Grade 3 Math Expressions Check Your Understanding Questions 1 Check Your Understanding Questions
Basic Facts Fluency Plan- Basic Additions and Subtractions
Grade 3
Unit
FP
Lesson
1
Activity
1
Page Number
N/A
Check Your Understanding
N/A
Check Your Understanding Questions
Unit 1- Place Value and Multi-Digit Addition and Subtraction
Grade 3
Unit
1
Lesson
Activity
1
Page Number
12
Check Your Understanding
Use a Place Value Drawing to show the number 187
using boxes, sticks, and circles.
2
13
Use a Place Value Drawing to show the number 166
using boxes, sticks, and circles.
3
14
16
How many hundreds are in 1,000? 10
Write these two numbers on the board and have
students use place value to compare them with the
greater than or less than symbols.
8, 230
>
2, 803
1
20
2
21
3
22
Build the number 465 with Demonstration Secret Code
Cards. Ask students the following questions:
What does the 4 represent? 400
What does the 6 represent? 60
What does the 5 represent? 5
Represent the number 428 with Secret Code Cards.
Check that the 400, the 20, and the 8 Secret Code Cards
are assembled correctly.
Make a money drawing for $12.28.
Extension
26
Write this number in expanded form. 76, 945
70,000 + 6,000 + 900 + 40 + 5
1
30
2
32
Represent the number 4, 283 with Secret Code Cards.
Check that the 4000, the 200, the 80, and the 3 Secret
Code Cards are assembled correctly.
Write this number in standard form. 3, 060
3 thousands + 6 tens
1
38
2
39
1
Math
Connection
1
1
1
2
3
4
Unscramble the place values and write the number. 826
6 ones + 8 hundreds + 2 tens
Have students solve this word problem. 8 pages; 45
stamps leftover
Alice had 845 stamps. She put them in a photo book
with a hundred stamps per page. How many pages
Grade 3 Math Expressions Check Your Understanding Questions 2 3
40
1
44
could she fill? How many stamps were left over?
Explain how you can add 70 + 80. 150; Methods will
vary. Sample methods: 7 tens + 8 tens. “Say 8 tens”
Then count until you have counted on 7 tens. “9 tens,
10 tens, 11 tens, 12 tens, 13 tens, 14 tens, 15 tens, or
150.”
Solve this word problem with a Proof Drawing. Check
students’ proof drawings: 584
267
317
1
1
1
5
2
46
3
48
1
52
2
53
3
54
Extension
56
1
60
6
7
Frank has a collection of 267 baseball cards
and 317 basketball cards. How many sports
cards does Frank have in all?
Use the Show All Totals Method to add 586 + 234.
586
+ 234
700
110
+ 10
820
Use any method to add 336 + 892. 1, 228; Check
students’ methods which may include New Groups
Below, New Groups Above, Show All Totals Method,
Proof Drawings, etc.
Have students solve this word problem and explain
their solution methods. 2, 345 people
There were 1, 356 people on the train yesterday. Today
the train held 989 people. How many people did the
train hold during the two days?
Have students use a piece of grid paper to add 1, 234 +
562. The separate boxes will help students line up the
places correctly.
1
2
3
4
+
5
6
2
1
7
9
6
Explain how you can subtract 150 – 60. 90; Methods
will vary. Sample methods: Think 60 + [?] = 150.
“Say 60” and then count by tens until you have reached
150. “70, 80, 90, 100, 110, 120, 130, 140, 150.” You
counted 9 tens so the answer is 90.
Have students solve this expression. 13, 534
4, 567 + 8, 967
Use the New Groups Below or the Show All Totals
Methods to add 447 + 862. 1, 309; Check students’
Grade 3 Math Expressions Check Your Understanding Questions 3 1
1
1
2
61
3
62
1
66
2
67
Problem
Solving
Strategy
68
1
72
2
73
Extension
74
1
78
2
81
8
9
10
methods.
When you add money amounts, do you add the pennies
or dimes place first? The pennies place
Have students share their word problems they wrote for
problem number 9 on Student Activity Book page 22
and have the class solve it. Check students’ work.
Write this equation on the board and have students
solve and explain where they need to group?
156 + 77= [ ] 233; Students need to group ones and
tens.
