Grade 4 Check for Understanding

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Grade 4 Math Expressions Check Your Understanding Questions 1 Check Your Understanding Questions
Unit: Fluency Plan
Grade 4
Unit
Fluency
Plan
Fluency
Plan
Fluency
Plan
Lesson
Activity
1
2
Page Number
2
4
3
9
4
12
1
2
16
18
3
20
4
21
5
23
1
29
Make a drawing to show a 3 by 6 array and then write a
multiplication equation to represent the total number of
objects. 3 x 6 = 18
2
31
The Commutative Property of Multiplication allows
you to rotate arrays in two different ways. Rotate a 3
by 6 array to show a 6 by 3 array.
3
32
Have students solve this problem. Check students’
drawings. The drawing should have 4 rows with 6
stamps in each row. You could arrange 6 rows of 4
stamps; 1 x 24 and 24 x 1; 2 x 12 and 12 x 2; 3 x 8 and
8 x 3.
Brendan has a page of stamps. There are 4 rows and 6
stamps in each row. Draw a picture of this page. Can
you arrange the stamps in different ways?
1
2
Check Your Understanding
What is 9 + 3? 12
How can you use the Associative Property of Addition
to add 90 + 20 + 80? Possible answer: First add the 20
+ 80 = 100 + 90 = 190.
How can you use counting on to subtract 8 from 15?
Start at 8 and count on up to 15: 9, 10, 11, 12, 13, 14,
15. I started at 8 and counted on 7 more to get to 15.
So 15 – 8 = 7.
How is the Commutative and Associative Properties of
Addition different? The Commutative Property of
Addition involves adding only 2 addends while the
Associative Property involves adding 3 or more
addends.
What is 7 x 8? 56
What three symbols can you use to represent
multiplication? • ∗ ×
List the 2s count-bys up to 20. 2, 4, 6, 8, 10, 12, 14, 16,
18, 20; List the 5s count-bys up to 50. 5, 10, 15, 20, 25,
30, 35, 40, 45, 50
List the 9s count-bys up to 90. 9, 18, 27, 36, 45, 54, 63,
72, 81, 90; List the 10s count-bys up to 100. 10, 20, 30,
40, 50, 60, 70, 80, 90, 100
Explain how you can use Quick 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.
3
Grade 4 Math Expressions Check Your Understanding Questions 2 Fluency
Plan
Fluency
Plan
Fluency
Plan
4
1
2
38
39
N/A
N/A
1
44
2
45
3
47
List the 3s count-bys up to 30. 3, 6, 9, 12, 15, 18, 21,
24, 27, 30
How can you use the 5s shortcut to find the product of 8
× 3? Multiply 5 times 3 first, which is 15, and then add
three more groups of 3, which is 9. 15 + 9 = 24.
Have students solve the problem and identify what type
of problem it is. 3 balloons
5
6
4
48
1
52
2
53
3
56
1
60
Complete the statement to make it true. 1; 0
62
When any number is multiplied by _______, the
result is that number. When any number is multiplied
by _______, the result is 0.
Complete the statement to make it true. 1; number
2
Fluency
Plan
Fluency
Plan
Fluency
Plan
List the 4s count-bys up to 40. 4, 8, 12, 16, 20, 24, 28,
32, 36, 40
How can you use the 5s shortcut to find the product of 9
× 3? Multiply 5 times 3 first, which is 15, and then add
four more groups of 3, which is 12. 15 + 12 = 27.
Copy and complete the Fast
8
Array.
3
24
Dividing a number into that number of equal groups
gives each group a size of _______. Dividing a number
into 1 group gives each group size equal to the
_______.
7
8
The clown brought 24 balloons to the party.
He divided the balloons equally among 8 children.
How many balloons did each child get?
What does the key in a pictograph tell you? The key
tells you how many each symbol in the graph
represents.
3
64
Write an addition expression and a multiplication
expression that equals the same answer. Possible
answers: 5 + 0 and 5 x 1
1
2
68
69
N/A
N/A
1
74
What are the 8 equations that go with this Fast Array
drawing?
4 × 7 = 28
7 × 4= 28
9
2
3
77
78
28 ÷ 4 = 7
28 ÷ 7 = 4
7
4
28 = 7 × 4 7 = 28 ÷ 4
28
28 = 4 × 7 4 = 28 ÷ 7
How can you check your division? use multiplication
N/A
Grade 4 Math Expressions Check Your Understanding Questions 3 1
Fluency
Plan
Fluency
Plan
Fluency
Plan
10
82
2
83
3
83
4
84
1
88
2
89
Math
Connection
92
1
96
2
99
3
102
11
12
Have students solve this word problem and then tell the
type of word problem it is and solve it. 48 roses;
Repeated-groups multiplication
There are 6 roses in each vase at the flower shop. If
there are 8 vases on display, how many roses are there?
Have students share their word problems they wrote for
problem number 5 on Student Activity Book page 33
and have the class solve them. Check students’ work.
Have students share their written word problems and
have the class solve them. Check students’ work.
What other operation can you use to divide? Repeated
subtraction
List the 6s count-bys up to 60. 6, 12, 18, 24, 30, 36, 42,
48, 54, 60
How can you combine 2 multiplications you know to
multiply 7 x 6? Sample combinations: (4 x 6) + (3 x 6)
= 24 + 18 = 42
If the pattern continues in the function table in problem
5 on Student Activity Book page 36, how much money
would 9 tickets cost? $72
List the 8s count-bys up to 80. 8, 16, 24, 32, 40, 48, 56,
64, 72, 80
List the 7s count-bys up to 70. 7, 14, 21, 28, 35, 42, 49,
56, 63, 70
Have students solve this problem. 6 butterflies
A butterfly movie lasted for 60 minutes. The movie
spent 10 minutes on each butterfly. How many different
types of butterflies were shown in the movie?
1
2
106
108
N/A
Fill in the unknown number in the Factor Triangle.
42
÷
Fluency
Plan
7
13
3
Fluency
Plan
6
N/A
Write these expressions on the board and have students
use greater than and less than symbols to compare the
expressions.
46 + 98 >
25 + 37
1
115
2
117
When you multiply a number by the same number (i.e.
7 x 7) what type of an array is formed? A square
What is 11 x 9? 99
1
2
3
122
123
124
14
15
×
109
110
Math
Connection
Fluency
Plan
÷
N/A
N/A
Grade 4 Math Expressions Check Your Understanding Questions 4 Fill in the unknown number in the Factor Triangle.
27
÷
9
1
128
÷
×
3
Give an example of these multiplication properties:
Sample answers:
Commutative Property of Multiplication: 5 × 7 =7 × 5
2
Fluency
Plan
16
3
Fluency
Plan
129
17
131
4
132
1
2
138
139
140
Math
Connection
Identity Property of Multiplication: 5 × 1 =5
Give an example of this multiplication property: Sample
answer:
Associative Property of Multiplication: (3 × 7) × 2 = 3
× (7 × 2)
Give an example of this multiplication property: Sample
answers:
Distributive Property of Multiplication: 3 × 4 + 3 × 4;
3 (4 × 2)
If parentheses are not written in an expression, what
operations are done first? Multiplication and division
are done before addition and subtraction.
N/A
N/A
Ask students if the symbol could have been 3 cars? 3
cars would not have worked as 3 is not a factor of 4, 20,
16 or 8. It only is the factor of 18.
Grade 4 Math Expressions Check Your Understanding Questions 5 Check Your Understanding Questions
Unit 1- Solve Multiplication and Division Problems
Grade 4
Unit
1
1
1
1
1
Lesson
Activity
1
2
Page Number
144
145
A table uses rows and columns to display
information. The rows go ______________
and the columns go ____________.
