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Measurement and Data 2MD4
Core Content
Cluster Title: Measure and estimate lengths in standard units.
Standard:4. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand that the differences in length can be measured.
• Understand how to express the difference in length between two objects in terms of
standard length unit.
Procedural:
• Compare objects visually, side by side, and measure the difference.
• Express that difference in terms of a standard length unit. Representational:
• Record length and unit of measure.
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand linear measurement and tools.
• Understand iterating (using one object, end to end, to measure another object).
• Understand units of measure (inches, feet, centimeters, meters, yards).
• Understand the concept of measuring length by comparing units. Identify which units
are smaller and larger; compare sizes.
Procedural:
• When comparing objects visually, the starting point of both objects must be the same. (Comparing is in first grade core.)
• When measuring, start with 0 on the measurement tool. Representational:
• Model the difference between the lengths of two different objects.
• Record length of difference and unit of measure.
Academic Vocabulary and Notation
Inch, foot, yard, yardstick, ruler, centimeter, meter, meterstick, measuring tape, length, customary, metric, measurement, measure, unit/s, difference, compare
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Instructional Strategies Used
Compare objects visually, side by side, and measure the difference.
Express that difference in terms of a standard length unit.
Assessment Tasks Used
Skill-based Task:
Have several pictures of items side by side on a worksheet. Have students measure and record the difference in length between the two items.
Resources Used
Let’s Measure It by Luella Connelly
Problem Task:
Measure and record the difference in length between two objects in your desk.
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Measurement and Data 2MD5
Core Content
Cluster Title: Relate addition and subtraction to length.
Standard:5. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand how to add and subtract lengths.
• Understand how to set up equations including the measurement unit and solve for the
unknown.
Procedural:
• Measure different lengths (objects or activities such as jumping distances).
• Record measurements.
• Compute different length equations with the unknown in different positions. Use a
variety of lengths within 100. (sum of 100 or less, ex. 45 + 36)
Representational:
• Record with pictures, words, and or numbers how to solve the measurement equations.
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understanding addition and subtraction within 100.
• Understand units of measure.
• Understand that numbers represent SOMETHING. For length, numbers represent a
linear quantity.
• Understand that a missing quantity or the unknown can happen at the start, the
change, or the result.
• Understand how to extract information from word problems, write equations, and
solve.
Procedural:
• Students should know how to keep their calculations organized so that the addition of measurement units does not pose a problem.
• Students should know how to write an equation using information from a word problem.
Representational:
• Record with pictures, words, and or numbers how to solve the equations.
Academic Vocabulary and Notation
Addition, subtraction, measurement, length, equation, unit, unknown, symbol
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Instructional Strategies Used
Measure, draw picture and record answer including equation.
Gather and chart measurement data. Use this class data to compare lengths, add lengths, or subtract lengths. Use this data in word problems.
Have students create their own word problems. They can create questions from the class data or create their own data.
Tell ‘fish’ stories. My fish was this big! Compare the sizes of the different fish.
Resources Used
Let’s Measure It by Luella Connelly (for fish stories)
Assessment Tasks Used
Skill-based Task:
I have 2 twelve-inch rulers in my desk. How many inches do I have? Draw a picture and write an equation to show your work.
Each lunch table is sixteen feet
long. How long are two tables together? Draw a picture and write an equation to show your work.
Problem Task:
Work with a partner. Mark a starting line. Each partner throws a small paper plate like a frisbee. Measure how far your plate went. Work with your partner to answer these questions and show the equation.
How far did Partner A throw?
How far did Partner B throw?
How far did you throw together?
How much longer distance did one travel than the other? How much shorter distance did one travel than the other?
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Measurement and Data 2MD6
Core Content
Cluster Title: Relate addition and subtraction to length.
Standard :6. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand that 0 represents the beginning point of the number line
• Understand that numbers can label an equal space marked on a number line
• Understand that numbers from 0 to 100 have a unique place on the number line.
• Understand that addition and subtraction problems can be solved using a number line
that does not begin at zero
Procedural:
• Consider the numbers in the addition or subtraction problem to determine the range of numbers needed for the number line.
• Create a number line using the numbers that correspond to an addition or subtraction problem.
• Solve using the number line to perform the operation in the problem. Representational:
• Draw a number line with equally spaced points to illustrate thinking used in finding sums and differences of given problems.
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand that numbers are assigned a position on a number line to represent equally spaced points.
• Understand that when using the number line, it is the space between each line that represents the number, not the line itself.
