Answers – Multiplying Fractions Name: _______________
Task: _______________
1 2 3 4 1 23 4
3/8 6/28 1/8 8
5 4/15 5 67
6 7 8
5/12 3/72 5/18
9 1/6
7/12 12
13 10 11 24/35 9 10 11 12
3/49 4/15 1/3
17 16
4/11 14 15 14/33 13 14 15 16
9/20 3/16 20
1/24 17 18 19 20
18 19
2/9 1/35
© Sarah Kiersh 2013
Answers – Multiplying Fractions and Name: _______________
Whole Numbers Task: _______________
1 23
1 2 3 4 4
2 2/3 2 1 1/5 5 67 8
5 1 1/2
6 7 8
2 1/2 2 2/3 4 4/5
9 1 4/5
7 1/2
13 10 11 12 9 10 11 12
3 3/7 5 2 4 2/3
17 13 14 15 16
30 14 15 16
5 5/6 24 24 17 18 19 20
18 19 20
16 10 5/12 28
© Sarah Kiersh 2013
Answers Answers
Find the LCM Finding Common Denominators
1 234 1 234
8 20 12 21
3/6 and 12/15 2/12 and 5/20 and
5 678 4/6 and 4/12 6/12 12/20
15 30 77 24
5 6 7 832/40
8/36 and 12/24 and
5/20 and 9/36 and 6/24 30/40
10/20
9 10 11 12 11 12
20/45
60 36 40 60 9 1500/60 and 3/18 and
12/28 and 27/45 8/18
13 14 15 16 and 36/60 16
14/28 15 8/10 and
60 24 18 200 13 14 12/42 8/10
17 18 19 20 27/45 and
4/9 and and 35/42 20
60 63 18 40 6/9 40/45 19 25/30
18 20/60 and
17 27/36 and 21/30
12/18 and 24/60
and 28/36
12/18
© Sarah Kiersh 2013
Converting Mixed Numbers and
Improper Fractions
14/3
Answers ANSWERS: Simplifying Fractions
Adding and Subtracting Mixed Numbers
1 234 1 234
6 1/2 4 11/12 5 7/10 2 9/14
1/4 1/9 1/2 2/3
5 6 7 8 5 6 78
12 1/4 8 5/8 7 1/8
8 12 1/3 21/40 1/3 5/6
26/35
9 10 11 9 10 11 12
4 1/16 1/9 7/10 3 5/12 5/12 7/8 6/13 1/3
13 14 15 16 13 14 15 16
1 4/15 1 1/2 1 3/5 3 1/4 1/2 2/11 2/3 3/5
17 18 19 20 17 18 19 20
1 24/35 1 2/3 4 7/8 8 17/20 17/24 1/3 4/9 5/6
© Sarah Kiersh 2013
© Sarah Kiersh 2013
Name: ANSWER KEY – Line Plots
1. 40 minutes 2. 8 students 3. 20 10/13 or 20R10
4. 6 days 5. 11 days 6. 7 ½, 7.5, 7R3
7x x
X
Xx
X xx
X xx
X xx x x
1 2 3 4 5 6 7 8 9 10 Number of best friends
8. Yes. 10 is an outlier because it is 9. The most friends anyone 10. 1 friend
unlike the rest of the data. reported having was 10 friends.
11. Cups of flour Frequency 12. Length of Pencils Number of Pencils
1 3
1 2 4 2
1 2/8 1 4½ 3
2 6/10 1 5 2
2 5/8 2 6 1
3 2/8 2 6½ 3
4 1/10 7 3
7½
13. The smallest pencil measured was 4
inches (sample answer) 14. 7 ½ inches
© Sarah Kiersh 2013
15. Score Number of Students X xx
6 xx
¼ 3 16XX.
2/4 2 ¾ 4/4 scores
¾ 2 Xx
4/4 Xx
X Xx
17. 13 students X
Xx ¼ 2/4
19. Frequency Xx
4 1/3 2/3 18. 1) 4 2) 6/13
Growth (in 2
cm) 20. 6 weeks
1/3
21. 2 2/3 cm
2/3
22. 8 cm
23. x x Liquid (L) No. of Beakers
x x 1 1/6 2
X x 1 ½ 1 4/6 1 5/6 1 2/6 3
X 1 4/6 2
1 1/6 1 2/6 1 5/6 1
24. 11 ½ L
25. 3 5/6 L
26. 5 ¾ L
© Sarah Kiersh 2013
Name: VOLUME ANSWER KEY
1. Cube 2. Rectangular 3. 6 faces, 8 vertices 4. 24 cubic units
5. prism 7. 8.