1
2
3
147
Extension
148
1
152
2
154
1
158
3
2
160
1
166
4
5
Check Your Understanding
N/A
Have students fill in the blanks below to complete the
statements. Across/right to left/horizontally; up and
down/top to bottom/vertically
2
168
1
172
2
173
3
174
Extension
176
Have students share their questions and table from
numbers 6 –7 on Student Activity Book page 59 and
have the class answer the questions. Tables, questions,
and answers will vary.
Look at the function tables on Student Activity Book
page 60. What do the equations at the bottom of each
function table show? The rule for the function table.
If you added another vegetable topping to the table of
combinations on Student Activity Book page 63, how
many different one-topping pizzas are there now? 12
pizzas
What are the different ways you can represent a
combination problem? Possible answers: numerically
with an equation, a Fast Array drawing, a Tree
Diagram, a table, etc.
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?
What is the letter used to represent an unknown in a
situation or solution equation called? a variable
Have students make comparison statements using
multiplication and division about this situation. Sample
comparison statements: Tran has 1/3 as many stuffed
animals as Renaldo. Renaldo has 3 times as many
stuffed animals as Tran.
Tran has 3 stuffed animals.
Renaldo has 9 stuffed animals.
What drawings/tools can you use to help you solve
word problems that compare things? Comparison bars
What does the key in a pictograph tell you? The key
tells you how many each symbol in the graph
represents.
How is a vertical bar graph arranged? A vertical bar
graph has the bars going up and down, not across.
What is a survey? Something used to collect
information and data.
Look at the Heights table on Student Activity Book
Grade 4 Math Expressions Check Your Understanding Questions 6 page 72. If another building was 67 stories high, how
would you add that piece of data to the stem and leaf
plot? You would add a row with a stem of 6 and a leaf
of 7.
1
1
6
7
1
181
2
183
Extension
184
1
188
Give examples of hidden information in a problem.
Possible answers: Week = 7 days; dozen = 12, etc.
1
2
196
197
N/A
Have students fill in the blanks to make these
statements correct. prime; composite
3
1
198
8
What does horizontal and vertical mean? Horizontal
means “going across” and vertical means “going up
and down.”
Name all the parts of a bar graph. Title, axes, bars,
scale, labels.
What does the key on a double bar graph tell you? What
each bar stands for.
A __________ number is a number greater than
1 that have 1 and itself as the only factors.
A _________ number is a number greater than
1 that has more than two factors.
Use Factor Fireworks (or a Factor Tree) to show all the
factors of the number 16.
16
8
×
2
4 × 2
4
201
1
206
2
207
2 × 2
What are multiples? Multiples are another name for
count-bys (i.e. 3, 6, 9, 12).
Use the running speed table on Student Activity Book
page 83 to answer this question. Pronghorn antelope
Which animal almost runs twice as fast as a house cat?
Have students fill in the blanks to make these
statements complete. Even; odd, even
The product of two even whole numbers will always be
___________. The product of two odd whole numbers
will always be ___________. The product of an even
and an odd whole number will always be ___________.
1
9
3
208
4
208
5
208
What if Cora had 3 boxes instead of 5 boxes, how many
muffins would go in each box? 10 muffins in each box
Have students point out the inverse operations in this
age riddle that “undo” each other. Multiplying and
dividing by 2;subtracting and adding 10.
Have students solve this word problem. 30 ÷ 7 is 4 R2.
5 pages
Edgar plans to write 30 math problems. He can fit 7
math problems on a page. How many pages will Edgar
need for all 30 math problems?
Grade 4 Math Expressions Check Your Understanding Questions 7 Check Your Understanding Questions
Unit 2- Quadrilaterals
Grade 4
Unit
2
Lesson
Activity
1
Page Number
216
2
218
3
220
4
221
Check Your Understanding
Have students draw two congruent triangles on their
MathBoard. Triangle shapes will vary, but make sure
the two shapes that are drawn are the same shape and
the same size.
Have students draw two similar triangles on their
MathBoard. Triangle shapes will vary, but make sure
the two triangles that are drawn are the same shape but
may differ in size.
Have students draw a triangle with a line of symmetry
on their MathBoard. Sample drawing:
1
Math
Connection
222
Have students read this statement and fill in the blank.
congruent
If a figure has a line of symmetry, the two figures
formed by the line of symmetry are _____________.
Have students read this statement and fill in the blank.
reflection
The figure on one side of a line of symmetry is a
mirror image called a _______________.
1
226
Draw parallel line segments and perpendicular lines.
Sample drawings:
Parallel line segments
2
227
Perpendicular lines
Have students name the line segments, vertex points,
and angles in this figure.
Line segments: AD, BC; vertex point: E; angles:
<BED,<DEC, <AEB, <AEC (angle names may vary).
2
A
2
B
E
C
3
228
D
Draw a triangle. Name it CDE and describe various
parts of the triangle. Sample triangle. Vertices: C, D,
E; angles: <CDE, etc.
C
E
D
Grade 4 Math Expressions Check Your Understanding Questions 8 2
2
2
2
1
232
2
3
233
235
Math
Connection
236
1
240
2
242
3
243
4
246
Problem
Solving
Strategy
248
1
252
2
3
253
255
Extension
256
1
260
2
261
3
263
Math
Connection
264
3
4
5
6
Look at Student Activity Book page 99. Which figures
have square corners/right angles? A, C, F, H, M
True or false, a quadrilateral is a closed figure. True
Name as many quadrilaterals as you can. Possible
quadrilaterals: square, rectangle, rhombus, kite,
diamond, square, parallelogram, trapezoid, isosceles
trapezoid
What type of a diagram can you use to sort
quadrilaterals? A Venn diagram
What are you measuring when you measure the
perimeter? You are measuring the distance/length
around a shape.
How can you find the area of a rectangle? Multiply one
side by the other.
What are the area and perimeter formulas for a square?
A= s x s; P = 4 x s
What are some different rectangles that have an area of
24 centimeters? What is the perimeter of each?
1 x 24 or 24 x 1 rectangle (P =50 centimeters); 2 x 12
or 12 x 2 rectangle (P =28 centimeters); 3 x 8 or 8 x 3
rectangle (P =22 centimeters); 4 x 6 or 6 x 4 rectangle
(P = 20 centimeters);
When using the Guess and Check Strategy, if your first
number you used gave an answer that was too high,
what do you know you have to do to your number? You
need to pick a smaller number.
How do you find the perimeter of a parallelogram?
Possible method: Add the length of the base (b) and the
length of the slant height (s). Multiply the total by 2.
(b + s) Ÿ 2 = P
How do you find the area of a parallelogram? A= b × h
True or false, the height of a parallelogram is parallel to
its base. False, the height is perpendicular to the base.
What do you need to do to the sides of a rectangle to
triple it’s perimeter? Triple both sides
Look at the new pool on Student Activity Book page
113. What shapes make up the new, complex figure? 2
rectangles or a rectangle and a square.
Have students show the different ways you can
decompose figures 10 and 11 on Student Activity Book
page 114. Check student’s decompositions.
What does the word dimension mean? Dimension
means measurement.
Have student pairs explain to the class how they
calculated the estimates of their feet outlines. Answers
will vary.
Grade 4 Math Expressions Check Your Understanding Questions 9 Check Your Understanding Questions
Unit 3- Place Value Multi-Digit Addition and Subtraction
Grade 4
Unit
3
Lesson
Activity
1
Page Number
272
2
273
3
274
Check Your Understanding
Write 4 + 2 on the left side of the board and 3 + 4 on
the right side. Ask, “Are these equal or not equal?”
Not equal. 6 ≠ 7 so 4 +2 ≠ 3 +4.
Which property of addition states that addition can be
done in any order, for example a + b = b + a.
Commutative Property of Addition
Write 8 related addition and subtraction equations for
this break-apart drawing.