Use Student Activity Book page 23 to solve this
question. $ 4.96
Darlene bought a glass of iced tea and a chicken
sandwich. How much money did she spend?
Use Student Activity Book page 24 to solve this
problem. Sneakers and socks; shirt and socks; cap and
shirt; cap and socks
Jose has $6.00 to spend. If he only wanted to buy two
items, which two items could he buy? Use the Guess
and Check Strategy to find which items he could buy.
Write this addition exercise on the board and have
students identify the errors and then correctly solve it.
Errors include: When adding 7 and 5, they didn’t carry
over the new 10 in 12. When they added 60 and 40,
they wrote 10 as in adding 6 and 4. 1, 212
867
+ 345
11,102
Use Student Activity Book page 25 to find out how
much money a peanut butter and jelly sandwich and a
mango shake cost. $5.06
Use Student Activity Book page 26 to find out how
much money three pigs and a rabbit would cost. $ 48.06
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.
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.
Grade 3 Math Expressions Check Your Understanding Questions 4 1
88
Use the Ungroup First Method to solve this problem.
There were 200 people on the train. 72 of them got off
at the first stop. How many people are still on the
train?
9
1 10 10
1
200
– 72
128
11
2
1
1
1
1
12
91
3
93
4
94
1
98
2
101
1
106
2
110
Extension
112
1
116
2
118
1
122
2
123
13
14
Have students use a proof drawing to solve this word
problem. $2.41; Check students’ proof drawing.
Sandy’s neighbour gave her $5.00 for taking out the
garbage cans. She spent $2.59 on a comic book. How
much money does she have left?
Subtract 500 – 376. Make a Proof Drawing to check
your work. 124
Decide if you need to ungroup in this subtraction
exercise. 367 – 158. 209; You need to ungroup to get
10 ones.
In which direction can you ungroup in a subtraction
problem? You can either ungroup left to right or right
to left.
How much does a paintbrush, a roller, and a set of
stampers cost? Do you have enough money to pay for
the items if you have a $5.00 bill? $0.29 + $1.17 + $
2.89 = 4.35; yes
How can you check your subtraction work? Use
addition.
Decide if you need to ungroup in this subtraction
exercise. 466 – 234. 232; You don’t need to ungroup at
all.
When you ungroup 1 thousand, how many hundreds do
you make? 10 hundreds
Decide if you need to ungroup in this subtraction
exercise. 740 – 390. 350; You need to ungroup to get
10 tens.
Have a student share their toy store ad and have the
class select two or three items they can buy with $6.00.
Items will vary depending on toy store ad.
Have students write addition and subtraction equations
that can be based on this Math Mountain. Sample
equations: 198 + 567 = 765
765 – 567 = 198
[?]
15
198
567
How much does a basketball, a baseball, and a fire
truck cost? Do you have enough money to pay for the
Grade 3 Math Expressions Check Your Understanding Questions 5 1
Math
Connection
124
1
128
2
129
3
130
4
130
5
130
16
items if you have a $10.00 bill? $3 + $1 + $6 = $10;
yes
Add the numbers 617, 988 and 451, 246 and check your
work with a calculator. 1, 069, 234
Have students share some of their word problems from
Student Activity Book page 41 and have classmates
solve the problem. Problems and answers will vary.
What does the word “outcome” mean? Outcome means
the result of an experiment or what comes out.
Dena has 4 pennies, 3 nickels, and 4 dimes in her
pocket. Suppose she takes 2 coins out of his pocket.
What are the different amounts of money he could take
out? 2¢, 10¢, 20¢, 6¢, 11¢, 15¢
Explain that 374 and 437 do not have the same value.
Sample explanation: 374 has only 3 hundreds while 437
has 4 hundreds.
Tim only has 50¢ now. Which toys can he buy now?
The toys that cost 15¢, 20¢, and 15¢ and 20¢.
Grade 3 Math Expressions Check Your Understanding Questions 6 Check Your Understanding Questions
Unit 2- Lines, Line Segments, and Quadrilaterals
Grade 3
Unit
Lesson
Activity
1
Page Number
139
2
1
2
141
1
147
Check Your Understanding
What tool do you measure a centimeter line segment
with? a centimeter ruler
What are you measuring when you measure the
perimeter? You are measuring the distance/length
around a shape.