6.
9. 8 cubic units 10. 12 cubic units 11. 24 cubic units 12. 320 cubic cm
13. 288 cubic meters 14. 285.12 ft. cubed 15. 246 3/32 units 16. 14 units cubed
cubed
17. Possible
dimensions: 18. Possible dimensions: 19. 21 feet 20. 80
2x12x2 3x3x4 squared cubes
4x6x2 6x2x3
8x3x2 12x1x3
48x1x1 9x2x2
21. 40 + 56 = 96 22. 67.5 + 130.975 = 23. 471.25 + 53.625 24. 148.8 + 90.3 =
units cubed 198.475 yards cubed = 524.875 in. cubed 239.1 m. cubed
25. Possible 26. Possible 27. The second 28. (16x16x16)x3 =
dimensions: dimensions: cereal box has a 12288
volume of 384
4x2x5 4x3x5 (3x5 for base inches cubed, while
2x2x10 of 15) the first has a
volume of 270
inches cubed.
ANSWERS COORDINATE GEOMETRY
1. A (1,3); B (2,8); C 2. E (2,1); F (3, 5); G 3. I (0,5); J (1,0); 4. M(1.5, 1); N(3,
K(5,5); L(9,4) 3.5); O(5.5,2): P(7.5,
(4,6); D (8,2) (5,8); H(6,3) 4.5)
5. 7 units (7-0) 6. 8 units 7. 5 units
8. Find the distance between two points by subtracting the y coordinates 9 and 3 to find a
distance of 6 units.
9. (2,3), (1, 2), (3,4) 10. Point C 11. (1,3); (2,5); (3,7) 12. Point B
13. 8 units 14. 5.5 units 15. 4.5 units 16. 4.5 units
17. 18.
X Y
3 5
4 6
5 7
6 8
7 9
8 10
19. 20.
X Y
1 4
2 5
3 6
4 7
5 8
5.5 8.5
21. Jill Jack Jill’s earnings22.
Time $1 $0 . Jill
Start $3 $2
10 minutes $5 $4 Jack’s earnings
20 minutes $7 $6 24. Jack will raise $36 Jill will raise $37.
30 minutes $9 $8
40 minutes $11 $10
50 minutes $13 $12
60 minutes $15 $14
70 minutes $17 $16
80 minutes $19 $18
90 minutes
23. Jill always has $1 more than Jack.
25. Number of Number of Individual Cookies26.
Cookies Students should label the y axis with
Number of 4 multiples of 4
Packages 8
1 12 Packages of Cookies
2 16 28. I would need to buy 9 packages to have
3 20 36 cookies.
4 24
5 28
6
7
27. The number of cookies is always four
times the number of packages.
Answer Key Classifying Polygons
1. Three sides, three 2. Right triangle 3. Isosceles triangle 4. Isosceles, acute
angles, three triangle
vertices, the sum of
the measures of the
three angles equals
180, acute angles
5. quadrilateral, 6. polygon, 7. polygon, 8. polygon,
polygon, quadrilateral, quadrilateral, quadrilateral,
parallelogram, trapezoid parallelogram, parallelogram,
rhombus rectangle rectangle, rhombus,
square
9. rhombus 10. Right trapezoid 11. rectangle 12. parallelogram
13. Incorrect. 14. Correct. Students 15. Incorrect. 16. Incorrect.
Students may draw may draw several Students may draw a Students may draw a
several images of squares and label four trapezoid and label rectangle and label
parallel lines or a set right angles and one pair of parallel four right angles.
of intersecting lines. parallel sides. sides.
17. Both polygons. 18. Triangles have 19. Both polygons. 20. The triangle has
Both have right only three vertices. A Both have at least two no right angles; the
angles. rectangle has four equal sides. rectangle has four
vertices. Rectangles right angles.
have parallel sides;
triangles do not.
21. Answers will vary. 22. The parallelogram – has 23. 24.
Students may choose Rhombus – all the
the middle trapezoid four sides Rhombus – no right angles angles are equal
because there are no The right triangle – has a
right angles. Other right angle The triangle – not a Trapezoid – not a
students may choose quadrilateral quadrilateral
the rectangle because it
is a parallelogram.
For this set of cards,
reasoning is most important.