1
46
3
3
2
Extension
276
1
280
2
284
1
288
2
289
3
289
1
294
3
46 = 25 + 21
46 = 21 + 25
21 = 46 – 25
25 = 46 – 21
25 + 21 = 46
21 + 25 = 46
46 – 21 = 25
46 – 25 = 21
25
21
How do you show greater than and less than in an
inequality? Greater than (>); less than (<)
What two types of change situations can you have?
Change plus and change minus
Have students share their change plus and change
minus problems on Student Activity Book page 126 and
have the class try and solve them. Problems and
answers will vary.
What are the three kinds of collection situations? No
action, Put Together, and Take Apart.
Write these two words on the board and ask students to
write an appropriate label for the two words. flowers
Rose daisy
Have students share their collection problems from
number 15 on Student Activity Book page 129 and have
the class try and solve them. Problems and answers will
vary.
Draw these comparison bars on the board and have
students state two comparison statements. Statements
will vary. Sample statements:
Devi has 8 more badges than Ali.
Ali has 8 fewer badges than Devi.
3
Devi
4
Ali
2
298
8
Have students share their comparison problems from
number 10 on Student Activity Book page 133 and have
the class try and solve them. Problems and answers will
vary.
Grade 4 Math Expressions Check Your Understanding Questions 10 3
1
302
2
304
5
Zoe is a pet sitter. On Tuesday she had 2 dogs,
3 cats, and 2 birds. On Wednesday she watched 3
dogs, 2 cats, 2 fish, and 3 birds. How many more
animals did Zoe watch on Wednesday?
1
3
3
3
3
308
Have students fill in the blanks to make this statement
complete. Addends; total; groups; size
Addition and subtraction problems involve two
_______ and a __________. Multiplication and
division situations involve repeated __________ of the
same ____________.
6
7
True or False, You can combine two steps of a problem
in 1 equation. True
Have students solve this two-step problem. 3 animals
2
312
Have students use the inverse operations of each
problem on Student Activity Book page 138 to check
their results. Check students’ work. Students should use
subtraction to check addition and vice a versa and
multiplication for division and vice a versa.
1
317
Have students show the number 143 on their dot array.
2
3
318
320
How many hundreds are in 1, 000? 10
Have students show the number 1, 228.
Math
Connection
322
How many hundreds, tens and ones are in $578? 5
hundreds, 7 tens, 8 ones
1
327
2
330
3
332
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.
Round the following numbers to the nearest ten: 40,
430, 880, 80
35 425 878 78
Round the following numbers to the nearest hundred:
400, 500, 800, 1, 000
350 470 820 950
1
336
2
337
8
9
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.
4, 286
> 4, 238
Write the greatest and least four-digit number possible.
Grade 4 Math Expressions Check Your Understanding Questions 11 3
339
Math
Connection
340
Use each of the 4 digits in the group exactly once.
7, 643; 3, 467
7346
Write each group of numbers in order from least to
greatest. Tell whether the first or last number is closer
to the middle number. 36, 63, 78; last number is closer
to the middle.
36, 78, 63
Have students fill in the blanks to make the statement
true. equal
An equality is an equation that indicates two amounts
are ___________, and includes an equals (=) sign.
3
3
3
3
1
344
2
348
1
352
2
354
3
356
Math
Connection
358
1
2
362
364
Add 67, 897, 654 + 4, 567, 238. 72, 464, 802
When adding numbers, what must you align? The place
value places
1
368
2
370
Estimate the total for this equation 628 + 367 = [ ].
600 + 400 is 1, 000.
Add the following numbers. Hint: look for “easy”
combinations. 25; some combinations may be 8 and 2, 7
and 3, 2 and 3, etc.
3
372
8+2+7+3+5
Solve this addition problem and then use estimation to
check your answer. 7, 463; 5, 000 + 3, 000 = 8, 000
10
11
12
Write this number using words. Thirty-seven thousand,
eight hundred ninety-five
37, 895
How many thousands make 1 million? 1, 000 thousands
Use any method to add 365 and 678. 1, 043; Methods
will vary.
Use the New Groups Above, New Groups Below or the
Show Subtotals Methods to add 447 + 862. 1, 309;
Check students’ methods.
Write this equation on the board and have students
solve and explain if they need to make new groups?
156 + 77= [ ] 233; Students need to group ones into a
new ten, and group tens into a new hundred.
Add $53 and $27. $80
13
4, 568 + 2, 895
3
3
1
376
2
378
1
2
382
386
14
15
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.
Estimate the total for this equation 628 – 367 = [ ].
600 – 400 is 200.
What is the inverse operation of addition? subtraction
Use addition to check this subtraction problem.
Grade 4 Math Expressions Check Your Understanding Questions 12 128 + 72 = 200
9
1 10 10
200
– 72
128
3
16
1
390
2
393
Math
Connection
394
In which direction can you ungroup in a subtraction
problem? You can either ungroup left to right or right
to left.
Decide if you need to ungroup in this subtraction
exercise. 367 – 158. 209; You need to ungroup 1 ten to
get 10 more ones.
Have students use a proof drawing to solve this word
problem. $29.41; Check students’ proof drawing.
Sandy’s neighbour gave her $50.00 for shovelling her
driveway all winter. She spent $20.59 on a comic book
collection. How much money does she have left?
3
3
3
17
18
1
398
2
401
3
402
1
406
2
407
Math
Connection
410
1
414
2
415
3
416
19
When making a Proof Drawing to check your
subtraction, do you draw both numbers with boxes,
tens, and ones and then subtract? No, you only draw the
large number and you take away the smaller number
from that drawing.
Decide if you need to ungroup in this subtraction
exercise. 3,670 – 1,580. 2,090; You need to ungroup a
hundred to get 10 tens.
Decide if you need to ungroup in this subtraction
exercise. 4,660 – 2,340. 232; You don’t need to
ungroup at all.
Subtract these large numbers. 1, 346, 297; Check
students’ ungroupings.
5, 789, 675 – 3, 567, 986
How can you check your subtraction work? Use
addition or “adding it up.”
Estimate the difference for this equation 6, 428 – 4, 867
= [ ]. 6, 000 – 5, 000 is 1, 000.
Have students share their price lists and word problems
from problem 5 on Student Activity Book page 171 and
have the class solve the problems. Price lists and
problems will vary.
Look at the total acre column on Student Activity Book
page 172 and choose the best rounding unit for each
measurement (the nearest ten thousand, the nearest,
hundred thousand, or the nearest million). Possible
rounded acreages listed from top to bottom: 800,000;
300,000; 50,000; 250,000; 1,500,000; 8,500,000;
1,000,000; 1,000,000; 500,000; 600,000; 50,000;
900,000; 200,000; Discuss different rounding units.
Have students share their real-world data and word
problems from problem 11 on Student Activity Book
page 173 and have the class solve the problems. Data
and problems will vary.
Grade 4 Math Expressions Check Your Understanding Questions 13 3
3
20
4
417
Problem
Solving
Strategy
418
1
422
2
424
1
428
2
429
3
430
4
430
5
430
21
When you use a calculator to check results, the
calculator does not always show commas. How do you
know where to insert the commas? The commas are
placed between the hundreds and thousands places, the
hundred thousands and millions places, etc.
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 (i.e. time, money,
distances, etc.) while others need to be exact.
What are the three types of problems that involve
addition and subtraction? Change plus/minus;
collection; comparison
List as many ways you can check you work/
computation on Student Activity Book page 176.
Possible methods: estimation, calculator, inverse
operations, proof drawing, etc.
Have students share their question from problem 3 on
Student Activity Book page 177 and have the class
answer it using the data table. Questions and answers
will vary.
Have students show their tally charts and bar graphs
from their surveys. Have the class make as many
statements that compare data in as many ways they can.
Statements and comparisons will vary.