Draw parallel line segments and perpendicular lines.
Sample drawings:
Parallel line segments
2
148
Perpendicular lines
Draw this figure on the board and ask the following
questions:
B
2
2
A
C
D
2
2
3
4
Which sides are adjacent to each other? A and B; B and
C; C and D; D and A
Which sides are opposite each other? A and C; B and D
Draw line segments that are neither parallel or
perpendicular. Sample drawing:
3
148
1
152
Draw this figure on the board and ask this question:
Is this quadrilateral a parallelogram? No, because one
set of opposite sides are not parallel.
2
153
3
154
4
155
Math
Connection
156
What type of corners do squares and rectangles have?
Square corners
How many sides do you need to measure to find the
perimeter of a rectangle, of a square? 2; 1
Name as many quadrilaterals as you can. Possible
quadrilaterals: square, rectangle, rhombus, kite,
diamond, square, parallelogram, trapezoid
Look at the body of the cat on Student Activity Book
page 59. What shapes do you see? 2 triangles, a
quadrilateral, or a parallelogram
1
160
Have students draw as many parallelograms they can on
their MathBoard. Check students’ shapes and make
sure they are quadrilaterals with both opposite sides
parallel.
Grade 3 Math Expressions Check Your Understanding Questions 7 2
2
161
Draw a rectangle with a perimeter of 8 cm. Sample
rectangles: 1 x 3; 2 x 2, 3 x 1
1
166
Draw a rhombus that does not have square corners.
Sample drawing:
2
168
Can you draw a parallelogram with 5 sides? This is not
possible as all parallelograms have 4 sides.
5
Grade 3 Math Expressions Check Your Understanding Questions 8 Check Your Understanding Questions
Unit 3- Addition and Subtraction Word Problems
Grade 3
Unit
Lesson
Activity
1
Page Number
176
Check Your Understanding
Write 8 equations for this Math Mountain.
8=6+2
8=2+6
2=8–6
6=8–2
8
2
3
3
178
1
2
3
182
4
184
1
188
2
189
1
194
6
2
Have students use any strategy to solve this word
problem.7 diners; Check students’ methods.
The café had 6 diners at 11:00. At noon, more
customers came. Now there are 13 diners.
How many people came at noon?
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.
Have students look at problem 6 on Student Activity
Book page 68. Then have them reword the question
with other math language from the chart. Possible reworded questions: How many juice boxes are left,
remain, etc.?
How can you use subtraction to solve this addition
equation? 4 + [ ] = 12 12 – 4 = 8
How can you use subtraction to solve this addition
equation? 6 + [ ] = 14 14 – 6 = 8
Have students represent this word problem. Sample
representation:
16
7
[9]
16 – 7 = [ 9 ]
3
3
2
196
6+2=8
2+6=8
8–2=6
8–6=2
7 + [ 9 ] = 16
Lydia read 7 chapter books and some picture books.
In all, she read 16 books. How many of them
were picture books?
Have students represent this word problem with math
tools. Sample representation:
14
[ ]
14 – 8 = [ 6 ]
8
[ 6 ]+ 8 = 14
8 + [ 6 ] = 14
Adele puts some pasta on a string. Then she puts 8
Grade 3 Math Expressions Check Your Understanding Questions 9 more pieces of pasta on the string. Now there are 14
pieces of pasta on the string necklace. How many
pieces of pasta did she start with?
1
200
2
202
Have students fill in the blanks to make this statement
true. “Comparison problems are situations in which
some amount is _________ or _________ than some
other amount.” More, less
Look at problem 9 on Student Activity Book page 78.
If Ivan had 7 fewer fish than Milo, how many fish does
Ivan have? Use comparison bars to find the solution. 7
goldfish
14
Milo
3
?
Ivan
4
3
205
7
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.
Devi
8
Ali
1
210
Have students show their comparison bars they used to
help solve problem 3 on Student Activity Book page
79.
14
Bettina
3
5
8
Gina
2
212
6
Use a comparison drawing to represent this situation.
Ivan has 4 more ribbons than Dan.
Ivan’s ribbons
Dan’s ribbons
1
3
6
216
Have students solve this problem using any method
they wish. 1, 500 miles; Check students’ methods.
