Grade 5 Math Expressions Check Your Understanding Questions 1 Check Your Understanding Questions
Unit- Fluency Plan
Grade 5
Unit
Fluency
Plan
Lesson
Activity
1
2
Page Number
3
4
3
6
4
8
1
Check Your Understanding
What is 7 x 8? 56
What three ways can you write the multiplication sign?
• ∗ ×
True or false, an equation does not have to include an
equals sign. False, an equation must have an equals
sign.
Have students solve this problem. 3 balloons
The clown brought 24 balloons to the party.
He divided the balloons equally among 8 children.
How many balloons did each child get?
Fluency
Plan
Fluency
Plan
Fluency
Plan
Fluency
Plan
2
3
1
2
12
14
What shape is an array? rectangle
What letters can you use to represent width and length
in rectangles? W and l
1
18
Give an example of this multiplication property: Sample
answers:
2
21
3
24
1
29
2
32
1
36
2
37
3
38
4
5
Commutative Property of Multiplication: 17 × 6 =6 ×
17
What is the inverse operation for this multiplication?
12 ÷ 3 = 4 or 12 ÷ 4 = 3
3 x 4 = 12
Have students call out as many “toughies” from section
4 as they can and have the class solve them. Answers
will vary.
Explain how you can use your fingers to show 9 x 4.
Bend down the 4th finger on the
left hand. There are 3 fingers to
the left of the bent finger and 6
fingers to the right of the bent
finger. This shows 3 tens and 6
ones. So the answer is 36.
What mental math strategy can you use to multiply
numbers by 5? Multiply by 10 and then take half of that
answer.
Look at the x6 table on Student Activity Book page 17.
Can you think of another strategy other than using
addition to find the product of 9 x 6? Possible answer:
Use subtraction; 9 x 6 = 10 x 6 = 60 – 6 = 54
Make an array for 3 x 6 and 9 x 2. Do they equal the
same amount? Yes
Give an example of these addition and multiplication
properties: Sample answers:
Commutative Property of Addition: 20 + 16 = 16 + 20
Commutative Property of Multiplication: 5 × 7 =7 × 5
Identity Property of Addition: 9 + 0 = 9
Grade 5 Math Expressions Check Your Understanding Questions 2 Identity Property of Multiplication: 5 × 1 =5
Associative Property of Addition: (6 + 7) + 5 = 6 + (7
+ 5)
Associative Property of Multiplication: (3 × 7) × 2 = 3
× (7 × 2)
Fluency
Plan
6
1
2
42
43
N/A
N/A
Grade 5 Math Expressions Check Your Understanding Questions 3 Check Your Understanding Questions
Unit 1- Multiplication and Division Word Problems
Grade 5
Unit
Lesson
Activity
1
Page Number
48
2
49
Check Your Understanding
If Joel took 4 shirts and 3 pairs of shorts to camp, how
many different outfits can he put together? 12 outfits
Have students make a tree diagram of Joel’s original
outfit combinations. Sample diagram:
Orange shirt
Green shorts
red shirt
Blue shirt
Outfits
1
1
Blue shorts
1
2
1
3
1
4
1
5
1
6
3
51
Problem
Solving
Strategy
52
1
56
Orange shirt
red shirt
Blue shirt
Solve this equation. p = 30
60 ÷ 2 =p
Have students solve this riddle. 9 and 2
The product of two numbers is 18.
Their sum is 11.
What are the numbers?
Have students solve this word problem. 15 hours
Stephanie practiced keyboard for 5 hours this week.
She spent 1/3 as much time practicing as Raul did.
How many hours did Raul practice this week?
Look at the computer pictograph on Student Activity
Book page 29. Change the key to have 1 computer
image equal 2 computers and then have them express
the comparison in two ways. Brownville bought 3 times
as many computers as Highland. Highland bought 1/3
as many computers as Brownville.
2
58
1
62
What are 4 multiplication situations you may have
when solving problems? Equal groups, array/area,
comparison, and combination
1
68
2
69
Have students share their word problems from Student
Activity Book page 35 and have the class solve the
problems. Problems will vary.
Where are the factors and products located in the
multiplication table? The factors are at the top and side
of the table and the products are inside the table.
1
74
2
75
1
80
Look at the function tables on Student Activity Book
page 37. What do the equations at the bottom of each
function table show? The rule for the function table.
Once you have agreed upon a rule for a function table,
can you only test the first set of input and output
values? No, you must test the rule to each pair of given
numbers to see if the rule applies to all of the sets of
pairs.
Solve this equation. b = 37
Grade 5 Math Expressions Check Your Understanding Questions 4 2
82
(6 x 7) – 5 = b
Have students solve this word problem. (7 x 6) – (5 x 8)
= t; t = 2; 2 trees
An apple orchard has 7 rows of 6 trees. A pear
orchard has 5 rows of 8 trees. How many more
trees are in the apple orchard.
1
1
1
1
86
2
89
1
94
7
1
Draw this Factor Puzzle on the board and have students
fill in the blanks. n = 35
5
2
3
7
8
9
15
n
6
14
5
2
3
7
2
98
N/A
1
103
2
105
Math
Connection
106
What number can you put in front of an unknown that is
alone to help you solve the equation? the number 1
Find the unknown number in this equation. k = 3
7k + 3k = 30
What are the Order of Operations? When solving
equations that include parentheses, first perform the
operations inside the parentheses. Second, multiply and
divide from left to right. Then, add or subtract from left
to right.
1
112
Give an example of this multiplication property:
2
1
On Student Activity Book page 41, if Bert’s Frozen
Yogurt Shop sold 4 kinds of yogurt and three different
containers (cone 1, cone 2, and a cup), how many
different combinations can be put together? 12
combinations
What drawings/tools can you use to help you solve
word problems that compare things? Comparison bars
10
Extension
114
1
118
2
119
11
Distributive Property of Multiplication: Sample answer:
3 × 4 + 6 × 4; 4 (3 × 6)
What are the similarities and differences between the
Identity Property of Addition and the Identity Property
of Multiplication? Similarities: in both properties, the
sum or the product is identical to the original addend
or factor; differences: in the addition property, adding
a 0 to any number gives the original number (5 + 0 =
5), but in the multiplication property, multiplying any
number by 1 gives the original number (5 x 1 = 5).
What does substitution mean? Possible answer:
substitution means putting numbers where letters are.
Then you are able to simplify expression.
Using the data from Student Activity Book page 51,
what predictions can you make about the likelihood of
an F4 or an F5 tornado occurring? Possible prediction:
Since there were no F4 or F5 tornados recorded in this
set of data, you can predict that is not very likely for
those tornados to occur.
Why would you need to use parentheses in some
Grade 5 Math Expressions Check Your Understanding Questions 5 3
120
4
120
5
120
expressions? It helps you know how to group and order
the operations.
In the climbing challenge, if you climbed down, then to
the left, and then climbed back up, would moving left
instead of right, change your expression, answer, and
drawing? Your expression and answer wouldn’t change,
but your drawing will change.
Have students share their own elevator problems and
have the class write expressions or show drawings that
represent the problem. Problems and representations
will vary.
Have students share any of their generalizations they
developed and have the class test them. Generalizations
will vary.
Grade 5 Math Expressions Check Your Understanding Questions 6 Check Your Understanding Questions
Unit 2- Perimeter and Area
Grade 5
Unit
Lesson
2
1
2
2
2
Activity
1
Page Number
128
2
130
1
137
2
138
Math
Connection
140
1
144
2
3
Problem
Solving
Strategy
145
147
148
1
152
2
154
2
3
Check Your Understanding
Have students list as many metric units of length as
they can. Possible answers: kilometre, meter,
millimeter, centimeter, decimeter, etc.