Have students use the same equation but use the
numbers, 5, 10, and 3. (5 + 10)/5 = 3
Would changing the scale to a 2-interval scale work
better for the 15, 5, and 20 bars? No, it would not be
better 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.
Bring in a grocery store or department store circular
advertisement and have students find as many different
ways to spend $9.00. Combinations will vary depending
on the advertisement.
Grade 4 Math Expressions Check Your Understanding Questions 14 Check Your Understanding Questions
Unit 4- Angles and Polygons
Grade 4
Unit
Lesson
4
1
4
4
4
Activity
1
Page Number
439
2
440
3
4
442
444
1
448
2
450
1
456
2
458
3
459
Can you draw an obtuse isosceles triangle? Sample
obtuse isosceles triangle:
Math
Connection
460
What is it called when you arrange, group, or sort
objects by a set of characteristics? classify
1
464
2
466
When you build a parallelogram from triangles, do you
have to use two congruent triangles (for example, 2
obtuse triangles) or can you use 2 non-congruent
triangles (for example an obtuse triangle and a right
triangle)? You have to use 2 congruent triangles
because the triangle edges have to meet up to form the
edges of a parallelogram.
When you divide a parallelogram on it’s diagonal, what
2
3
4
Check Your Understanding
What is the name of an angle that is smaller than a right
angle? Acute angle
What measurement tool is used to measure angles?
protractor
What is a 180° angle called? a straight angle
What kinds of angles do the lines of the compass on
Student Activity Book page 185 form? right angles
When you rotate a half turn clockwise or counter
clockwise around a clock, what kind of an angle do you
make? Straight angle or 180° angle
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°
True or false? A right triangle has 3 right angles? False,
only one angle in a right triangle can be a right angle.
Draw this triangle and ask students what the little marks
mean. The little marks on the sides of the triangle tell
you that the sides are congruent.
Grade 4 Math Expressions Check Your Understanding Questions 15 4
4
5
figures are formed? 2 triangles
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.
Extension
468
1
472
2
473
3
475
1
2
480
482
True or false, a polygon is a closed figure. False
Draw this figure and ask students to describe it as
concave or convex. concave
3
483
How would you find the perimeter of an octagon?
P=8 × s
1
488
Draw a 270° clockwise rotation about Point A.
How do you find the perimeter of an equilateral, an
isosceles, and a scalene triangle? 3b = P; 2b + (c) = P;
b+c+d=P
How do you find the area of a right triangle? A= ½ ×
length × width
When measuring triangles, if the measurement is not a
whole number, what can you do? You can round the
measurement to its nearest whole unit of measure.
6
A
2
489
Have students fill in the blank to make this statement
true. slide
Another name for a translation is called a ________.
3
4
490
7
4
Extension
491
492
Have students fill in the blank to make this statement
true. reflection
A ____________ is the movement of a figure across a
line producing a mirror or congruent image of the
figure.
Have students fill in the blank to make this statement
true. congruent
For two figures to be ___________, they must
be exactly the same size and shape.
Continue this pattern and describe the rule with the
word translation, rotation, or reflection. translation
Grade 4 Math Expressions Check Your Understanding Questions 16 Check Your Understanding Questions
Unit 5- Multi-Digit Multiplication
Grade 4
Unit
Lesson
5
1
5
2
Activity
1
Page Number
502
2
503
1
508
2
510
1
514
Check Your Understanding
Write out the steps for finding 4 x 60 by factoring the
tens. 4 x 60 = (4 x 1) x (6 x 10) = (4 x 6) x (1 x 10) =
24 x 10 = 240
Write out the steps for finding 30 x 40 by factoring the
tens. 30 x 40 = (3 x 10) x (4 x 10) = (3 x 4) x (10 x 10)
= 12 x 100= 1, 200
How is 30 x 40 similar to 3 x 4? 30 x 40 is 120 and 3 x
4 is 12
How is 70 x 40 similar to 7 x 4? 70 x 40 is 280 and 7 x
4 is 28
Use the Area Model to multiply 34 x 3 on your
MathBoard. 102
30
+
4
3
5
3
2
516
4 x 3= 12
30 x 3 = 90
(in the first rectangle, there are 30 dots across by 3 dots
down; in the second rectangle there are 4 dots across
by three dots down)
Use Rectangles to multiply 4 x 56. 224
50
+
6
6 × 4 = 24
50 × 4 = 200
Math
Connection
518
Have students solve this word problem and explain the
method they used. $336; Methods will vary.
A train ticket costs $42. How much will 8 tickets cost?
5
4
1
522
2
525
Use rounding frames to estimate the product of 42 x 4.
Rounding frames: 40 x 4 = 160 and 50 x 4= 200; the
product is closer to 160.
Estimate this product and then solve to check that your
estimate is reasonable. 4 x 70 = 280; 4 x 67 = 268 so
estimate was reasonable.
4 x 67
1
530
Use the Expanded Notation Method to multiply 36 x 4.
144
36 =
30
+
6
4
5
5
4
30
36 = 30 + 6
× 4
4
4 x 30 = 120
4 x 6 = 24
144
+
6
Grade 4 Math Expressions Check Your Understanding Questions 17 5
2
532
Use the Algebraic Notation Method to multiply 36 x 4.
4 Ÿ 36 = 4 Ÿ (30 + 6)
= 120 + 24
= 144
1
536
Use the Shortcut Method to multiply 36 x 4.
Step 1
Step 2
2
2
36
36
×
4
×
4
4
144
2
538
Have students use any method they choose to multiply
78 x 6. 468; Check students’ methods.
1
542
Draw an area model to multiply 5 x 300. 1, 500
6
300 =
5
2
543
200
+
5 x 200 =
1, 000
100
5 x 100=
500
5
Use the Rectangle Sections Method to multiply 4 x 568.
2, 272
5
500
7
4
3
545
Math
Connection
546
+
60
+
60 × 4 =
240
500 × 4 =
2,000
8
8×4=
32
Have students use any method they choose to multiply
587 x 3. 1, 761; Check students’ methods.
Have students solve this problem. $35.96
Each small pizza costs $8.99. How much would it cost
for a family to buy 4 pizzas?
1
551
Use the Expanded Notation Method to multiply 568 x
4. 2,272
568 = 500
+
60
+ 8
4
4
500
5
+
60
+
8
568 = 500 + 60 + 8
× 4
4
4 x 500 = 2, 000
4 x 60 = 240
4x 8=
32
2, 272
8
2
552
3
555
Extension
558
Use the Shortcut Method to multiply 364 x 5. 1, 820
Step 1
Step 2
Step 3
3 2
3 2
3264
3 64
3 64
× 5
×
5
×
5
0
20
1, 820
Use rounding frames to estimate the product of 846 x 3.
Rounding frames: 800 x 3 = 2,400 and
900 x 3 = 2,700; the product is closer to 2,400.
Have students use any method they choose to multiply
Grade 4 Math Expressions Check Your Understanding Questions 18 6, 876 x 4. 27, 504; Check students’ methods.
1
562
Read aloud this story problem and have students
identify the extra information and solve the problem.
The extra information is about his 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?
5
9
2
564
Read aloud this story problem and have students
identify the missing information. The missing
information is how much money she earned the rest of
the month to see if she has $19.99 saved up.
Melinda has saved $6.50 already. She saved
some more during the month. Does she have
enough to buy the doll for $19.99?
1
5
5
568
10
Identify the hidden information and solve this problem.
the hidden information is the number of days in a week
(7); 21 days
Tamara was away for a week. Kyle was away for two
weeks. How many days were both kids away for?
Usually, what are the two things you must place in your
answer when solving a word problem? The numerical
answer and the correct label.
2
570
1
574
Use the Rectangle Model to multiply 34 x 56. 1,500 +
180 + 200 + 24 = 1, 904
56 =
50
+
6
34
30 × 6 =
30 × 50 =
=
180
1,500
30
+
4
50 × 4 = 200
6 × 4 = 24
2
576
Have students use an area drawing to multiply 58 x 37.