• Understand that the sum of a problem will be a greater number and the difference will be a smaller number.
• Understand that as you move to the right on a number line the numbers will be greater, but as you move to the left on a number line the numbers will be less.
• Understand what a number line looks like. Procedural:
• Expose students to the visual concept of a number line using numbers within 100. Representational:
• Create a classroom number line and demonstrate classroom contextual situations.
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Academic Vocabulary and Notation
Number line, Sum, Difference, Greater, Less
Instructional Strategies Used Resources Used
Model using the number line to solve
addition and subtraction equations within http://illuminations.nctm.org/LessonDetail.aspx?ID=L5
100.
Guide students in using the number line to solve addition and subtraction.
Provide opportunities for using a number line during practice.
Assessment Tasks Used
Skill-based Task:
Have students use a number line to solve addition and subtraction equations. (e.g. 5 + 4 = 9)
3
Problem Task:
Have students use a number line to solve addition and subtraction situations in context (e.g. We have 11 girls and 13 boys in our class. How many total students are in our class?)
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Measurement and Data 2MD7
Core Content
Cluster Title: Work with time and money.
Standard:7. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand the numbers on an analog clock are divided into increments of 5.
• Understand that a day is 24 hours long and is divided into two 12 hour segments, one
being called a.m. and the other p.m. Procedural:
• Look at a clock, count by fives and figure out the time.
• Use analog and digital clocks.
• Write time using correct format (5:40 p.m.)
Representational:
• Use both digital and analog clocks.
• Include a.m. and p.m.
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand that there are 60 minutes in an hour and 30 minutes in a half-hour.
• Understand the difference between analog and digital clocks.
• Understand the minute hand and how it moves (goes around the clock in 1 hour).
• Understand the hour hand and how it moves (goes around the clock in 12 hours).
Procedural:
• Skip count by fives (2.NBT.2)
Representational:
• Use both digital and analog clocks.
Academic Vocabulary and Notation
Time, clock, analog, digital, hours, minutes, a.m., p.m.
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Instructional Strategies Used
Use commercial or homemade student clocks. Move the minute hand around the clock 5 minutes at a time (skip counting by fives).
Match times on digital and analog clocks.
Use real life examples to teach a.m. and p.m.
Assessment Tasks Used
Resources Used
http://www.k- 5mathteachingresources.com/measurement-and-data- activities.html
http://www.fi.edu/time/Journey/JustInTime/contents.html http://www.ixl.com/math/grade-2
Skill-based Task: Problem Task:
Ask students to tell time to the Have students record their activities throughout the day, labeling nearest five minutes from an them as a.m./p.m. Activities could include: wake up, eat
analog clock. Give them breakfast, start school, recess, school ends, sports practice, context to determine if the time music practice, play with friends, eat dinner, and go to bed.
is a.m. or p.m.
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Measurement and Data 2MD8
Core Content
Cluster Title: Work with time and money.
Standard :8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ sy many cents do you have?
MASTERY Patterns of Reasoning:
Conceptual:
• Recognize the different coins and their names.
• Understand the values of each of the coins and bills.
• Understand that coins represent a part of a dollar.
• Understand that only one money symbol should be used ($ for dollars, ¢ for cents only).
(Since students haven’t been exposed to decimals, use problems with either only dollars or only cents.)
Procedural:
• Introduce each of the coins individually. Teach its name and value.
• Introduce money symbols ($ for dollars, ¢ for cents only).
• Practice counting money, starting with the larger values and adding on the smaller ones.
• Write monetary amounts using the correct notations (57¢ or $1).
Representational:
• Represent money by writing amounts. (25¢ + 30¢ =55¢)
Supports for Teachers
Critical Background Knowledge
*Since money is not addressed in other grades’ core curriculum, background knowledge must not be assumed. The basics, including recognition, value, and counting, must be included to successfully teach this standard.
Procedural:
• Skip count by 1s, 5s, and 10s.
Academic Vocabulary and Notation
Bills, coins, value, penny, nickel, dime, quarter, dollar, $, ¢.
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Instructional Strategies Used
Introduce one coin at a time (starting with the smallest). Teach its name, value, and correct symbol (penny, 1¢ or dime, 10¢).
Have students make sets of coins equivalent to other values up to $1 (2 nickels in 1 dime, 5 nickels in 1 quarter, 4 quarters in $1).
Use money to solve problems with real-life context.