How do you find the metric area of a rectangle? Length
times width (l x w) or base times height (b x h).
What are the area and perimeter formulas for a square?
A = s x s; P = 4 x s
Have students solve this word problem. 6 square yards
of tiles
David wants new tiles for his bathroom. The bathroom
is 3 yards long and 2 yards wide. How many square
yards of tile does he need to order?
Have students pair up and trace their feet on centimeter
grid paper and estimate the area of their foot. Then
have them explain to the class how they calculated the
estimates of their feet outlines. Answers will vary.
What is the name of an angle that is smaller than a right
angle? Acute angle
How do you find the area of a right triangle? A=½ ×b x h
How do you find the area of a parallelogram? A = b × h
Look at Student Activity Book page 68, problem 2.
How many toothpicks do you need to make a row of 20
triangles? 41 toothpicks
How do you find the area of any triangle? A= ½ × base
× height or A = b x h ÷ 2
Draw this parallelogram and have students name both
triangles. Names may vary. Triangles HFG and GIH
F
4
H
2
2
5
6
1
158
2
159
3
160
4
162
1
2
166
171
G
I
True or false, you need to find the height of a triangle to
find the perimeter of a triangle. False, the height isn’t a
part of the distance around a triangle.
How do you find the areas of rectangles,
parallelograms, and triangles? A = l x w; A = b × h ; A
= ½ × base × height
Look at Student Activity Book page 75, problem 25.
What different figures make up the complex figure? 2
triangles and a rectangle.
How can you find the area of a pentagon? Measure the
base and height of one triangle and find it’s area. Then
multiply by 5.
How many inches are in a foot? 12 inches
About how many centimeters are equal to an inch?
about 2 ½ centimeters
Grade 5 Math Expressions Check Your Understanding Questions 7 Check Your Understanding Questions
Unit 3- Addition and Subtraction of Whole Numbers and Decimals
Grade 5
Unit
Lesson
3
1
3
3
2
3
Activity
1
Page Number
180
2
183
1
188
2
192
1
201
2
204
1
211
Check Your Understanding
In a decimal number, why do we add a 0 before the
decimal point? It helps remind us to look at the decimal
point; that the number is less than 1 but greater than 0;
and it may help the decimal numbers look more like
equivalent fractions.
Write 6/10 as a decimal number. 0.6
Write the equivalent number of hundredths and
thousandths. 0.70; 0.700
0.7
Model the decimal number 0.375 with Decimal Secret
Code Cards. Check that the 0.3, the 0.07, the 0.005
Decimal Secret Code Cards are assembled correctly.
Represent the number 4, 283 with Secret Code Cards.
Check that the 4,000, the 200, the 80, and the 3 Secret
Code Cards are assembled correctly.
Write the mixed number as a decimal number and then
say it. 77.07; 77 and 7 hundredths
77 7/100
Solve this problem.
3.157
.67
3.827
Have students fill in the blanks to make the statements
true. multiply; divide
+
2
3
213
4
As you move to the left of the Place Value Parade
(towards the tens and hundreds), each place gets
larger and you __________ by 10. As you move to the
right of the place value chart (towards the tenths and
hundredths), each place gets smaller and you
__________ by 10.
3
1
218
2
220
3
224
Extension
226
5
Represent the number 73, 456, 281, 090 with Secret
Code Cards on the frame on Student Activity Book
page 93 and then have them read aloud the number.
Check the cards on the frame; seventy-three billion,
four hundred fifty-six million, two hundred eighty-one
thousand, ninety.
Look at the Patterns from Billions to Billionths chart.
Circle the words hundreds and hundredths. Describe
the relationship between the hundreds and hundredths
positions. Each is 2 places from the ONES place.
Write these numbers on the board and have students use
greater than and less than symbols to compare the
numbers. Encourage students to use place value
drawings to help them.
345, 286
> 345, 238
Have students write the number 26 with Roman
Numerals. XXVI
Grade 5 Math Expressions Check Your Understanding Questions 8 3
3
3
1
230
2
233
Math
Connection
234
1
238
2
240
1
244
2
246
1
251
6
7
8
What is the largest 4-digit whole number you can make
with the digits 5, 3, 9, and 1? 9, 531
Have students read aloud 66, 486, 387, 235. Sixty-six
billion, four hundred eighty-six million, three hundred
eighty-seven thousand, two hundred thirty-five.
Find the value of n in this equation. n = 79
55 + 47 = n + 23
Use the New Groups Above, New Groups Below or the
Subtotal Methods to add 447 + 862. 1, 309; Check
students’ methods.
Add $53 and $0.27. $53.27
Use the New Groups Above, New Groups Below or the
Subtotal Methods to add 4,789,447 + 8,783,602.
13,573,049; Check students’ methods.
Use the New Groups Above, New Groups Below or the
Subtotal Methods to add 789,447 + 783,602. Then have
them discuss their preferred method. 1,573,049; Check
students’ methods and explanations.
Use addition to check this subtraction problem.
128 + 72 = 200
9
1 10 10
3
3
3
200
– 72
128
9
2
252
Why should you draw a magnifying glass around the
top number in a subtraction problem? The magnifying
glass helps you remember to look at the top number
closely and check if you have to do all the ungrouping
before you subtract.
1
260
Look at the data about large creatures on Student
Activity Book page 107 to solve this problem. 325
million years/325,000,000 years
2
261
Problem
Solving
Strategy
262
1
266
10
About how much longer have sharks been
on Earth than whales?
Have students share their word problems from problem
10 on Student Activity Book page 108 and have the
class solve the problems. Problems will vary.
When you estimate, does your answer have to be
correct? No, estimating is just trying to make a close
guess of what you think the answer or measurement will
be. Some answers can be estimates in certain situations
(i.e. time, money, distances, etc.) while others need to
be exact.
Write this addition problem and have students find a
quick way to solve it using mental math. 100,000 +
100,000 + 67,000 = 267,000
11
50,000 + 67,000 + 25,000 + 50,000 + 75,000
Grade 5 Math Expressions Check Your Understanding Questions 9 3
3
3
3
3
3
2
268
Have students share their situations about the
Commutative Property and have the class discuss
whether the situation is or is not a good example.
Situations will vary.
1
272
2
275
3
276
What does the key in a pictograph tell you? The key
tells you how many each symbol in the graph
represents.
If the key was 2 million buttons on the pictograph on
Student Activity Book page 113, how would that
change the data. It would double the data. There would
be 14 million red buttons and 8 million blue buttons.
Have students show their pictographs for problems 11
and 12 on Student Activity Book page 114. Discuss
why there are different rounding units on the
pictographs and have students explain which ones are
more reasonable. Keys will vary. Check students’
graphs.
1
281
2
282
Math
Connection
284
1
289
2
290
1
295
2
298
1
303
12
13
14
15
16
17
2
305
3
307
4
308
1
312
Round the following numbers to the nearest hundred:
400, 500, 800, 1, 000
350 470 820 950
Have students name situations in which they should use
safe estimations. Situations that deal with time or
money need safe estimations.
Use front-end estimation to add 6,784 + 23,894. 6,000
+ 20,000 = 26,000
Why do you need a key on a double bar graph? The key
tells you what the colored bars stand for.
Name all the parts of a bar graph. Title, axes, bars,
scale, labels.
Round this number to the nearest whole number,
nearest tenth, and nearest hundredth. 5, 4.8, 4.78
4.783
Use estimation to round both of these money amounts.