Darren and Olive are flying across the country. Their
first flight was 1, 200 miles. After they took their
second flight, they had travelled 2, 700 miles. How
Grade 3 Math Expressions Check Your Understanding Questions 10 many miles was their second flight?
2
3
217
219
4
220
1
224
Have students solve this problem using any method
they wish. 1, 131 boxes of cereal; Check students’
methods.
Today a shopkeeper sold 456 boxes of cereal. At the
end of the day 675 boxes of cereal were left over. How
many boxes of cereal did the shopkeeper have at the
beginning of the day?
Have students solve this problem using any method
they wish. 238 pages; Check students’ methods.
A book has 388 pages. Marla has read 150
pages of the book. How many pages must Marla
read to finish the book?
What are the three symbols that show inequality? >, <,
≠
Have students show comparison bars they would use to
compare this situation.
Dario has $350 in his savings account and
Vanessa has $200 in her savings account. How much
less does Vanessa have than Dario?
$350
Dario
Vanessa
2
3
227
$200
?
Have students show comparison bars they would use to
compare this situation.
The football team gave 156 footballs to fans. 898 fans
came to the game. How many fans didn’t get footballs?
7
footballs
fans
Problem
Solving
Strategy
Math
Connection
229
230
156
?
898
Have students use logical reasoning to solve the story
problem. Derek, Joy, Alison
Derek, Joy, and Alison are measuring how tall they are.
Alison is shorter than Joy. Derek is the tallest.
List the children in order from tallest to shortest.
Write an equation that can represent this problem.
7 + [ ] = 15
There are 15 boys and girls at the park. 7 of the
children are boys. How many girls are at the park?
Have students solve this problem using a situation
equation. 246 + [ ] = 350; 104 books
3
8
1
234
Belinda had 246 picture books in her collection.
Then she bought some more. Now she has 350 books.
Grade 3 Math Expressions Check Your Understanding Questions 11 3
9
Math
Connection
238
1
242
2
243
3
244
4
244
How many books did she buy?
Have students share their missing digit problems from
the back of Student Activity Book page 91 and have
other students solve them. Check students’ problems
and answers.
Now have your students find the difference between the
height of the Empire State Building (1, 250 ft) and the
height of the teacher. 1, 244 – 1, 245 ft
Look at the timeline on Student Activity Book page 94.
The students eat a snack at 10:30. Mark that on the
timeline. Check that students have marked snack time
halfway between 10 and 11:00.
Do you think all rectangles can be divided into 4
triangles? Support this with an example. Yes.
Draw a picture to solve this problem. 15 birds;
c
5
244
c
c
c
c
c
c c
There are 7 birds on the fence. 8 more birds flew to the
fence. How many birds are there in all?
Have students read this problem and decide who is
right? Milo bought 5 loaves of bread and Darien is
correct.
Milo bought 3 loaves of white bread and 2 loaves of
multigrain bread.
Darien says Milo bought 5 loaves of bread and Danikka
says Milo bought 1 loaf of bread.
Grade 3 Math Expressions Check Your Understanding Questions 12 Check Your Understanding Questions
Unit 4- Figures, Angles, and Triangles
Grade 3
Unit
4
Lesson
Activity
1
Page Number
252
2
253
3
256
Math
Connection
257
1
Extension
258
1
262
Check Your Understanding
Look at the figures on Student Activity Book page 97.
Which figures don’t have parallel and perpendicular
sides? 2, 8, 9, 10, 12
Have students draw a triangle with a line of symmetry
on their MathBoard. Sample drawing:
Have students draw two congruent triangles on their
MathBoard. Shapes will vary, but make sure the two
shapes that are drawn are the same shape and the same
size.
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 draw two similar triangles on their
MathBoard. Shapes will vary, but make sure the two
triangles that are drawn are the same shape but may
differ in size.
Draw a triangle. Name it CDE. Sample triangle.
C
4
2
D
E
2
263
Can you draw a diagonal in this trapezoid? Sample
diagonal shown.
C
D
E
4
1
268
2
269
3
273
4
274
3
F
What is the name of an angle that is smaller than a right
angle? Acute angle
True or false? A right triangle has 3 square angles?
False, only one angle in a right triangle can be a right,
square angle.