2, 146; check students’ models.
1
582
2
585
When drawing your rectangles in a two-digit by twodigit multiplication model, what is different compared
to a one-digit by one-digit multiplication rectangle
model? You have 4 rectangles instead of 2 because you
have to break both numbers up into tens and ones.
Use the Shortcut Method to multiply 36 x 52. 1, 872
Step 1
11
1
5
12
36
×5 2
2
Step 2
1
36
×5 2
72
Grade 4 Math Expressions Check Your Understanding Questions 19 Step 3
3
1
36
×5 2
72
0
Step 4
3
1
36
× 52
72
180
Step 5
3
1
36
× 52
72
+180
1, 8 7 2
5
1
590
2
591
3
593
Problem
Solving
Strategy
594
13
Have students solve 67 x 45 using any of the 4 methods
(Rectangle Sections, Expanded Notation, Algebraic,
and Shortcut) and explain their thinking. 3, 015; Check
students’ methods and explanations.
Use rounding to estimate the product of 34 x 56. 30 x
60 = 1, 800
Use rounding to estimate the product of 65 x 27 and
then solve. Write whether your estimate was an
overestimate or an underestimate. 70 x 30 = 2, 100;
1,755; overestimate
Have students solve this word problem. Estimate the
amount needed and then find the exact cost. $15 x 30 =
$450; $389.74
The movie tickets cost $14.99 each. How much would it
cost for 26 fourth graders to attend the movie?
5
14
1
598
2
600
Math
Connection
602
Have students solve 76 x 23 using the shortened
Expanded Notation or Shortcut method. 1,748; Check
students’ methods and make sure they have reduced
and dropped some of the written steps.
Use rounding to estimate the product of 45 x 88. 50 x
90 = 4, 500
Use Lattice Multiplication to multiply 36 x 47. 1, 692
3
1
6
1
2
2
2
4
4
2
7
4
1
6
9
2
Grade 4 Math Expressions Check Your Understanding Questions 20 5
5
15
16
1
606
2
608
1
613
2
614
1
618
Have students use any method to solve 23 x 400. 9,
200; Check students’ methods.
Why do problems that include an even number times 5
appear to have an extra 0? The even 5s products end
with a 0 already.
Have students use rectangles to multiply 3 x 4, 000.
12, 000; Check students’ models.
Have students use any method to solve 33 x 7, 000.
231, 000; Check students’ methods.
Have students place the following years on the timeline
on Student Activity Book page 257. Check students’
timelines for correct placement.
1908
5
2
619
3
620
1915
1939
1955
1962
Why do you need a key on a double bar graph? The key
tells you what the colored bars stand for.
Have students solve this problem. 22 pencils
A pencil box contains 36 pencils. Some of the
pencils have an eraser. The box contains 8
more pencils with erasers than without erasers.
How many pencils have erasers?
17
4
620
5
620
What does congruent mean? Congruent means having
the same size and shape.
Use the rectangle method to find the product of 46 x 39.
1, 200 + 180 + 360 + 54 = 1,794
46 =
40
+
6
39
40 × 30 =
30 × 6 =
=
1,200
180
30
+
9
6 × 9 = 54
40 × 9 = 360
Grade 4 Math Expressions Check Your Understanding Questions 21 Check Your Understanding Questions
Unit 6- The Metric Measurement System
Grade 4
Unit
Lesson
Activity
1
Page Number
628
6
1
2
3
630
632
1
636
2
638
3
639
Problem
Solving
Strategy
640
1
644
2
647
3
648
1
2
652
653
3
654
1
658
2
659
3
660
6
6
6
6
2
3
How many square centimeters are in 2 sq dm? 200 sq
cm
Look at Student Activity Book page 268. How can you
find the area of the parts of the school shown? You can
measure the side length of the library (w) and measure
the combined side lengths From Mrs. Lee’s room to the
end of library (l) and multiply them together.
What is the difference between measuring distance and
area? When measuring distance, you can use the base
metric unit- the meter, but when measuring area, you
can use the base metric unit- the square meter.
Look at problem 3 on Student Activity Book page 270.
If Adita used 2 yellow tiles for every 2 red tiles, how
many of each color did she use? Hint: Use a simpler
problem (draw one tile) to show this. We
know Adita used 9 (4-square designs) so
9 x 2 = 18. 18 red and 18 yellow equal
36 tiles. Sample drawing shown:
4
5
Check Your Understanding
What are the three different markings within a meter
stick? A decimeter, a centimeter, and a millimetre
How many centimeters are in 2 meters? 200 cm
Which is the best unit you would use to measure the
distance between states? Kilometer
What is the formula for finding the volume of a
centimetre cube? Volume = length × width × height
What is the basic metric unit for measuring volume?
Cubic meter
What is the basic metric unit for measuring capacity or
liquid volume? Liter
What is the basic metric unit for measuring mass? gram
What other types of graphs could have you used to
show the data on Student Activity Book page 274?
Possible graphs: vertical bar graph, circle/pie graph,
pictograph, line plot
If you were measuring mass, would you ever use the
unit pound? No, pound refers to weight, mass refers to
the metric base unit gram.
What are the two temperature measurement scales?
degrees Fahrenheit or degrees Celsius
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
(length), cup (capacity); clock (time), protractor (angle
measurement)
Grade 4 Math Expressions Check Your Understanding Questions 22 Check Your Understanding Questions
Unit 7- Multi-Digit Division
Grade 4
Unit
Lesson
Activity
1
Page Number
668
Check Your Understanding
Write this division example on the board and have
students label which numbers are the divisor, the
quotient, and the dividend. 5- divisor; 80- quotient;
400- dividend
5
7
2
674
3
675
Math
Connection
676
1
80
400
What is a remainder in a division problem? Sample
explanation: A remainder is the leftover quantity that is
not large enough to make another whole group.
True or false, a remainder can be larger than the divisor.
False, a remainder must be smaller than the divisor
because if it was the same as or larger than the divisor,
another group could be made.
Have students solve this problem. $40
Talia earned $200 in 5 days. If she earned the
same amount of money each day, how much money
did she earn in one day?
Have students solve this problem using any division
method. 53 packages
7
1
680
2
682
2
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 265
vegetables. How many packages did they sell?
How can you check a division problem. Multiply the
divisor by the quotient and add the remainder. The
answer should be the dividend.
Have students use the partial quotients method to divide
678 by 7.
7
Math
Connection
686
678
630
48
42
6
90
6
96
96 R6
1
7
690
Have students solve this problem using any division
method. 40 packs
A store clerk suggests selling cans of tomato sauce in
packs of 4. How many packs of 4 can be made from
162 cans of tomato sauce?
3
2
693
Math
Connection
694
Have students divide 2, 346 by 4 using any division
method. 586 R2
What is 70 ÷ 10 and 700 ÷ 10? 7 and 70
Grade 4 Math Expressions Check Your Understanding Questions 23 7
4
1
698
2
699
700
Math
Connection
7
7
1
704
2
707
Problem
Solving
Strategy
708
1
712
2
714
3
718
5
6
Why did you know that 7 was not the right number in
the Puzzled Penguin’s quotient on Student Activity
Book page 289? The difference (6) was larger than the
divisor (4) so you knew you could make another group.
What is 6, 570 ÷ 9? 730
When do you think you should choose mental math
over using a calculator 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.
Solve using any method. Then check your answer by
rounding and estimating. 1, 892 R2; Check student’s
methods; estimates: 6, 000 ÷ 3 = 2,000
5, 678 ÷ 3
Solve using any method. Then check your answer by
rounding and estimating. 765; Check student’s
methods; estimates: 4, 000 ÷ 5 = 800
3, 825 ÷ 5
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 while others need to
be exact.