$7 + $7 =$14.00; Estimates may vary, check that
estimates are reasonable.
$7.25 + $6.89
Have students fill in the blanks to make these
statements complete. Discrete, continuous
____________ data usually involve counting,
and ____________ data usually involve
measuring and time.
What types of data does a line graph show? Change
over time data
Why do you need a key on a double or triple line
graph? The key tells you what the colored lines stand
for.
Have students share their word problems from problem
33 on Student Activity Book page 128 and have the
class solve the problems. Problems will vary.
Look at both graphs on Student Activity Book page
129. Could you have used a bar graph for the Ana’s
Height line graph and a line graph for the Common
Grade 5 Math Expressions Check Your Understanding Questions 10 3
2
313
3
314
1
318
2
322
18
Beetles bar graph? You could have used a bar graph for
Ana’s graph, but you could not have used a line graph
for the beetles graph because it doesn’t show a change
over time.
Have students share their graphs from problem 14 on
Student Activity Book page 130 and have the class
create and solve other word problems for that graph.
Problems will vary depending on the graph.
Why do we use a histogram? We use a histogram when
we need to group data.
What two types of change and collection situations can
you have? What are the three kinds of collection
situations? Change: Change plus and change minus;
collection: No action, Put Together, and Take Apart
Have students make comparison statements about these
comparison bars. Ariel has 4 times as many comic
books as Pasqual. Pasqual has ¼ as many comic books
as Ariel.
Ariel
Pasqual
1
3
326
19
2
329
1
335
6
6
6
6
6
Have students write situation and solution equations for
this problem and solve it. Situation equation: 8o = 32;
solution equation: o x 8 = 32 or 32 ÷ 8 = o; o = 4
Bali put 32 oranges into 8 equal cartons.
How many oranges were in each carton?
Have students share their word problems from problem
15 on Student Activity Book page 139 and have the
class write situation and solution equations to solve the
problems. Problems will vary.
Draw these comparison bars on the board and have
students state two comparison statements. Statements
will vary. Sample statements:
Devi has 1,200 more badges than Ali.
Ali has 1,200 fewer badges than Devi.
3
20
Devi
Ali
3
1,400
m
200
2
337
Use mental math to add 8,000 + 10. 8, 010
1
342
2
343
3
344
True or False, You can combine two steps of a problem
in 1 equation. True
Have students share their map word problems and have
the class solve the problems. Problems will vary.
Read aloud this story problem and have students
identify if there’s too much information and solve the
problem. The “too much information” is about his
21
Grade 5 Math Expressions Check Your Understanding Questions 11 brother; 101 sports’ cards
Brendan has 45 baseball cards and 56 football cards.
His brother, Damien, has 36 baseball cards. How
many sports’ cards does Brendan have altogether?
3
22
Math
Connection
348
Would having a 2-interval scale be a good choice for
this set of data (15, 5, 20)? No, it wouldn’t be the best
scale because the 2-interval scale would only evenly
match the 20-bar. The 15 and 5 bars would not match
on a 2-interval scale.
1
352
2
353
3
354
4
354
5
354
What can you use to test a hypothesis? Possible
answer: A survey
What are the two types of data students can collect?
numerical or categorical data
Have students share one of their problems that support
their generalizations and have the class test them.
Generalizations and problems will vary.
When using process of elimination, how do you know
when you can automatically eliminate a choice?
Possible answer: You can eliminate choices that you
know are incorrect without even testing them just by
using the information you already know from the
problem.
What type of graphs can you use to show categorical
and numerical data? Categorical: bar or line;
numerical: line
Grade 5 Math Expressions Check Your Understanding Questions 12 Check Your Understanding Questions
Unit 4- Circles, Polygons, and Angles
Grade 5
Unit
Lesson
Activity
1
Page Number
363
Check Your Understanding
Draw parallel line segments, perpendicular lines and
oblique lines. Sample drawings:
Parallel line segments
Perpendicular lines
Oblique lines
4
1
2
364
3
365
What measurement tool is used to measure angles?
Protractor
Have students fill in the blanks to make these
statements complete. Complimentary, supplementary
Two angles are __________ if the sum of their
measures is 90°. Two angles are __________ if the
sum of their measure is 180°.
4
4
4
4
2
3
1
371
2
372
1
376
Have students draw two congruent polygons. Sample
drawings:
2
377
3
380
What is it called when you arrange, group, or sort
objects by a set of characteristics? classify
When given clues for drawing polygons, if one of the
clues given was the polygon’s total measure of its
angles was 180°, which type of polygon do you know
you will be drawing? a triangle
1
384
2
386
1
390
4
5
What is the total of the three angle measures of a
triangle? 180°
What is the total of the measures of the angles of any
quadrilateral? 360°
What is the diameter of the circle? The length of a line
segment that goes from one side of the circle to the
other and passes through the center.
What type of turn moves 270° around the center of a
circle? A three-quarter turn
Have students draw a triangle with a line of symmetry.
Sample drawing:
Grade 5 Math Expressions Check Your Understanding Questions 13 4
6
2
391
Draw this figure and ask students if the figure has
rotational symmetry. Then have them write the number
of degrees of the rotation. Yes; 180°
1
2
396
397
3
398
How many degrees make up a circle graph? 360°
True or false, all pieces of a circle graph have to be
equal. False, each piece of the graph shows a part of
the whole and can be different sizes.
Describe a sample type of data each graph may show.
Answers may vary. Sample data shown.
Bar graph: favourite hobbies
Pictograph: Books checked out at the library
Line graph: temperature change
Circle graph: types of birds
4
7
1
402
2
404
What is the circumference of a circle? The distance
around the circle.
What are the formulas to find the circumference of a
circle? C= πd or C = 2πr
Grade 5 Math Expressions Check Your Understanding Questions 14 Check Your Understanding Questions
Unit 5- Addition and Subtraction with Fractions
Grade 5
Unit
5
5
5
Lesson
Activity
1
Page Number
412
2
417
1
422
2
424
3
426
1
430
2
431
1
2
3
Check Your Understanding
Have students give a examples of unit fractions.
Possible unit fractions: ½, 1/3, ¼, 1/5, 1/6, (any
fraction with a 1 as the numerator), etc.
Write ¾ on the board and have students sketch a
representation of the fraction. sample drawing:
Write these two fractions on the board and have
students compare them with the greater than, less than,
or equal to symbols.
1/5
< 1/3
Write these two fractions on the board and have
students use a number line to compare them. Have them
write the greater than, less than, or equal to symbols.
1/5
> 1/10
Write these two fractions on the board and have
students compare them with the greater than, less than,
or equal to symbols.
4/5
> 3/10
Use fraction bars to subtract 1/5 from 4/5. 4/5 – 1/5 =
3/5
Have students fill in the blanks to make these
statements true. numerator, denominator
The top number in a fraction is called the
________________ and the bottom number in a
fraction is called the ____________________.
5
5
1
437
2
438
1
443
Draw this on the board and have students write the
fraction of the shaded square. 1/8
2
446
Have students use the tenths fraction bars on their
MathBoards. Ask students to represent the following
situation. 4/10
4
Find an addend that totals 1. 5/7
2/7 + n/d = 1
Look at the problems on Student Activity Bok page
188. How do you know how many parts you need to
draw in order to solve the problem? Look at the
denominator and that will tell you how many parts to
draw.
5
Grade 5 Math Expressions Check Your Understanding Questions 15 A family ordered 10 pizzas. 4 pizzas were cheese and
the rest were veggie. What fraction of the pizzas were
cheese?