Resources Used
http://www.k- 5mathteachingresources.com/measurement-and- data-activities.html
http://illuminations.nctm.org/ (search money) http://www.ixl.com/math/grade-2
Assessment Tasks Used
Skill-based Task:
Ashley has 1 quarter, 4 dimes, and 2 nickels in her piggy bank. How much money does Ashley have?
Problem Task:
Parker has 6 dimes and 7 pennies. He bought a pack of gum for 25¢. How much money does Parker have left?
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Measurement and Data 2MD9
Core Content
Cluster Title: Represent and interpret data.
Standard:9. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand that a line plot is a visual representation of data.
• Understand and interpret data on a line plot
• Understand data and how to transfer it to a line plot
Procedural:
• Take measurements and collect data.
• Make a line plot. Include a horizontal scale, title, labels, and straight columns of data
marks.
• Transfer measurement data to the line plot.
• Read information from the completed line plot.
• Make comparisons from the data.
Representational:
• Represent data in a visual line plot.
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand linear measurement.
• Understand units of measure (inches, feet, yards, centimeters, meters)
• Understand the concept of measuring length by comparing units. Identify which units
are smaller and larger.
• Understand how to organize data.
Procedural:
• When measuring, start with 0 on the measurement tool.
• Draw straight lines. Representational:
• Record length and unit of measure.
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Academic Vocabulary and Notation
Data, line plot, horizontal scale, inch, foot, yard, yardstick, ruler, centimeter, meter, meterstick, measuring tape, length, customary, metric, measurement, measure, units, difference, compare
Instructional Strategies Used
Have students measure similar objects of varying length (pencils, crayons, height of students, etc.) or measure an activity (how far students can jump or toss a ball). Use measurement data to create a line plot.
Teach organizational strategies, such as using grid/graph paper to keep information straight.
Assessment Tasks Used
Skill-based Task:
Create a line plot from measurement data.
Resources Used
http://www.amathsdictionaryforkids.com/dictionary.html
http://www.ixl.com/math/grade-2/interpret-line-plots
Problem Task:
What is length of items in your desk? Measure 8 or more items in your desk. Record the data. Transfer your data to a line plot.
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Measurement and Data 2MD10
Core Content
Cluster Title: Represent and interpret data.
Standard:10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to fou problems using information presented in a bar graph.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand what a picture graph is and what the pictures represent
• Understand what a bar graph is and what the data represents
• Understand how to organize data in picture and bar graphs
• Understand the parts of a graph and how to label them
• Understand how to read and interpret bar and picture graphs
• Understand that data can be used to solve problems Procedural:
• Read and understand data
• Organize data into up to four categories
• Draw a graph representing these categories
• Label the parts of a graph
• Analyze and solve problems using a graph
Representational:
• Using procedural steps, create a picture graph and bar graph to represent data
• Solve simple problems using these graphs
• Make comparisons within data sets
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand that there are different types of graphs
• Understand that a given data set can create a variety of graphs
• Understand the data collection process
Procedural:
• Collect, organize, and represent the data in categories Representational:
• Collect and categorize data
• Create graphs (represent multiple data sets) with class
• Record answers to simple questions and comparisons taken from analysis of a given
graph
Academic Vocabulary and Notation
Key, data, graph, survey, category, title, labels, columns, picture graph, bar graph, compare
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Instructional Strategies Used Resources Used
Collect data as a class
Using data collected, create a graph with
students http://www.k-
Use this time to model the process of creating a 5mathteachingresources.com/measurement-and- graph (using student mastery procedural skills) data-activities.html
Upon completion, let children create another
graph on their own using another data set
Analyze and interpret the data presented in the
graph
Ask students questions about the data set
http://illuminations.nctm.org/ (search for graph activities)
Assessment Tasks Used
Skill-based Task:
Problem Task:
Use the data to complete the graph, then answerA survey was taken to find out the favorite color
the questions that follow.
in Mr. Parker’s class. The results are listed
below: Mrs. Castro asked her students which fruit they
blue
green
blue
had eaten for lunch. Here are the results: Apples: 5
Grapes: 9
Pears: 2
Bananas: 7
Which fruit did most students choose at lunch? Which fruit did the least number of students choose?
How many more children ate grapes than pears?
How many children ate fruit at lunch that day? How many less children chose pears than bananas?
If 2 more children ate apples, how many children would have eaten apples at lunch?
yellow pink green blue green
yellow blue pink green green
pink green pink yellow blue
Organize these results into a bar
graph. Analyze the graph and write 5 sentences telling what you learned from this graph (ex: most popular, least favorite, etc.)
graph or picture
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Geometry 2G1
Core Content
Cluster Title: Reason with shapes and their attributes.