There are many types of remainders. Explain these
types of remainders.
1. left-over remainder: the remainder cannot be used in
the context of the problem and is ignored.
2. another whole remainder: the remainder causes the
answer to be rounded up.
3. fractional part remainder: 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. a decimal remainder: 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 questions (i.e. the extra person
who cannot participate).
Divide and write the remainder as a fraction. 4 2/4 or 4
1/2
18 ÷ 4
Have students solve this problem. 8 R3, so 9 boxes.
The remainder makes it necessary to buy 9 boxes
instead of 8.
Davio wants to buy some new baseball card boxes. He
has 67 cards. Each box holds 8 cards. How many
baseball card boxes does Davio need to buy?
1
7
722
7
2
724
Have students write solution and situation equations for
this problem. Solution: b = 3 + 2; situation: b – 3 = 2
Marla had some oranges. She gave 3 oranges
to her friends. Now she has 2 oranges. How
many oranges did have in the beginning?
Have students solve this problem and explain their
Grade 4 Math Expressions Check Your Understanding Questions 24 methods. 360 – 10 = 350; 350 – 3 = 347; 350 + 347 =
697; 697 balls
A team from each school had 360 foam balls
and a bucket. The Springfield team dunked
3 fewer balls than the Oak Hill team. The Oak Hill
team dunked all but 10 of their balls. How many
balls did the two teams dunk in all?
7
7
7
8
1
728
2
730
3
733
Math
Connection
734
1
739
How do you find the mean of a set of data? To find the
mean or the average, you add the values in the set of
data and divide that sum by the number of values.
What is the mode, when describing data? The mode is
the value that appears most frequently in a set of data.
How do you find the range of a set of a data? The range
is the difference between the greatest number or
maximum value and the least number or minimum value
in a set of data (greatest number/max value – least
number/min value = range).
If a number is divisible by another number, is there a
remainder? No there is no remainder.
Divide the following to see the pattern. 7, 7, 7, 7
7÷1
70 ÷ 10
700 ÷ 100
7,000 ÷ 1,000
9
Extension
740
What is 3 x 12? 36
1
744
2
745
3
746
What does a digital clock usually tell us that an analog
clock does not show? Whether the time is a.m. or p.m.
How many hours have passed from 9:30 am to 11:00
am? 1 ½ hours
Calculate this elapsed time.
10
9:50 a.m
– 8:33 a.m.
Math
Connection
748
1
752
1 h and 17 min
How many years is a century? 100 years
Use the Identity Property to simplify this expression.
15f
13f + f + f = ______
7
7
11
12
2
755
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
760
Have students identify which one of these examples is
NOT an expression. a + 3 = 6
16
b
a+3=6
6c
f÷5
6–c+b
Grade 4 Math Expressions Check Your Understanding Questions 25 7
13
2
762
True or false, an inequality is a statement that two
expressions are equal. False, an inequality shows that
two expressions are not equal.
1
766
Solve this single step equation. y = 4
2
768
4y = 16
Solve this two-step equation. y = 4
4y + 3 = 19
7
25
1
774
Have students draw a triangle with a line of symmetry
on their MathBoard. Sample drawing:
2
3
775
776
4
776
5
776
Which would you prefer? 3 x $1 or $1, 000 x 0? 3 x $1
If you support an argument, what does that mean? It
means you agree with an argument and you use
evidence to back up your argument.
What are some different rectangles (with whole number
sides) that have an area of 24 square centimeters? What
is the perimeter of each?
1 x 24 or 24 x 1 rectangle (P =50 centimeters); 2 x 12
or 12 x 2 rectangle (P =28 centimeters); 3 x 8 or 8 x 3
rectangle (P =22 centimeters); 4 x 6 or 6 x 4 rectangle
(P = 20 centimeters)
Using your estimate from the 200th person in line, how
long can you assume that the 400th person in line must
wait? 3 hours and 20 min
Grade 4 Math Expressions Check Your Understanding Questions 26 Check Your Understanding Questions
Unit 8- Patterns, Functions, and Graphs
Grade 4
Unit
8
8
Lesson
Activity
1
Page Number
785
Check Your Understanding
Draw the next figure in the pattern.
2
786
Draw this growing pattern on the board and ask
students to decide what comes next.
Extension
788
What shapes are formed by cutting this figure into
parts? Sample shapes:
1
792
Describe the pattern and identify the next term in it.
Subtract 4; 72
2
793
1
2
96, 92, 88, 84, 80, 76, …
Have students fill in the blanks to make the statement
true. Addition; multiplication; subtraction; division
If the terms in a pattern are becoming larger, the
pattern is likely to involve _________ and _________.
If the terms in a pattern are becoming smaller, the
pattern is likely to involve _______ and _________.
8
8
1
798
2
799
3
801
1
807
3
What does inverse operations mean? The opposite
operation
What describes the mathematical relationship shared by
two sets of numbers? A rule
When you are trying to find the rule of 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 numbers.
Have students fill in the blanks to make the statement
true. x; y
The first coordinate represents distance along the
_______ axis. The second coordinate represents
distance along the _______ axis.
4
2
808
3
810
Name two points on Student Activity Book page 332
that form a straight angle. Sample angle: <CW
Have students draw another square or rectangle on the
coordinate plane on Student Activity Book page 333.
Then have pairs find the length of line segments.
Grade 4 Math Expressions Check Your Understanding Questions 27 8
8
5
Extension
812
1
816
2
818
3
820
Extension
822
1
826
2
830
Answers will vary.
Look at problem 1 on Student Activity Book page 334.
Translate the top square 2 units to the right and write
the vertices of the translated square. (4, 7), (7, 7),
(4, 10), (7, 10)
What type of function is shown on Student Activity
Book page 335? Linear function
Sometimes the letters in a function table may not be x
and y. In this example, the variables c and p stand for
which axes? C is the x-axis and p is the y-axis.
How can you predict other points on a linear graph?
Use the pattern they see in the other ordered pairs.
Have students draw two other points (C and D) on the
grid on Student Activity Book page 338. Then have
them choose and describe a path between both points.
Paths will vary. Check students’ descriptions.
What types of data does a line graph show? Change
over time data
Have students fill in the blanks to make the statement
true. scale
6
Since it’s difficult to graph points that are between
grid lines, it’s best if all or most data points fit
exactly on the ______________.
Grade 4 Math Expressions Check Your Understanding Questions 28 Check Your Understanding Questions
Unit 9- Fractions
Grade 4
Unit
Lesson
9
1
9
2
Activity
1
2
Page Number
838
840
Check Your Understanding
What does the term fraction mean? Part of a whole
Write ¾ on the board and have students write the word
name for the fraction. Then have them sketch a
representation of the fraction. Three fourths; sample
drawing:
3
842
Have students give an example of unit fractions.
Possible unit fractions: ½, 1/3, ¼, 1/5, 1/6, (any
fraction with a 1 as the numerator), etc.
1
2
848
850
What does 5/5 equal? 1
Find the unknown partner in this equation.4/6
2/6 + d = 6/6
9
1
854
2
856
3
858
3
Have students complete this fraction-partner equation.
4 sevenths; 4/7; 7 sevenths equals 3 sevenths plus 4
sevenths.
3/7 + [ ] = 7/7
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 compare them with the greater than, less than,
or equal to symbols.
4/5
1
864
>
3/10
Draw this on the board and ask students to decide if the
statement is true or false. False, since the whole pies
are different sizes, the three pieces in each pie are not
equal in size.
Hettie says that ¾ of pie A is the same as ¾ of pie B.
9
9
4
5
2
865
1
870
A
B
Have students share their word problems they wrote
and have the class solve them and explain their
thinking. Problems and answers will vary.