5
1
450
2
452
6
What is a mixed number? A mixed number is a whole
number “mixed” with a fraction.
Draw this on the board and have students write the
mixed number and improper fraction the drawing
shows. 1 + 1 +1/3 = 2 1/3; 3/3 + 3/3 + 1/3 =7/3
+
5
5
1
456
2
458
1
462
2
464
7
8
+
Add these mixed numbers with or without a number
line. 4 2/5
2 4/5 + 1 3/5
Complete this equation. 5 5/8
3 1/8 + 2 4/8 = _____
Subtract these mixed numbers. 1 1/5
2 4/5 – 1 3/5
Look at Student Activity Book page 193 to answer this
question. Day 2- 2 7/8 in.
On which day, did the rabbit eat the
biggest amount of carrot?
1
5
5
5
468
2
469
3
471
Problem
Solving
Strategy
472
1
476
2
478
1
482
9
10
11
Have students solve this word problem. Marla ate 1/8
more of pizza or Marla ate 1 more pizza than Wayne.
Marla eats 4/8 of the pizza. Wayne eats 3/8 of the
pizza. Who ate more? How much more?
Use the number line on Student Activity Book page 195
to solve this problem. Remind students to add on and
then check with subtraction. 5 2/5; Note- students may
have a problem when subtracting 9 1/5 – 3 4/5. You
can’t subtract 4 from 1. You need to borrow 1 or 5/5
from the 9 so 9 1/5 becomes 8 6/5 and then subtract 3
4/5, which equals 5 2/5.
How much farther did the cyclist travel than the skier?
How much shorter is Robby’s hand than Samantha’s
hand? 6 7/8 – 6 1/8 = 6/8 or 3/4 inches shorter
Write these numbers in order from greatest to least.
2 2/6, 1 1/6, 4/6, 3/6
3/6, 2 2/6, 4/6, 1 1/6
Write these two equations on the board and have
students tell which equation is correct and which is
incorrect. Equation 1 is incorrect as it shows
subtraction, not addition.
1.) 6 4/8 + 3 2/8 = 3 2/8
2.) 6 4/8 + 3 2/8 = 9 6/8
Have students share their word problems from problem
2 on Student Activity Book page 197 and have the class
solve the problems. Problems will vary.
When you are finding equivalent fractions equal to ½,
what kind of fracturing or splitting are you doing? 2fracturing or 2-splitting
Grade 5 Math Expressions Check Your Understanding Questions 16 5
5
5
5
5
5
12
13
2
484
Use multiplication to find an equivalent fraction for 2/3.
Sample equivalent fraction: 4/6; 2/3 = 2 x 2/ 3 x 2 =
4/6
1
493
2
496
Simplify the fraction 9/12. 3/4; 9/12 = 9 ÷ 3/ 12 ÷ 3 =
¾
Write a fraction chain that begins with 2/3. 2/3, 4/6, 6/9,
8/12, etc.
1
500
2
501
3
503
Math
Connection
504
1
508
2
511
Math
Connection
514
1
518
2
520
Math
Connection
522
1
526
2
527
1
532
14
15
16
Write a fraction chain that begins with 1/3. 2/6, 3/9,
4/12, 5/15, etc.
How do you simplify and unsimplify fractions? To
simplify fractions, divide the numerator and
denominator by the same number; to unsimplify
fractions, multiply the numerator and denominator by
the same number.
Look at the Vehicle graph on Student Activity Book
page 206. How did you find the denominator (100)?
You find the total number of vehicles by adding vans
(30) + cars (45) + trucks (25) which equal 100.
What are multiples? Multiples are another name for
count-bys or the product of two whole numbers (i.e. 3,
6, 9, 12).
Rename fractions for 1/6 and 1/3 and use fraction bars
to subtract. 2/12 and 4/12; 4/12 – 2/12 = 2/12
When you rename fractions to have the same
denominators, what kind of denominators are you
looking for? Common denominator
What is the greatest common factor (GCF) of 16 and
10? 2
Subtract these mixed numbers. 5 6/8 – 3 4/8 = 2 2/8 or
2 ¼.
5 6/8 – 3 2/4
Add these mixed numbers. 5 6/8 + 3 4/8 = 9 2/8 or 9
¼.
5 6/8 + 3 2/4
Have students solve this equation. 3
3 3/6 – 2/4 = _______
How can you use inverse operations to check your work
on Student Activity Book page 211? 2 7/10 + 6 7/10 =
8 14/10 = 9 4/10 = 9 2/5
If you don’t have a common factor between both
denominators, what do you do to rename fractions?
Multiply both denominators to produce a new
denominator for both fractions.
Draw the following on the board and tell students that
figures represent boxes of white and black marbles. box
A; 5/9; 6/9
A
B
17
Suppose you take one marble from box A without
looking and one marble from box B without looking.
Grade 5 Math Expressions Check Your Understanding Questions 17 From which box are you more likely to get a white
marble?
What is the probability of choosing a black marble from
box B?
2
5
5
5
5
535
20
A
B
B
B
Math
Connection
538
Which graph would you use to display how often or
frequent things occur? line plots
1
545
2
547
What does the small line over 0.3, 0.16, and 0.6 stand
for? It’s a special notation of a bar over a numeral to
show that the number goes on and on.
Write 6/8 as a decimal. 0.750 or 0.75
1
553
2
555
3
557
Math
Connection
559
1
564
2
567
1
572
2
573
3
574
4
574
5
574
18
19
What is the probability of choosing a white marble from
box A?
What is the probability the arrow will land in the space
marked B? 3/4
21
When you compare fractions with the same
denominators, how do you know which fraction is
greater? The denominator tells which is greater.
Is 4/10 closer to 0, 1, or ½? ½ because 4/10 is close to
5/10 and 5/10 is equal to ½.
Write the decimals in order from least to greatest. 0.25,
0.65, 0.8, 1.7
0.8, 0.25, 1.7, 0.65
Is 5/100 equal to 50¢? No, it’s 5 cents; 50 cents would
be 50/100.
What are the three fractional benchmarks used to
compare fractions? 0, ½, 1
What are the three decimal benchmarks used to
compare decimals? 0, 0.5, 1
What is the overlapping circle drawing that represents
data called? Venn diagram
What does the word “outcome” mean? Outcome means
the result of an experiment or what comes out.
What makes a game fair or unfair? A game is fair if
each person has an equal chance of winning. A game is
unfair if one person has more of a chance of winning.
Tulah has ¾ yard of fabric. Is that closer to 0 yards of
fabric, ½ yard of fabric or 1 yard of fabric? Explain
how you know. 1 yard because ¾ is close to 4/4 (1).
What does it mean to have more than 1 solution? Your
problem can have more than one correct answer.
Grade 5 Math Expressions Check Your Understanding Questions 18 Check Your Understanding Questions
Unit 6- Volume, Capacity, and Weight
Grade 5
Unit
Lesson
6
1
6
6
6
6
6
Activity
1
Page Number
582
2
583
3
584
1
588
2
589
3
590
Problem
Solving
Strategy
592
1
596
2
3
597
598
1
602
2
3
603
604
1
2
610
611
3
4
613
614
1
618
2
620
3
621
4
622
2
3
4
5
6
Check Your Understanding
What are each square sides of a cube called? the faces
of the cube.
What does volume measure? Volume measures the
number of unit cubes that will fit in the box.
What is the formula for finding the volume of a
rectangular prism? Volume = length × width × height
(V= l x w x h) or Volume = base x height (V = bh)
Have students define what it means to be 1dimensional, 2-dimensional, and 3-dimensional. 1-D:
only has length; 2-D: has length and width; 3-D: has
length, width, and height.