Standard :1. Recognize and draw shapes having specified attributes, such as a given number of angles or a give and cubes.
Note: Sizes are compared directly or visually, not compared by measuring.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand two-dimensional and three-dimensional shapes have angles.
• Understand three-dimensional shapes have faces.
• Understand the difference between two-dimensional shapes and three-dimensional shapes.
• Recognize the attributes of a triangle, quadrilateral, pentagon, hexagon, and a cube.
• Recognize that all four sided shapes are quadrilaterals.
Procedural:
• Identify and describe a two-dimensional shape.
• Identify and describe a three-dimensional shape.
• Identify the number of angles on a triangle, quadrilateral, pentagon, and hexagon.
• Identify the number of equal faces on a cube.
Representational:
• Draw a two-dimensional shape when given a specific number of angles.
• Draw a three-dimensional shape when given a specific number of equal faces.
• Build/find shapes when given specific attributes.
• Write about the differences between a two-dimensional shape and a three-dimensional shape.
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand the attributes of a shape. (e.g., angles, faces, number of sides, sides of
equal length)
Procedural:
• Identify and describe two-dimensional shapes (rectangles, squares, triangles, circles, half circles, and quarter circles).
• Identify and describe three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular
• cylinders). Representational:
• Build and draw shapes to possess specific attributes.
Academic Vocabulary and Notation
Two-dimensional (plane shape), three-dimensional (solid shape), side, edge, angle, face, triangle, quadrilateral, pentagon, hexagon, and cube.
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Instructional Strategies Used
• Have students find real world representations of three- dimensional and two- dimensional shapes (e.g., a shape scavenger hunt, shape walk, etc.)
• Have students create two- dimensional shapes using a number of different methods (e.g.,white boards, geoboards, pretzels, etc.)
• Have students create a cube using a number of different methods (e.g., paper, toothpicks as sides and marshmallows as corners, clay, etc.)
• View the shapes in different orientations.
• Manipulate and combine pattern blocks into different shapes.
• I have... who has? (I have a triangle. Who has a quadrilateral with 4 equal sides? I have a square. Who has a two-dimensional shape with 6 angles?)
• Sort shapes in various ways (by number of angles, number of faces, three-dimensional shapes vs. two-dimensional shapes, etc.)
• Draw a picture using specific two-dimensional shapes (e.g., a picture of a house using a quadrilateral, triangle, pentagon, hexagon, etc.)
Resources Used
www.amathsdictionaryforkids.com
The Greedy Triangle by Marilyn Burns
Shapes in Nature by Judy Feldman
http://www.brainpopjr.com/math/geometry/
Shapes Galore lesson plan -
http://www.uen.org/Lessonplan/preview.cgi?LPid=21489
That’s So Square lesson plan -
http://www.uen.org/Lessonplan/preview.cgi?LPid=10964
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Assessment Tasks Used
Skill-based Task:
Look at the shape below. Name the shape and identify the number of angles.
Name of shape: ________________
Number of angles: ______________
Number of sides:________________
Problem Task:
Farmer Brown wants to plant a garden. He wants his garden to have five angles and five equal sides. Draw the shape of Farmer Brown’s garden.
Name the shape of the garden: _____________________
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Geometry 2G2
Core Content
Cluster Title: Reason with shapes and their attributes.
Standard:2. Partition a rectangle into rows and columns of same-size squares and count to find the total number
MASTERY Patterns of Reasoning:
Conceptual:
• Understand that a row is horizontal.
• Understand that a column is vertical.
• Understand the meaning of partition.
Procedural:
• Identify and describe a row.
• Identify and describe a column.
• Determine the number of same-size squares in a rectangle.
Representational:
• Draw and partition a rectangle into rows and columns of same-size squares
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand the attributes of a rectangle.
• Understand that a rectangle can be divided into same-size squares. Procedural:
• Identify a rectangle.
• Identify a square.
• Determine if squares are the same size.
Representational:
• Draw a rectangle and square. Academic Vocabulary and Notation
Rectangle, row, column, same-size, partition, and square.
Instructional Strategies Used Resources Used
• Compose and decompose rectangles using
square tiles. http://www.k-
• Use grid paper to create a rectangle when 5mathteachingresources.com/geometry-
given the number of rows and columns. • Have students create a quilt square. Put
the student’s squares together in rows and columns to create a class quilt. Count the number of quilt squares in each row and column.
activities.html
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Assessment Tasks Used
Skill-based Task:
Partition the rectangle into 2 rows and 3 columns. Record the total number of squares.