What is the diameter of the circle? The length of a line
Grade 4 Math Expressions Check Your Understanding Questions 29 9
9
segment that goes from one side of the circle to the
other and passes through the center.
What is the radius of the circle? A line segment that
connects the center of a circle to any point on that
circle. Also the length of that line segment.
What is the circumference of the circle? The distance
around the outside of a circle.
2
872
Extension
874
1
878
Have students divide a circle into 6 equal pieces.
Sample circle:
2
879
Extension
882
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.
What percentage do all the pieces of a circle graph add
up to? 100%
1
886
2
888
1
892
6
7
Use fraction bars to add 3/10 and 4/10. 3/10 + 4/10 =
7/10
Use fraction strips to subtract 1/5 from 4/5. 4/5 – 1/5 =
3/5
Add 4/6 and 2/6 with Class Fraction Cards. 6/6
1/6
9
8
2
893
3
896
1/6
1/6
1/6
9
+
1
903
Add these improper fractions. 12/6
2
905
8/6 + 4/6
Subtract these mixed numbers. 1 1/5
3
906
2 4/5 – 1 3/5
Write these mixed numbers on the board and have
students use a greater than, less than, or an equal to
symbol to compare the mixed numbers.
2 1/2
9
9
10
1
910
915
2
918
11
> 2 1/4
Have students identify the greater fraction. ¾
¾
1
1/6
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
+
9
1/6
+
4/8
Use division to find an equivalent fraction for 4/6.
Sample equivalent fraction: 2/3; 4/6 = 4 ÷ 2/ 6 ÷ 2 =
2/3
Complete this fraction equation.
Grade 4 Math Expressions Check Your Understanding Questions 30 9
9
3
920
1
925
2
929
3
930
1
934
2
935
3
936
12
13
1 × 6 =6
3 × 6
18
Simplify the fraction 9/12. 3/4; 9/12 = 9 ÷ 3/ 12 ÷ 3 =
¾
Use fraction bars to add ½ and 2/8. ½ = 4/8, 4/8 + 2/8
= 6/8
Use the Multiplication table to find an equivalent
fraction for 2/3. Sample equivalent fraction: 4/6; 2/3 =
2 x 2/ 3 x 2 = 4/6
Find a common denominator to add these fractions. 6/8
+ 1/8 = 7/8
3/4 + 1/8
Find equivalent fractions for 1/6 and 1/3 and then
subtract. 2/12 and 4/12; 4/12 – 2/12 = 2/12
Write these fractions on the board and have students use
a greater than, less than, or an equal to symbol to
compare the fractions. Hint: find equivalent fractions
before you compare.
1/5 < 1/3
Order the fractions from least to greatest. 1/8, 2/4, ¾
¾, 1/8, 2/4
9
1
940
2
941
14
Math
Connection
942
For this pair of fractions, find an equivalent fraction,
then compare the fractions, add them, and then subtract
them. 1/8 and 4/8; 1/8 < 2/4; 5/8; 3/8
1/8, 2/4
Have students solve this word problem. Sonja cannot
make this statement from picking only 5 marbles. She
can only make a prediction.
Sonja has 50 red and yellow marbles. She pulls out 5
marbles, returning each to the bag after she pulls it out.
If she pulls out 2 red marbles and 3 yellow marbles, can
she say that there are 20 red marbles and 30 yellow
marbles?
Subtract these mixed numbers. 5 6/8 – 3 4/8 = 2 2/8 or
2 ¼.
5 6/8 – 3 2/4
9
15
1
947
2
949
If you repeat the same experiment two times in a row,
will you get the exact same results? Not likely, as
probability tells us what’s expected to happen, not
exactly what will happen.
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
Suppose you take one marble from box A without
looking and one marble from box B without looking.
Grade 4 Math Expressions Check Your Understanding Questions 31 From which box are you more likely to get a white
marble?
What is the probability of choosing a black marble from
box B?
3
9
9
9
16
950
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
B
B
B
4
951
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.
Math
Connection
954
1
959
2
962
1
966
Multiply 3 x ¼ and draw a shape to show the solution.
¾
2
967
Solve 7 x 2/3 =. 14/3
1
2
972
973
Solve 1/8 x 16 =. 2
Solve 3/8 x 16 =. 6
1
978
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.
Which graph would you use to display how often things
occur? line plots
What is the mode, when describing data? The mode is
the value that appears most frequently in a set of data.
17
18
Ariel
Pasqual
9
A
19
2
979
3
980
6
6
6
6
6
Have students share their comparison bars from
problem 6 on Student Activity Book page 398. Then
have the class state each comparison both ways.
Comparisons will vary depending on the two rides
being compared.
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?
Grade 4 Math Expressions Check Your Understanding Questions 32 9
9
20
1
986
2
987
1
992
2
994
21
3
994
1
998
2
999
3
1000
Label a new point (I at 1 3/8 or 11/8) on a number line
on Student Activity Book page 401. Point I should be
located on the 4th number line down on the tick mark
right before 1 4/8.
Label a new point (I at 9/10) on number line 10 on
Student Activity Book page 402. Point I should be
located on the number line on the tick mark right before
1.
Write these fractions on the board and have students use
a greater than, less than, or an equal to symbol to
compare the fractions.
2/8 < 3/6
Have students solve this word problem. 24 books
Dahlia has 36 books. She’s read 2/6 of them already.
How many books hasn’t she read?
Label a new point (K at 5 1/8) on number line 37 on
Student Activity Book page 404. Point K should be
located on the number line on the tick mark right after
the 5.
Use a hexagon pattern block to make a tessellation
pattern. Check student’s tessellations.
What are the two types of data students can collect?
numerical or categorical data
Can you make a generalization from your doubling
proof, that tripling the data would yield the same results
to the mode and the range? Give an example to back up
your generalization. Generalization: If the values in a
group of data are tripled, then the mode and the
numbers that show the range are also tripled.
Original data {2, 5, 5, 7, 8} Mode: 5; Range: 6
4
9
1000
22
5
1000
Tripled data {6, 15, 15, 21, 24} Mode: 15; Range: 18
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
Line plot: number of siblings
Circle graph: types of birds
Use the whole numbers and fractions you have already
written on the board and have students use these clues
to find out which fraction you are describing now. 4/7
2/5 1/8 4/7 7/10 5 ¾
The numerator is an even number and the denominator
is an odd number.
The sum of the denominator and the numerator is 11.
Which could be Sam’s number?
Grade 4 Math Expressions Check Your Understanding Questions 33 Check Your Understanding Questions
Unit 10- Three-Dimensional Figures
Grade 4
Unit
Lesson
10
1
10
10
2
Activity
1
Page Number
1008
2
3
1010
1012
1
1016
2
1018
3
1019
Math
Connection
1020
1
1024
2
1025
3
1026
3
Check Your Understanding
How is a sphere different from a circle? A sphere is 3-D
and a circle is 2-D.
How many squares make up a cube net? 6 squares
How do you know there are hidden cubes even if you
can’t see them? The hidden cubes are holding up the
cubes that you can see.
Why do you think all your prism nets are made from a
different amount of separate rectangles? Depending on
what type of prism you are folding determines the
number of rectangular faces you have. For example, a
pentagonal prism has 5 rectangular faces plus the two
pentagon faces.
How are a cylinder and a cone alike and different? Both
figures have circular bases, but a cone has only one
base and a point on top.
How do you find the surface area of a solid figure? It’s
the total area of all of its faces.
What is a net? A 2-D pattern that can be folded into a
3-D figure.
What is a face, an edge, and a vertex? Face: a plane
(flat figure); edge: side of a face; vertex: a corner
where edges meet.
True or false, a pyramid has a pair of congruent bases.