The sides of a cube are 5 centimeters long. What is the
area of each face and what is the volume of the cube?
25 sq cm; 125 cu cm
Use the doubling pattern to figure out the area of a 16by-3 rectangle. A = 48 sq cm
When measuring area, is it always okay to estimate?
Possible answer: Sometimes it’s okay to estimate, but if
you need precise measurements, you cannot estimate.
What is the difference between volume and capacity?
They both measure the amount of space inside an
object, but volume is “dry” and capacity is “wet.”
Which is smaller, a kiloliter or liter? liter
Which holds more, a pint or a gallon? A gallon
True or false, the terms mass and weight can be used
interchangeably. False
What is the basic metric unit for measuring mass? gram
Which weighs less, an ounce or a pound? An ounce
How many quarts are in 3 gallons? 12 quarts
Can you add and subtract measurements with different
units? No, you have to be adding or subtracting with the
same units.
Which is more, 1 cup or 1 milliliter? 1 cup
If you are estimating with capacity, weight, and mass,
what tools can you use to check the reasonableness of
your estimates? To check capacity, you could use real
liter and gallon containers; To check weight and mass,
you could use a scale.
What Fahrenheit temperature does water freeze and boil
at? Freeze- 32°F and Boil- 212°F
What Celsius temperature does water freeze and boil
at? Freeze: 0°C and Boil: 100°C
Does 32°F and 0°C feel different? No, they are the
same temperature (the temperature where water
freezes).
Have students name as many tools as they can and
explain what those tools measure. Possible tools: scale
(weight or mass); thermometer (temperature); ruler
Grade 5 Math Expressions Check Your Understanding Questions 19 6
5
623
Math
Connection
624
1
628
2
630
7
(length), cup (capacity); clock and/or calendar (time),
protractor (angle measurement)
Look at the temperature stem and leaf plot on Student
Activity Book page 249. If another temperature was
added to the data (85 degrees), how would you add that
to the stem and leaf plot? You would add a row with a
stem of 8 and a leaf of 5.
True or false, integers are only positive numbers. False,
integers are negative whole numbers too.
How many hours have passed from 9:30 am to 11:00
am? 1 ½ hours
Calculate this elapsed time.
9:50 a.m.
– 8:33 a.m.
3
632
1 h and 17 min
How many hours are in 12 days? 288 hours
Grade 5 Math Expressions Check Your Understanding Questions 20 Check Your Understanding Questions
Unit 7- Multiplication and Division with Whole Numbers and Decimals
Grade 5
Unit
Lesson
7
1
7
2
Activity
1
Page Number
641
Check Your Understanding
When you multiply a number by 10, how many places
does the amount move to the left? By 100? By 1,000? 1
place to the left; 2 places to the left; 3 places to the left
and the empty places are replaced with zeros.
Use patterns to multiply 3 x 4 and 30 x 40. 12; 1,200
2
646
1
651
Use the Rectangle Sections Method to find the product
of 46 x 39. 1, 200 + 180 + 360 + 54 = 1,794
46 =
40
+
6
39
30 × 6 =
40 × 30 =
=
180
1,200
30
+
9
40 × 9 = 360
6 × 9 = 54
2
652
Use the Expanded Notation Method to multiply 46 x
39. 1, 794
46 = 40 + 6
×39 = 30 + 9
40 x 30 = 1200
40 x 9 = 360
30 x 6 = 180
6 x 9=
54
1,794
7
7
1
657
2
659
Problem
Solving
Strategy
660
1
664
2
666
3
4
Have students solve 76 x 23 using the Rectangle Rows
or Short Cut method. 1,748; Check students’ methods.
Even when you use numeric methods to multiply
numbers, what can you draw to help you multiply or
check your work? a rectangle method
In most Work Backward problems, you need to undo
the operations. Explain what that means. You have to
do the inverse operation, or opposite operation.
Have students solve 679 x 453 using any of the 4
methods (Rectangle Sections, Expanded Notation,
Rectangle Rows, and Short Cut) and explain their
thinking. 307, 587; Check students’ methods and
explanations.
Have students solve this word problem. 62, 500 square
feet
If the base of the Great Pyramid is a square
about 250 feet on each side, how many square
feet of ground does it cover?
1
7
5
671
Have students fill in the blanks to make these
statements complete. Total; 1
When an odd number followed by all zeros is multiplied
by 5, the number of zeros in the product is the
_________ number of zeros in both factors. When an
even number followed by all zeros is multiplied by 5,
the number of zeros in the product is _________ more
Grade 5 Math Expressions Check Your Understanding Questions 21 7
7
7
7
7
6
7
672
1
676
2
677
Problem
Solving
Strategy
678
1
684
2
3
685
686
1
690
2
694
When you multiply a number by 0.1, how many places
does the amount move to the right? By 0.01? By 0.001?
1 place to the right; 2 places to the right; 3 places to
the right.
Multiply 0.03 x 0.02. 0.006
1
2
700
702
Multiply 4.2 x 0.01. 0.042
Multiply 0.07 x 0.08. 0.00560 = 0.0056
1
708
2
709
Use rounding to estimate the product of 65 x 27 and
then find the exact answer. 70 x 30 = 2, 100; 1,755
Have students solve this word problem and then
estimate to check your answer. $389.74; $15 x 30 =
$450
8
9
than the total number of zeros in both factors.
Use the Fives Patterns to multiply. 450; 1,600
90 x 5
80 x 20
2
10
Have students solve 834 x 67 using any of the 4
methods (Rectangle Sections, Expanded Notation,
Rectangle Rows, and Short Cut) and explain their
thinking. 55, 878; Check students’ methods and
explanations.
Have students make up their own word problems that
can be solved by multiplying a 3-digit number by a 3digit number. Then have the class solve them.
Problems will vary.
Use rounding to estimate the product of 34 x 56. 30 x
60 = 1, 800
How can you check your multiplication with decimals?
Use repeated addition
Multiply 0.6 x 4. 2.4
Use the Zero Pattern to multiply 30 x 0.06. 3 x 10 x 6 x
0.01 = 180 x 0.01 =1.80
The movie tickets cost $14.99 each. How much would it
cost for 26 fourth graders to attend the movie?
7
7
11
1
2
714
715
Problem
Solving
Strategy
716
1
724
12
2
3
725
726
Multiply 43.2 x 46. 1,987.2
How can you check that your word problems are
reasonable? Possible strategy: round your numbers and
use estimation.
When do you think you should choose mental math
over using a calculation to help solve a problem? You
may choose mental math if the problem can be done
using a simpler problem or if it follows a pattern.
Have students solve this problem using any division
method. 573 packages
A vegetable stand sells packages containing 1
cucumber, 1 potato, 1 squash, 1 bunch of broccoli, and
1 pepper each. One week they sold a total of 2,865
vegetables. How many packages did they sell?
How can you check your division? Use multiplication
Solve using any method. Then check your answer by
Grade 5 Math Expressions Check Your Understanding Questions 22 estimating using compatible numbers. 811 R1; Check
student’s methods; estimates: 5, 600 ÷ 7 = 800
5, 678 ÷ 7
7
7
7
7
1
731
2
732
1
737
2
739
13
14
15
16
Extension
740
1
745
2
746
1
750
2
752
Where does the decimal point belong in the quotient in
the long division format? The decimal point in the
quotient belongs directly above the dividend.