Place Value – ANSWER KEY
1.) Word form: nineteen million, five hundred seventy thousand, two hundred sixty
one.
Expanded form 10,000,000 + 9,000,000+500,000+70,000+200+60+1
2.) Standard form 8, 336, 697
3.) Expanded form 2,000,000 + 500,000 + 60,000+5,000+ 600+30+5
4.) 0.30 5.) 65 cubes 6.) 80 cubes or 8 7.) 1 whole and 24
tens cubes
9.) sample answers – 2.4, 2.42, 2.45 10.) 7.6 > 2.36 OR 2.36<7.6
11.) Three hundred seventy nine and 12.) 8.23
seven tenths 8+0.2+0.03
300+70+9+0.7
13.) $40 18.) 2.45>2.05 14.) 7/100 20.) 6.75<6.05
15.) 104/1000 16.) 0.014
17.) 0.2 19.) 4.632<4.9
© Sarah Kiersh 2013
Answer Key Adding and Subtracting Decimals
1.) 1.85 2.) 1.05 3.) 3.33 4.) 3.44
8.) 22.15
5.) 2.27 6.) 8.34 7.) 52.55
9.) 0.05 10.) 0.23 11.) 0.59 12.) 1
13.) 7.78 14.) 0.48 15.) 1.96 16.) 1.47
17.) 0.6 18.) 5.6 miles 19.) $1.01
20.) 47.05lbs, Mark’s
bags will be allowed
onboard.
21.) The decimal is 22.) The smaller 23.) There was no 24.) There was no
not lined up. Answer number was on top. borrowing. The carrying. The answer
should be 17.75. The answer should answer should be should be 7.5.
be 0.26. 0.65.
0.4 shaded 4 times = 0.25 shaded
1.6 three times
= 0.75
0.5 x 0.3 0.6 x 0.5 =
= 0.15 0.30
Students might shade0.1 at a time until they’ve Similar method as 13. Shade 0.1 until you’ve shaded 25 tenths, then
drawn 1.8, then count how many are in one group. count how many are in one group.
First shade 2.4, then circle groups of 0.8. The Shade 1.25, then circle groups of 0.25. The
answer is the number of groups = 3. answer is the number of groups = 5.
Multiplying and Dividing Decimals Answer Key
1.) 1.6 2.) 0.75 3.) 0.15 4.) 0.30
5.) 0.868 6.) 15.1 7.) 57.378 8.) 146
9.) The student 10.) The decimal 11.) 3.75 miles 12.) $12.20
did not place a point must move 16.) 5
decimal point. one more place to
the left.
13.) 0.6
14.) 0.25 15.) 3
17.) 0.37 18.) 0.4 19.) 0.2 20.) 2.1
21.) $8.50 22.) 57.5 miles 23.) 7 pieces 24.) 11
partnerships
25.) the student did not 26.) The student 27.) The 4 pack is a
better value because 28.) each must
move the decimal in flipped the divisor and each ticket is $10.50, contribute $3.06, but
which is less than they will still need 0.01
the divisor. the dividend. $10.75. to pay the full bill.
Answer Key Dividing Whole Numbers Task Cards
1.) 8, 80, 8, 800 2.)6, 60, 6, 600 3.) 3, 30, 3, 300 4.) 20 TABLES, 5.) 221.16 OR 6.) 409
20 TABLES, 21 221 r 1
TABLES
7.) 28 r 10 OR 8.) 210.33 OR 9.) The student 10.) The 11.) The 12.)The student
placed the 3 in student did not student multiplied
28.83 210 r 5 the ones place drop the zero subtracted incorrectly.
instead of the down to incorrectly.
tens place. complete the
problem.
13.) 1 14.) 7 15.) 7 16.) 93 17.) 150 pounds 18.) 80
students
(ignore the
remainder)
19.) $11 20.) 162 21.) 74 feet 22.) 80 feet 23.) 200 feet 24.) 120 feet
kilometers
Place Value Party ANSWERS 5.NBT.1, 5.NBT.2
1.) c 2.) d 3.) c 4.)a
5.) c 6.) b 7.) b 8.) c
9.) 0.80 / 10 = 0.08 each; students 10.) $15.86 / 10 = $1.586 per day; a
might explain that dividing by ten reasonable solution would be to
means that they move the decimal round to the nearest cent, so $1.59
one place to the left. per day
11.) 185/10 = 18.50 per week; 12.) 400 x 10 = 4,000 cans; students
students can check this equation might explain that they counted the
with 10 x 18.50 = 185 number of zeroes in the factors and
used that number in the product.