When you build quadrilaterals from triangles, do you
have to use two of the same triangles (for example, 2
obtuse triangles) or can you use 2 different triangles
(for example an obtuse triangle and a right triangle)?
You have to use 2 of the same triangles because the
triangle edges have to meet up to form the edges of a
quadrilateral.
Draw this figure and ask students to describe it as
concave or convex. concave
Grade 3 Math Expressions Check Your Understanding Questions 13 4
4
1
2
3
280
283
284
What is the measure of a right angle? 90°
What is the measure of a straight angle? 180°
What is the sum of the measures of angles in a triangle?
180°
Grade 3 Math Expressions Check Your Understanding Questions 14 Check Your Understanding Questions
Unit 5- Use Addition and Subtraction
Grade 3
Unit
Lesson
5
1
5
5
Activity
1
Page Number
294
2
296
1
301
2
302
3
303
Extension
304
1
308
2
311
1
316
2
319
2
3
Check Your Understanding
Round the following numbers to the nearest hundred:
400, 500, 800, 1, 000
350 470 820 950
Estimate the total for this equation 628 + 367 = [
600 + 400 is 1, 000.
Round the following numbers to the nearest ten: 40,
430, 880, 80
35 425 878 78
Liam has 40¢ and he wants to buy something for 160¢.
Which money amount is the most reasonable estimate
of how much more money he needs? 120¢
1200¢ 120¢
12¢ 12,000¢
Make a stack of books (between 30 – 40) and have
students estimate the quantity of books. Encourage
them to find out what 10 books look like and use that as
a benchmark to estimate the rest of the books.
Use front-end estimation to estimate the sum. 700 +
500 = 1, 200
780 + 543
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 these expressions on the board and have students
use greater than and less than symbols to compare the
expressions.
46 + 98 >
25 + 37
How many pennies, nickels, and dimes equal a quarter?
25 pennies; 5 nickels; 2 ½ dimes
How can you show the money amount $3.61?
Combinations will vary. Possible way:
$1
5
$1
$1
4
3
320
D
D
D
D
D
D
1
324
2
325
5
P
Write these two money amounts on the board and have
students compare them with a greater than or less than
symbol.
$1.68 <
5
].
$1.86
How do you make 25 cents with the fewest amount of
coins? 2 dimes and 1 nickel
Let’s pretend we are shopping for things with exact
Grade 3 Math Expressions Check Your Understanding Questions 15 change. If the customer wants to buy an apple for $1.29
and a banana for $1.35, what is the total cost the
shopkeeper finds? Then draw a possible coin
combination for the total. $2.64; Possible coin
combination:
$1
1
5
5
5
331
6
2
332
1
336
2
338
7
8
Extension
340
1
2
344
347
Math
Connection
349
Math
Connection
350
D
D
D
P
P
D
D
D
P
P
$1
The customer buys something for $3.46 and pays with a
$5.00 bill. Use Counting On to show how much change
the shopkeeper gives back. $1.54
3.47, 3.48, 3.49, 3.50 (4 pennies)
3.60, 3.70, 3.80, 3.90, 4.00 (5 dimes)
5.00 (1 Dollar)
Use Student Activity Book page 138 to act out a
shopping scene. The customer buys a loaf of bread and
a carton of milk and pays with a $5.00 bill. Find out
how much change the shopkeeper should give back to
the customer. $1.16
Round $5.76 to the nearest dime and nearest dollar.
$5.80; $6.00
Have students use estimation to see if they have enough
money to buy the items. Then have them solve the
problem and see if their estimates were accurate.
Round $2.58 to $3.00 and $1.56 to $2.00. That is $5.00
and since the actual amounts are less than the rounded
amounts, they should have enough money. $4.14 is the
actual amount.
Jarrod has $2.58 and Brett has $1.56. They want to
combine their money to buy dinner that costs $5.00. Do
they have enough money?
Use estimation to add these money amounts. $3.67,
$4.56 and $ 2.35. Possible estimation method: round to
the nearest dollar- $4.00 + $5.00 + $2.00 = $11.00
In a table, does a row go across or up and down? across
If you added data from April to the table on Student
Activity Book page 144, where would that data go? You
would place the April row between March and 3Month Total (which would change to 4-Month Total).