If you can’t complete the division, what do you need to
add to the dividend? Add a zero
Look at the number line in problem 23 on Student
Activity Book page 304. Look at the small line over
0.3 and the 0.6. What does that mean? It’s a
mathematical symbol for a repeating decimal.
Have students solve this word problem. 6/8 = 6.000 ÷ 8
= 0.750
Darryl got 4 hits in 7 at bats. What
was his batting average?
If a number is divisible by another number, is there a
remainder? No there is no remainder.
When you are dividing by a 2-digit divisor, what do you
have to do to that number so you can estimate place by
place. You have to round the divisor up or down.
How do you know if you have over-estimated and your
digit you chose is too high? It will have a new product
that is too big to be subtracted. You’ll have to pick the
next number down.
How do you know if you have under-estimated and
your digit you chose is too small? When you multiply
and subtract, it will have a difference that is greater
than the divisor. You will have to choose a greater
number.
Have students solve this word problem. 60 scooters
The scooters at the shop sell for $85 each. This week
the shop owner sold $5,100 worth of scooters. How
many scooters were sold?
1
7
756
17
2
758
There are many types of remainders. Explain these
types of remainders.
1. whole number only: the remainder cannot be used in
the context of the problem and is dropped.
2. round up: the remainder causes the answer to be
rounded up and adds 1 more to the quotient.
3. fractions: the remainder can be fractured and shared
(i.e. things to eat) and we write the answer as a whole
number and a fraction.
4. decimal numbers: the remainder can be shared (i.e.
money) and we write the answer as a decimal.
5. remainder only: the remainder is the only part
needed to answer the question (i.e. the extra person
who cannot participate or an amount of food someone
will get).
Have students share their word problems from problem
14 on Student Activity Book page 313 and have the
class solve the problems. Problems will vary.
Grade 5 Math Expressions Check Your Understanding Questions 23 7
18
1
762
2
3
764
765
When converting dollar amounts to cents, how many
places does the amount move to the left when
converting to dimes? pennies? tenths of a cent? 1 place
to the left; 2 places to the left; 3 places to the left and
the empty places are replaced with zeros.
How many tenths are in 3 wholes? 30
Explain how to move the decimal points to divide.
Then, explain how your dividend changes as well.
Finally, solve. Move the decimal point 2 places; change
48 to 4800; 1,200
0.04 ÷ 48
7
7
7
7
1
771
2
772
Extension
774
1
778
2
779
1
784
19
20
2
785
3
786
4
787
1
792
2
794
3
795
21
22
Does the same shift pattern occur when dividing a
whole number as when dividing a decimal number? Yes
the numbers stay the same, but the digits move 1, 2, or 3
places to the left when divided by 0.1, 0.01, and 0.001.
Explain how to move the decimal points to divide.
Then, explain how your dividend changes as well.
Finally, solve. Move the decimal point 2 places; change
0.08 to 8; 2
0.04 ÷ 0.08
How do you know a number is divisible by 9? A
number is divisible by 9 if the sum of the digits is
divisible by 9.
Suppose you know that 1,770 ÷ 30 = 59. Use that to
solve 1.770 ÷ 0.30. 5.9
What does estimating using compatible numbers mean?
Using compatible numbers makes numbers easy to
compute mentally.
Have students decide which operation to use and then
solve the problem. Multiply; 43.4 or about 43 visitors
Most months, about 62 visitors visit the petting zoo.
This month, however, only 0.7 as many visitors visited
the zoo. How many visitors visited this month?
When you multiply a whole number by a decimal, is
your answer bigger or smaller than the whole number?
smaller
Which is greater, 332 ÷ 15 or 332 ÷ 0.15? How do you
know? 332 ÷ 0.15; Possible explanation: In the first
division, we are finding how many groups greater than
1 are in 332 and in the second division we are finding
how many parts less than 1 are in 332.
Multiply 77.8 x 62. 4,823.6
How do you find the mean of a set of data? To find the
mean or the average, you add the numbers in a set of
data and divide that sum by the number of addends.
If you add new data or change data from an original set
of data, how can that affect the mean, median, mode,
and range? Sometimes it changes those values and
sometimes they stay the same.
What does a graph’s shape tell you about data? Possible
answer: In a line graph, if the line is going up, it tells
Grade 5 Math Expressions Check Your Understanding Questions 24 7
Extension
796
1
800
2
801
3
802
4
802
5
802
23
you the value is increasing; if the line stays the same, it
tells you the values aren’t changing; and if the line is
going down, the values are decreasing.
Why may you use a stem and leaf plot? It shows the
shape and distribution of data and shows where gaps,
clusters, and outliers are and the mode and the median.
When you investigate something. Is the hypothesis the
question you ask or the proposed answer to the question
you ask? The answer
What is a complex polygon? A polygon made up of two
or more polygons.
When using process of elimination, how do you know
when you can automatically eliminate a choice?
Possible answer: You can eliminate choices that you
know are incorrect without even testing them just by
using the information you already know from the
problem.
The ad frame says it’s 100 centimeters tall and 70
centimeters wide. Would you be measuring the
perimeter or area to check if the frame would fit?
perimeter
Have students solve this problem. Explain which
operations you used and describe if the remainder has
an effect of the answer. 32 pizzas; multiplication
/addition and division
There were 125 students on the class field trip to the
museum. For lunch they needed to order enough pizzas
for students to equally get 2 slices each. How many
pizzas do they need to buy if each pizza has 8 slices?
Grade 5 Math Expressions Check Your Understanding Questions 25 Check Your Understanding Questions
Unit 8- Algebra, Functions, and Graphs
Grade 5
Unit
Lesson
8
1
8
8
8
8
8
8
2
3
4
Activity
1
Page Number
810
2
813
1
818
Extension
820
1
824
2
827
1
832
2
833
3
834
1
838
2
841
3
842
1
847
2
849
Extension
850
1
854
5
6
7
Check Your Understanding
Have students represent a number in exponential form.
Sample number: 54
What is the prime factorization of 18? 3 x 3 x 2
What are the Order of Operations? When solving
equations or expressions that include parentheses, first
perform the operations inside the parentheses. Second,
multiply and divide from left to right. Then, add or
subtract from left to right.
What are the Order of Operations if your expression or
equation have exponents? When solving equations or
expressions that include parentheses and have
exponents, first perform the operations inside the
parentheses. Second, simply exponents. Third, multiply
and divide from left to right. Then, add or subtract
from left to right.
Solve this equation. t = 9.4
t – 3.8 = 5.6
What property helps you solve problem 32 on Student
Activity Book page 353? Commutative Property of
Addition
Have students to give some expressions for the number
25. Possible expressions: 5 x 5; 7 + 18; 30 – 5; 5 x (4 +
1), etc.
What is a variable? A variable is any letter that you use
to stand for a number.
What are all the symbols of inequality? >, <, ≤, ≥, ≠
True or false, when you have a two-step function
machine, it doesn’t matter which operation you do first?
False
If the function table continued for 8 weeks on Student
Activity Book page 359, problem 11, what would the
total savings be? $120
If the pattern continues to 7 days in the first function
table on Student Activity Book page 360, how many
total pages were read? 84 pages
How can you name a point on a coordinate grid? With
an ordered pair (x, y)
Have students share their ordered pairs from the
rectangles they drew on Student Activity Book page
362, problem 11. Then have the class draw the shape
and find the perimeter of the figure. Answers will vary.
Can you have more than one route between two places?
There is usually more than one route between point A
and point B, but people usually choose to go the
shortest route.