© MissKinBK 2014
Decimal Dance ANSWERS 5.NBT.3a, 5.NBT.3b
1.) b 2.) d 3.) a 4.)d
5.) b 6.) d 7.) a 8.) b
9.) twenty three million, eight hundred nine 10.) possible answers: 7.21, 7.222,
7.25 lbs
thousand, two hundred twenty four and
eighteen hundredths 12.) possible answers: 0.51, 0.52, 0.53,
20,000,000 + 3,000,000 +800,000 + 9,000 +200 0.55
+20 +4 + 0.1 + 0.08
11.) 1.1 < 0.9
0.9 > 1.1
1.04 < 1.1
© MissKinBK 2014
Rounding Revelry ANSWERS 5.NBT.4
1.) b 2.) a 3.) b 4.)c
5.) a 6.) c 7.) a 8.) d
9.) sample answer: 4.1, 4.05, 3.99 10.) 7 + 1 + 5 = 13 miles
11.) $3.30 x 3 = $3.90; this is an 12.) His method is incorrect. He
overestimate because I rounded up should round 1.85 before he
to $3.30. multiplies, not after.
Other sample answer: $3 x 3 = $9.
This is an underestimate because I
rounded down to $3. © MissKinBK 2014
Multiplication Mixer ANSWERS 5.NBT.5
1.) d 2.) a 3.) d 4.)d
5.) b 6.) d 7.) b 8.) b
9.) 216 students can attend. 10.) 3,344 feet sq. Students should
Students might draw 6 circles and draw an area model and label two
label each with the number 36. of the dimensions.
11.) 35 x 16 = (30 +5) x (10 +6) = 12.) 2 sheets x 27 students x 20 days =
(30 x 10) + (30 x 6) + (5 x 10) + (5 x 6) 1,080 sheets of loose leaf, so 150 isn’t
= even close to enough for the month!
300 +180+50+30 =
560
© MissKinBK 2014
Division ANSWERS 5.NBT.6
1.) a 2.) c 3.) c 4.)b
5.) c 6.) b 7.) d 8.) b
9.) 5115/15 = b 10.) 122+124+103 = 349; 349/20 =17
b = 341 boxes R9. The PTA needs 18 bags to hold
all of the labels because there was
a remainder. This remainder means
we need to add another group to
the quotient.
11.) 164 / 8 = 20 R 4; we need 21 12.) 2332/22 = $106 Sample answer: I
chaperones otherwise there will be 4 solved this problem using the long
students who do not have anyone to division algorithm. Students may also
take them to the zoo. show their work with area models or
© MissKinaBKr2r0a14ys.
Decimal Jamboree ANSWERS 5.NBT.7
1.) d 2.) b 3.) b 4.)b
5.) c 6.) c 7.) c 8.) b
9.) $1.89 x 5 = $9.45, so $9 is not 10.) Jill can go to the bowling alley 7
enough. times. 25/3.25 = 7 R $2.25. The
remainder is not enough for another
trip to the bowling alley.
11.) 12.) (0.30x 124) +(0.75x98)+(1 x72) =
Each payment will be $46.14 $182.70
because $205.75 + $24.95 = $230.70
and $230.75/5 = $46.14 per payment.
© MissKinBK 2014
Answer Key Converting Measurements
1.) 40 x 1000 = 2.) 4 quarts x 2 3.) 1,760 x 2 = 4.) 3 pounds x 16
40,000 pints = 8 pints 3,520 yards ounces = 48
ounces
5.) 8 pints / 2 = 4 6.) 5280 feet / 2 = 7.) 2500 x 1000 = 8.) 16 mm / 10 =
pints 2640 feet 2,500,000 1.6 cm
9.) 2.5 x 16 = 40 10.) 3.25 x 12 = 39 11.) 0.75 x 2000 = 12.) 0.1 x 100 =10
cups
inches 1500 pounds cm
13.) (7 x 16) + 3 = 14.) 115 + (6.5 x 4) 15.) 16 ounces / 5 16.)5000 meters/ 4
115 oz
= 141 ounces sandwiches = 3.2 obstacles = 1250
ounces meters
17.) 4 quarts x 4 18.) (4x12) +7 + 8 19.) 18 inches / 20.) 2000/8 =
cups = 16 cups 250mL
= 63 inches 0.5 = 36 DVDs
Copyright 2014 Sarah Kiersh