Problem Task:
Aunt Sue is making a quilt. Her quilt is partitioned into 8 rows and 6 columns of squares. How many quilt squares will she need to make her quilt?
Number of squares: ____________
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Geometry 2G3
Core Content
Cluster Title: Reason with shapes and their attributes.
Standard:3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand the meaning of partition.
• Understand circles and rectangles can be divided into two, three, and four equal shares.
• Recognize halves, thirds, and fourths of a shape.
• Understand that two halves equal one whole, three thirds equal one whole, and four
fourths equal one whole.
• Recognize that equal shares of identical wholes do not necessarily have the same
shape.
Procedural:
• Identify two, three, and four equal shares of a whole.
• Identify equal shares by using the vocabulary halves, half of, thirds, third of, fourths, and
fourth of.
• Identify that equal shares within identical circles/rectangles may not have the same shape.
• Describe a circle/rectangle as having two halves, three thirds, or four fourths.
Representational:
• Draw a circle/rectangle showing two, three, or four equal shares.
• Partition two identical circles/rectangles in different ways to show that equal shares do not need to have the same shape.
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Supports for Teachers
Critical Background Knowledge
Conceptual:
• Recognize halves and fourths.
• Understand equal shares.
• Understand a shape can be divided into two and four equal shares.
• Understand that decomposing into more equal shares creates smaller shares.
• Understand that fourths and quarters have the same meaning. (This comes from first
grade core)
Procedural:
• Identify a shape as being divided into halves and fourths/quarters.
• Describe a shape as being divided into halves, fourths/quarters.
• Describe the whole as two of, or four of the shares.
Representational:
• Draw circle/rectangles show two or four equal shares.
• Partition circle/rectangles into halves, fourths, quarters. Academic Vocabulary and Notation
Partition, circle, rectangle, halves, thirds, fourths, and equal shares.
Instructional Resources Used Strategies Used
Give students three circles or rectangles. Have them partition the shapes into halves, thirds, and fourths. Makesurethestudents partition the shapes in different ways to show that equal shares do not need to have the same shape.
Use geoboards to create rectangles and divide them into halves, thirds, and fourths.
http://www.k-5mathteachingresources.com/geometry-activities.html http://www.ixl.com/math/grade-2/halves-thirds-and-fourths www.beaconlearningcenter.com/WebLessons/IWantMyHalf/default.htm http://www.uen.org/Lessonplan/preview.cgi?LPid=18835 http://www.uen.org/Lessonplan/preview.cgi?LPid=10811
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Assessment Tasks Used
Skill-based Task:
Partition the circle into fourths:
Problem Task:
Alex has a candy bar he wants to share with his three friends. He divides the candy bar into equal
shares. Show two different ways Alex can partition the candy bar. How many equal pieces will Alex need to share with his friends?
Partition the rectangle into thirds:
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Pacing Guide
The Provo City School District grade three reading program, Wonders, has a pacing guide that is aligned with the ELA Essentials document to create a comprehensive pacing guide.
Once you have logged into Wonders, you can access the Wonders Scope & Sequence at:
https://catalog.mcgraw- hill.com/repository/private_data/DOC/50001412/11/29.pdf.
ELA Essential Learning Standards
Grade 2: Essentials–Language Arts
Core Standards
Term 1 (Wonders Unit 1 – Unit 2, week 2)
Phonics: Decode words with short vowel sounds; decode words with long vowel sounds (a,I e,o and u with final e); decode words with inflectional endings s, es, ed, and ing; decode words with two letter blends r, s, t, l (ask, plan, crack, etc,) with automaticity (3 seconds or less
RF2.a, d
Fluency: Read the following 70 high-frequency words from Wonders in 100 seconds; ball, blue, both, even, for, help, put, there, why, yellow, could, find, funny, green, how, little, one, or, see, sounds, boy, by, girl, he here, she, small, want, were, what, another, done, into, move, now show, too, water, year, your, all, any, goes, new number, other, right, says, understands, work, because, cold, family, friends, have, now, off, picture, school, took, change, cheer, fall, five, look, open, should, their, won, yes.
RF2.4.b
Comprehension: Identify characters and settings of narratives.
RL2.1, 7
Comprehension: ask/answer questions such as who, what, where, when, why and how to demonstrate understanding of key details of a story.