How can you represent functions? Possible answers:
equation; a table of ordered pairs; verbal rule; a line
Grade 5 Math Expressions Check Your Understanding Questions 26 2
856
3
857
Extension
858
on a coordinate grid
In an ordered pair, which is the x-coordinate and which
is the y-coordinate? The x is the first number in the pair
and the y is the second number in the pair.
What did you use to graph points in this activity on
Student Activity Book page 367? An equation
Can you use a graph to solve a problem in which the
pattern changes and does not stay the same? No, the
pattern must be consistent and stay the same.
Grade 5 Math Expressions Check Your Understanding Questions 27 Check Your Understanding Questions
Unit 9- Multiplication and Division with Fractions
Grade 5
Unit
Lesson
9
1
9
2
9
3
9
9
9
9
9
9
4
5
6
7
8
Activity
1
Page Number
866
2
869
1
2
874
876
What is 2/6 of 12? 4
Solve the problem pairs. 2; 6
1/8 of 16 = ______
3/8 of 16 = ______
1
2
882
883
Multiply 1/6 x 4. Use a drawing to help. 4/6
Multiply 3/6 x 4. Use a number line to help. 12/6 or 2
1
2
3
889
890
892
Multiply 1/6 x 1/4. 1/24
Multiply 2/6 x ¾. 6/24
Express how you would multiply 2/6 x ¾ in algebraic
terms. a/b x c/d = a x c/b x d
1
897
2
898
3
899
Simplify to multiply. 4 x 2/6 x 3 = 4 x 1/ 3 x 3 = 4/9
4/6 x 2/3
Multiply. Simplify first if you can. 3 x 3/6 x 2 = 3 x 1/ 2
x 2 =3/4
3/6 x 3/2
Have students solve this problem. 1/4
6 of the 24 workers in the ski shop don’t know how to
ski or snowboard at all. ½ of the workers only know
how to ski. The rest of the workers snowboard. What
fraction of the workers snowboard?
1
904
2
906
1
2
910
911
914
Write a decimal equivalent to 3/6 and 4/8. 0.50
Write a decimal equivalent to 3/4. 0.75
Have students solve this problem. Delma
Helena made 3/8 of her free throws this year. Her
teammate Delma made 0.46 of her free throws this
year. Who has a better free-throw record?
1
2
3
918
920
922
Divide 3 ÷ 5. 0.6
Divide 9 ÷ 1/3. 27
Which expression is greatest? 6 ÷ 1/8
6 ÷ 8 1/8 ÷ 6 6 ÷ 1/8
1
926
2
928
Compare, add, subtract, and multiply these two
fractions. Compare: ¾ > 2/6; add: 13/12 or 1 1/12;
subtract: 5/12; multiply: ¼
2/6 and ¾
Have students solve this problem. 2 7/16 or 2.4375
Math
Connection
9
Check Your Understanding
Have students solve this. 3 markers
Isabel has ¼ of a set of 12 markets. How many
markers does Isabel have?
Write an equation chain like the ones shown on Student
Activity Book page 371. 1/7 x 42 = 42 ÷ 7 = 42/7 = 6
1/7 of 42
Solve the problem pairs. 10/12 or 5/6; 2/12 or 1/6
1/3 + 2/4= ______
1/3 x 2/4 = ______
Which property shows that 1/3 x 2/4 is equal to 2/4 x
1/3? Commutative Property
Grade 5 Math Expressions Check Your Understanding Questions 28 quarts of jelly left. Discuss how most people in this
situation would say they have about 2 ½ or 2.5 quarts
of jelly left.
Mrs. Godfrey made 3 ¼ quarts of apple jelly. She used
1/4 of that for breakfast that morning. How many
quarts of jelly are left?
9
10
1
2
934
936
Divide 3/9 ÷ 2/3. 1/6
Multiply 3/8 x _____ = 6/24 2/3
9
11
1
2
940
943
Divide 3 1/3 ÷ 3/6. 6 2/3
Divide 4/16 ÷ 3/4. 1/3
1
948
2
950
Show how you can use multiplication to divide a/b ÷
c/d. a/b x d/c
Have students share their word problems from problem
6 on Student Activity Book page 395. Have the class
show how to solve the problem. Problems will vary.
1
954
9
9
9
9
12
13
2
956
1
962
2
964
3
965
1
970
2
971
3
972
4
972
5
972
14
15
Have students fill in the blank to make these statements
correct. Multiplication; division
____________ tells how many times we are taking a
number. ___________ can tell how many of a certain
number are inside another number.
Which has the greater answer? 36/75 ÷ 12/50
36/75 x 12/50
36/75 ÷ 12/50
Explain how to divide 4/16 ÷ ¾. Sample explanation:
flip the factor and multiply: 4/16 ÷ ¾ = 4/16 x 4/3 = 4/4
x 1/3 = 4/12 or 1/3
Tell which c is greater than (>) or less than (<) a. <
a – n/d = c c ( ) a
Have students share their word problems from problem
30 on Student Activity Book page 403. Have the class
show how to solve the problem and find the mean.
Problems and solutions will vary.
What formula do you need to know to solve problem 3
on Student Activity Book page 405? A = ½ bh
Have students use an octagon pattern block to find out
whether you can tessellate an octagon. You cannot
tessellate an octagon. The interior angle of an octagon
is 135° and there is no multiple of 123 that equals 360.
Draw this top view of a stack of
cubes on the board. Have students
describe the fewest number of
cubes that could make this top
view. 8 cubes
True or false, a line segment runs parallel to the base.
False
If you toss 3 balls into circular targets numbered 1, 2, 6,
and 7, in how many ways can you score a total of
exactly 15 points? Show those ways. 2 ways; 7 + 6 + 2
= 15; 7 + 7 + 1 = 15
Grade 5 Math Expressions Check Your Understanding Questions 29 Check Your Understanding Questions
Unit 10- Patterns and Transformations
Grade 5
Unit
10
10
10
10
Lesson
Activity
1
Page Number
980
Check Your Understanding
Draw the next figure in the pattern.
2
981
Draw this growing pattern on the board and ask
students to decide what comes next.
3
982
Draw this shrinking pattern on the board and ask
students to decide what comes next.
1
986
Draw this shape pattern on the board. Have students
write a numerical pattern for that shape pattern. 5, 4, 4,
3, 5, 4, 4, 3
2
987
3
988
What operations do you usually use in a growing
pattern? Multiplication and/or addition
What operations do you usually use in a shrinking
pattern? Division and/or subtraction
1
2
992
993
3
4
994
995
1
2
3
What is another name for a turn? A rotation
What is another name for a flip or a mirror image? A
reflection
What is another name for a slide? A translation
Have students fill in the blank to make these statements
true. congruent
If you rotate, reflect, or translate a figure, the
resulting figure is ______________.
Extension
996
Continue this pattern and describe the rule with the
word translation, rotation, or reflection. translation
1
1000
2
1001
Which transformation did you use to find the distance
between points? Translation or slide
Have students fill in the blanks to make these
statements true. same
4
When a figure is reflected, each of the corresponding points is
exactly the __________ distance from the line of reflection.
Extension
1002
True or false, you can only use 1 transformation to
move a figure across the coordinate plane. False
Grade 5 Math Expressions Check Your Understanding Questions 30 Check Your Understanding Questions
Unit 11- Ratio, Proportion and Percent
Grade 5
Unit
Lesson
11
1
11
11
11
11
11
Activity
1
Page Number
1010
2
1012
3
1014
1
1018
2
1019
1
2
1024
1025
3
1026
1
1031
2
1032
3
1034
1
1038
2
1044
1
2
1048
1049
2
3
4
5
6
Check Your Understanding
Have students use Student Activity Book page 427 to
find out how much money Noreen would have in her
bank on Day 9 and 10. $27 and $30
What kind of a table was used to show Noreen’s
savings? A Multiplication Column Table
Can you use a Multiplication Column Table to
represent a data pattern that changes and does not stay
the same? No, the pattern must be consistent and stay
the same.