False
Using the pattern on Student Activity Book page 418,
find the number of sides on base, number of faces,
number of edges, and number of vertices on an
octagonal prism. 8, 10, 24, 16
Grade 4 Math Expressions Check Your Understanding Questions 34 Check Your Understanding Questions
Unit 11- Decimal Numbers
Grade 4
Unit
Lesson
11
1
11
2
11
3
Activity
1
Page Number
1036
2
1044
1
1054
Write this number in decimal form. 0.22
22 hundredths
1
1064
Write the word name of the number. Six tenths
0.6
1
11
Check Your Understanding
What unit fraction can you write to represent how many
dimes are in a dollar? 10/100 or 1/10
Write a fraction and a decimal to represent 80 cents out
of a dollar. 80/100 or 8/10; 0.80 or 0.8
1068
4
2
1074
Have students fill in the blanks to make the statements
true. multiply; divide
As you move to the left of the place value chart
(towards the tens and hundreds), each place gets
bigger 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.
Write the equivalent number of hundredths and
thousandths. 0.70; 0.700
0.7
11
5
1
1082
2
1084
Where can a zero be inserted in a decimal number
without changing the value? Zeros can be inserted to
the right of the number without changing the value.
Write these decimals on the board and have students
use greater than and less than symbols to compare the
decimals.
0.45 < 0.54
11
11
1
1088
2
1090
1
1094
2
1098
6
7
Draw a square at 0.67 on problem 5’s number line on
Student Activity Book page 439. Then round this
hundredth to the nearest tenth. Check children’s square
location; 0.7
What is $3.50 rounded to the nearest dollar? $4.00
Continue to call out more whole numbers and have
students plot and label the numbers at those positions.
Numbers and positions will vary.
Draw a 0 – 3 number line on the board and have
students plot 1.5 and 2 ¾ on that number line. Check
number lines. Relative locations of points shown:
0
11
8
1
1102
1
1.5
2
2¾ 3
Have students solve this problem. $0.63
Dario has 2 quarters, a dime and 3 pennies. What
Grade 4 Math Expressions Check Your Understanding Questions 35 decimal part of a dollar does he have?
1
1106
Display a 10 x 10 grid on the overhead and represent
this addition. Then solve. 0.5 + 0.3 = 0.8
0.5 + 0.3
11
9
2
1108
Solve this problem.
1110
3.157
.67
3.827
Align decimal numbers to add. $35.78 + 25¢
+
3
+
1
1114
35.78
.25
$ 36.03
Display a 10 x 10 grid on the overhead and represent
this subtraction. Then solve. 0.5 – 0.3 = 0.2
0.5 – 0.3
11
10
2
1116
3
1118
Find the difference between these numbers. 0.46
0.76 and 0.3
Have students solve this problem. $2.66
Mrs. Grande has earned $2.34 so far. How much
more money will she need to earn to have $5.00?
11
1
1123
2
1125
Math
Connection
1126
11
Write the amount for 3 quarters, 1 dollar, and 5 nickels.
$2.00
Have the students solve this problem by writing the
names and numbers of coins and bills you could use to
make change. Coins for change may vary; 2 quarters, 1
dime, 4 pennies
The cost of an item is 36¢. You give the clerk a dollar.
Write the next term in the sequence. 51.4
52.4, 52.2, 52.0, 51.8, 51.6 _________
Grade 4 Math Expressions Check Your Understanding Questions 36 11
1
1130
2
1132
Math
Connection
1134
12
Estimate the answer by rounding each number to the
nearest tenth. 0.8 + 0.4 = 1.2
0.76 + 0.35
Select a rounding unit that allows you to estimate the
answer mentally. Write your rounded problem and
your estimated answer. 0.8 + 0.3 = 1.1
0.765 + 0.25
Estimate the answer by rounding these metric
measurements to the nearest tenth. 6.5 + 2.3 = 8.8
6.45 grams + 2.345 grams
11
13
1
1139
Math
Connection
1140
Order these decimals from greatest to smallest. 15.6,
12.2, 4.5, 0.675
12.2
15.6
0.675 4.5
Multiply.
×
11
11
14
1
1144
2
1148
1
1152
2
1153
3
1154
4
1154
$ 3.15
6
$ 18.90
Is 2/5 closer to 0, ½, or 1? 2/5 is closer to ½ as 2/4 is
equal to ¼ and 2/5 is very close to 2.4.
Use the table on Student Activity Book page 460 to
estimate these measurements. 1 5/8 + 3/4 = 1 ½ + 1 =
2 ½ cups.
wheat flour + white flower
Have students show their final building design from
Student Activity Book page 461 and have the class
describe the building including the names of the
geometric solids used. Buildings and descriptions vary.
Color this drawing so that the colors of sections that are
next to each other are not the same color. How many
colors did you use? 3, sample color pattern shown:
15
5
1154
Write 7 + 4 < 6 + ______ on the board. Have students
use reasoning and the process of elimination to decide
which number (3, 4, 5, 7) makes the statement true. 7
Use logical reasoning and the clues to find the heights
of these dogs. Then make a bar graph to graph your
height data. Darien: 45 in.; Clara: 15 in.; Toby: 20 in.;
Brenda: 30 in.; Check bar graphs.
Darien’s height is 3 times the height of Clara.
Clara’s height is 5 inches shorter than Toby.
Toby’s height is 20 inches.
Brenda’s height is 2 /3 the height of Darien.
Do 0.05 and 0.5 have the same value? No, 0.05 is 5
hundredths and 0.5 is 5 tenths.
Grade 4 Math Expressions Check Your Understanding Questions 37 Check Your Understanding Questions
Unit 12- The U.S. Customary System
Grade 4
Unit
12
12
Lesson
Activity
1
Page Number
1162
2
3
1164
1165
Problem
Solving
Strategy
1166
1
2
1170
1171
3
1172
1
2
Check Your Understanding
Which is the best unit you would use to measure the
distance between states? mile
How many inches are in a foot? 12 inches
People used to say an inch was the size of a man’s
thumb. How could knowing this help you with
estimation? You could use your thumb to estimate
length if you did not have a ruler.
Have student volunteers explain how they used the
Word Backward strategy to solve problems 2-4.
Observe student’s methods.
What is the area formula for a rectangle? A = b x h
What is the formula for finding the volume of a
rectangular prism? Volume = length × width × height
Have students complete the statement to make it
correct. square; cubic
The ________ unit is always included in an
area measurement. ________ units are always
included in volume measurements.
12
12
12
3
1
2
3
1176
1177
1178
Which weighs less, an ounce or a pound? An ounce
How many pounds equal a ton? 2,000 pounds
What tool can you use to measure weight? Balance
scale
1
2
3
1182
1183
1184
Which holds more, a pint or a gallon? A gallon
How many quarts are in 3 gallons? 12 quarts
Have students name as many tools as they can and
explain what those tools measure. Possible tools: scale
(weight or mass); thermometer (temperature); ruler
(length), cup (capacity); clock (time), protractor (angle
measurement)
1
2
1188
1189
3
Extension
1190
1192
What fraction of a year is three months? 3/12 or ¼
What Fahrenheit temperature does water freeze and
boil? Freeze- 32°F and Boil- 212°F
What are numbers below zero called? negative numbers
True or false, integers are only positive numbers. False,
integers are negative whole numbers too.
4
5
Grade 4 Math Expressions Check Your Understanding Questions 38 Unit
Lesson
Extension
1
Extension
Extension
2
3
Activity
1
Page Number
1200
1
1208
2
1210
1
1216
2
1219
Check Your Understanding
Write the percent for this fraction. 80%
80/100
Which word can you use to write the unit rate without
the 1? per
Change the unit rate to $5 per gallon for problem 13 on
Student Activity Book page 1211 and adjust the cost.
$5, $10, $15, $20, $25, $30, $35
When you read a ratio, when you see the colon (:) what
word do you say for the colon? to
If you added 90 to column c, what would the ratio of
customers to prizes (p) be? 90:27
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