RF2.4.a, RL2.1
Writing: Write a paragraph with an introduction, a body with details, and conclusion.
W2.1, 2, 3
Language: Write with mostly conventional capitalization and punctuation.
L2.2
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Term 2 (Wonders Unit 2, week 3– Unit 3, week 5)
Phonics: Decode words with long a with ay and ai, long i with igh, ie, and y, long o with oa, oe, and ow, long e with ee, ea, and y, contractions with ‘s, ‘re, n’t, ‘ll, ‘ve, consonant digraphs, (ch, tch, sh, ph, th, ng, wh) and prefixes un-, re-, dis-, and suffixes –ful, and –ess with automaticity (3 seconds or less).
RF2.3.a,b, d
Fluency: Read the following 80 high-frequency words from Wonders in (115 seconds): almost, buy, food, out, pull, saw, sky, straight, under, wash, baby, early, eight, isn’t, learn, seven, start, these, try, walk, bird, far, field, flower, grow, leaves, light, orange, ready, until, about, around, good, great, idea, often, part, second, two, world, also, apart, begin, either, hundred, over, laces, those, which, without, better, group, long, more, only, our, started, three, who, won’t, after, before, every, few, first, hear, hurt, old, special, would, America, beautiful, began, climbed, come, country, didn’t, give, live, turned.
RF2.4.b
Comprehension: Ask/answer questions such as who, what, where, when, why, and how to demonstrate understanding of key details of a story.
RL2.1
Writing: Write paragraph (narrative or informative) that includes an introduction, appropriate sequencing of events, details, and a closing sentence.
W2.2, W2.3
Language: Write with mostly conventional capitalization and punctuation.
L2.2
Term 3 (Wonders Unit 4, week 1- Unit 5, week3)
Phonics: Decode words with r-controlled vowels (ar, er, ir, or, ur) and the following phonograms: are, air, eer, ere, ear, ore,oar, and ire; silent letters kn, wr, mb; with automaticity (3 seconds or less).
RF2.3
Fluency: Read the following 80 high-frequency words from Wonders in (115 seconds): below, colors, don’t, down, eat, many, morning, sleep, through, very, animal, away, building, found, from, Saturday, thought, today, toured, watch, ago, carry, certain, everyone, heavy, outside people, problem, together, warm, again, behind, eyes, gone, happened, house, inside, neither, stood, young, among, bought, knew, never, once, soon, sorry, talk, touch, upon, answer, been, body, build, head, heard, minutes, myself, pretty, pushed, brought, busy, else, happy, I’ll, laugh, love, maybe, please, several, air, along, always, draw, during, ever, meant, nothing, story, won’t.
RF2.4.b
Fluency: Read grade-°©-level Text with Sufficient accuracy, speed, and expression to support comprehension (70+ wcpm).
RF2.4.b
Comprehension: Identify the main idea of informational texts and retell narrative texts.
RI2.2, RL2.2
Writing: Write an informative/explanatory paragraph that introduces a topic, gives facts, and includes a closing sentence.
W2.2
Language: Write with mostly conventional capitalization and punctuation.
L2.2
99


Term 4 (Wonders Unit 5, week 4- Unit 6, week5)
Phonics: Decode words with the following phonograms with automaticity (3 seconds or less): vowel patterns oo, ou, ew, oe, ue, aw, au, ow, ou, oi, oy;
RF2.3
Phonics: Decode compound words with automaticity (3 seconds or less).
L2.4.d
Fluency: Read the Following 70 high-frequency words from Wonders in (100 seconds): city, father, mother, o’clock, own, questions, read, searching, sure, though, anything, children, everybody, instead, paper, person, voice, whole, woman, words, door, front, order, probably, remember, someone, tomorrow, what’s, worry, yesterday, alone, became, beside, for, hello, large, notice, round, suppose, surprised, above, brother, follow, listen, month, soft, something, song, who’s, wind, against, anymore, complete, enough, river, rough, sometimes, stranger, terrible, window, afternoon, ahead, anyone, everything, pretended, scientist, somehow, throughout, trouble, wherever.
RF2.4.b
Fluency: Read grade-level text with Sufficient accuracy, speed, and expression to support comrehension (80+ wcpm).
RF2.4.b
Comprehension: Retell fiction and non-fiction texts.
RI2.2, RL2.2
Writing: Write a paragraph stating an opinion, with supporting reasons, and a conclusion.
W2.1
Language: Write with mostly conventional capitalization and punctuation.
L2.2
100