Which operation(s) are you using when finding unit
rate? Multiplication or division
What number does per stand for? 1
N/A
True or false, the unit rate has to make a constant
change for each unit. true
Have students look at Student Activity Book page 436
and explain why tables 12 and 14 are not Multiplication
Column Tables. The unit rates do not have constant
changes.
What is the regular relationship or constant change
shown in a multiplication column table called? ratio
What kind of a table was used to show Noreen’s
savings now? A Ratio Table
Which tables on Student Activity Book page 440 are
not Ratio Tables? B and D
What is a proportion? Two multiples of a ratio or two
rows from a Ratio Table.
What type of a puzzle can you use to help you solve
proportion problems? Factor Puzzles
N/A
Use a Factor Puzzle to solve this proportion problem.
45 girls
Girls
Boys
3
1
5
15
15
45
5
15
5
15
3
1
At 9:00 at Long Pond, there were 15 girl ice skaters for
each 5 boy ice skaters. By 11:00, there were 15 boys
skating. How many girls were skating on the pond?
11
1
2
1054
1055
3
1056
7
N/A
Solve this proportion. 6
4 : 12 = _____ : 18
Which problems on Student Activity Book page 447 are
not proportion problems? problems 6 and 9
Grade 5 Math Expressions Check Your Understanding Questions 31 11
11
11
11
4
1058
Why is table D on Student Activity Book page 448 not
a ratio table? The ratios shown don’t increase by a
constant change.
1
2
1062
1063
3
1064
N/A
If you don’t use a Factor Puzzle to solve a proportion
problem, what two-steps can you use to solve the
proportion? Division and multiplication
Why are tables A and B on Student Activity Book page
450 not ratio tables? The ratios shown don’t increase by
a constant change.
1
2
1068
1069
3
1070
1
2
1074
1076
3
1078
1
1082
Draw this on the board and tell students that it
represents 50% of a figure. Then have students draw
100% of the figure. Possible drawing:
2
1086
Have students solve this problem. 80%
8
9
10
N/A
Have students share their proportion problems and
discuss as a class the reasonableness of their problems.
Problems will vary.
What makes problems 3, 4, 7, and 8 proportion
problems on Student Activity Book page 452? The
rates were the same and constant.
What mathematical symbol shows percent? %
Show 78% as an equivalent fraction and decimal. 78%
= 78/100 = 0.78
You have 36¢. Write the equivalent percent of a dollar,
dollar amount, decimal, fraction, and simplest fraction.
36%, $0.36, 0.36, 36/100, 9/25
11
Erin made 45 ham sandwiches for the class picnic.
36 were eaten. What percentage of the sandwiches
were eaten?
1
11
11
12
13
2
1090
1092
1
1096
2
1097
3
1099
Have students solve this problem. 225
Suppose we take out 40 coins and find out that 9 are
pennies. How many of the 1,000 coins are likely to be
pennies?
What are your chances of the spinner landing on B?
75%
A
B
B
B
What are similar figures? Figures that have equal,
corresponding angles and corresponding sides that are
proportional.
What do you have to do to some figures to make ratios?
Rotate or reflect similar figures
Sometimes shadows make what kind of figures to help
you find the heights of objects? Similar triangles
Grade 5 Math Expressions Check Your Understanding Questions 32 11
11
11
11
Extension
1100
Which type of figure is drawn to show a rectangular
prism on Student Activity Book page 466? Similar
rectangles
1
1104
2
1106
What does an = sign stand for on a map’s scale? The =
sign stands for “represents” rather than “has the same
value as.”
Have students look at map. How many miles does ½
inch equal? Measurements will vary.
1
1110
2
1112
1
1116
2
1118
1
1122
2
1123
3
1124
14
15
16
17
4
1124
5
1124
What does the scale in a scale drawing tell you? The
scale tells how the measurements in the drawing relate
to the actual measurements.
On a scale drawing, if 1 inch equals 3 feet, how long
would a 27-foot object be on that drawing? 9 inches
long
What kind of scale drawing do designers use when
planning the design of a room? A floor plan
Why do you think people use scale drawings and floor
plans? The actual measurements are too large to
display.
What percentage should all the pieces of the magazine
layout page seen on Student Activity Book page 475
add up to? 100%
What is the possible question that the hypothesis
answers on Student Activity Book page 476? Possible
question: What is the most popular candle and soap
scent?
Have students solve this problem. No, you can only
know that combined they make up 25% of the students.
Four classes were on the playground for recess. Class
A made up 25% of the students, Class B made up 50%
of the students. Can you know exactly the percentage of
students in Class C and D?
If a percentage is greater than 100%, will the new
amount be greater or less than the original amount?
greater
Why can’t you just multiply 100 x 150 to find the
grassy area of the yard? You have to take into account
the 10-foot strip of shrubs, flowers, and walkways that
won’t be grassy.
Grade 5 Math Expressions Check Your Understanding Questions 33 Check Your Understanding Questions
Unit 12- Three Dimensional Figures
Grade 5
Unit
Lesson
12
1
12
12
12
2
Activity
1
2
3
Page Number
1132
1134
1136
4
1137
1
1144
2
3
1145
1146
1
1150
2
1151
3
1153
1
2
1158
1160
3
4
Check Your Understanding
How many faces does a rectangular prism have? 6 faces
How do you name a prism? By the shape of its base
What is a net? A 2-D, flat figure that can be folded to
form a 3-D, solid figure.
How do you find the surface area of a prism? It’s the
total area of its bases and the combined areas of its
faces.
True or false, a pyramid has a pair of congruent bases.
False
How do you name a pyramid? By the shape of its base
How do you find the surface area of a pyramid? It’s the
total area of its base and the combined areas of its
faces.
What are the three views of a solid figure? Front, side,
and top views
When looking at the top view of a solid figure, does
that tell you how many total cubes make up the figure?
No, it just tells you how many cubes you can see from
the top.
Using the information on Student Activity Book page
495 to help you, find the number of sides of a base,
number of faces, number of edges, and number of
vertices on an octagonal prism. 8, 10, 24, 16
How many degrees are in a complete rotation? 360°
When does a solid figure have rotational symmetry? A
figure looks identical after less than one complete 360°
rotation.
Grade 5 Math Expressions Check Your Understanding Questions 34 Unit
Lesson
Extension
1
Activity
1
2
Page Number
1168
1169
3
1170
1174
1176
Add –3 + –5. –8
What is absolute value? The distance between the point
of the integer and 0.
Whenever you use a number line to add integers, where
do you begin on the number line? At 0
Add –2 + –8. –10
Extension
2
1
2
Extension
3
1
1182
2
1184
1
1188
2
1191
3
1193
4
1194
Extension
4
Check Your Understanding
What are numbers below zero called? negative numbers
Are negative numbers to the left or right of the 0? To
the left
Have students use the number line on Student Activity
Book page 502 to help them find the distance between 5
and –8. 13 units
When you start measuring when trying to locate a point
using an ordered pair? 0
How do you find the missing values in a function table
where a rule is given and values for x. Use substitution
for each value of x to find the value of y.
Look at the table in number 11 on Student Activity
Book page 1193. What do the m and the d stand for?
x and y respectively
Have students give an example of an additive inverse.
Sample answer: 7 + –7