Look at the table in problem 2 on Student Activity
Book page 145. If the pattern continued to 9 weeks.
What would the money amount be? $180
Have students create a function table that follows the
rule: add 25. Sample function table:
Rule: Add 25
Input
15
20
25
30
Output
40
45
50
55
Grade 3 Math Expressions Check Your Understanding Questions 16 5
5
5
1
354
2
356
3
358
1
364
2
366
1
370
9
10
11
2
372
Have students give an example of a row, a column, and
a cell from the table on Student Activity Book page
147. Sample answers: row: Tuesday; column: Ferris
Wheel; cell: 671
What operation do you have to do to fill in the empty
“Loaves left” cells on Student Activity Book page 148?
Subtract “loaves sold cells” from “loaves baked cells”.
Have students share their own logical reasoning
problem on the back of Student Activity Book page 149
and see if the class can solve the problem. Check
students’ work.
Do you think two different volunteers would have
similar data to Sanjay and Gwen’s coin toss data? Yes,
although it may not be exactly the same, probability
would predict that the results would be similar.
What operation do you have to do to fill in the empty
“Red” cells on Student Activity Book page 152?
Subtract “total cells” from “white cells”.
Read aloud this story problem and have students
identify the extra information. He also ate a piece of
apple pie.
Brendan has 12 bananas and 4 apples.
He also ate a piece of apple pie.
How many pieces of fruit does he have?
Identify the hidden information and solve this problem.
21 days; the hidden information is the number of days
in a week (7).
Tamara was away for a week. Kyle was away for two
weeks. How many days were both kids away for?
1
5
12
2
376
379
Do you have enough information to solve this problem?
If not, what information could you add to solve it?
There isn’t enough information. Possible information
you could add: Marley has 5 muffins;11 muffins.
Dean has 6 muffins. His friend Marley has some too.
How many muffins do they have in all?
Do you have enough information to solve this problem?
If not, what information could you add to solve it?
There is enough information. 19 legs
There are 5 chairs in the rooms with 4 legs each.
One has a broken leg. How many chair legs
in the room are not broken?
1
5
13
14
Have students solve this word problem. 28 apples
Li hao picked 16 apples. Celine picked 4 fewer
apples than Li Hao. How many apples did they
pick altogether?
1
5
384
392
Have students solve this word problem. 18 pizzas
Batai delivered 6 pizzas. Then he delivered 7 more
pizzas that night. He delivered 5 fewer pizzas than
Grade 3 Math Expressions Check Your Understanding Questions 17 2
5
5
5
5
15
16
17
18
395
Problem
Solving
Strategy
396
1
400
2
401
3
403
4
405
Extension
406
1
410
2
413
1
418
2
419
1
424
2
425
3
426
Salina. How many pizzas did Salina deliver?
Use Student Activity Book page 162 to answer this.
Sample combinations: Sit (3) + Stay (6) + Fetch (5) +
Come (2) = 16; Roll over (7) + lie down (4) + Come
(2) + Sit (3) = 16, etc.
Marika has 16 treats. List as many different
combinations of 4 tricks she can teach Rufus
with that amount of tricks.
Have students share their own working backward
problem on the back of Student Activity Book page 163
and see if the class can solve the problem. Check
students’ work.
What does the key in a pictograph tell you? The key
tells you how many each symbol in the graph
represents.
What does horizontal and vertical mean? Horizontal
means “going across” and vertical means “going up
and down”
Do you need a key for a bar graph? No, not for a single
bar graph. You need one for a double bar graph.
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).
How do you show 5 with tally marks?
Look at the bar graph on Student Activity Book page
169. Why is the scale marked off in 50-mile increments
rather than 1-mile increments? The bar graph would be
too large to go from 0 – 400 in 1-mile increments.
Look at the graphs on Student Activity Book page 171.
Could the table in problem 13 be made into a vertical
bar graph as well as a horizontal one? Yes, you can
display the data both horizontally or vertically.
What is the mode, when describing data? The mode is
the value that appears most frequently in a set of data.
Which graph would you use to display how often things
occur? line plots
Have students explain how they came up with the
solution to problem 1 on Student Activity Book page
175. Possible explanation: You could use estimation.
315 cm is about 300 cm. 300 x 3 = 900 and the length
of the race is 1,000 cm. She would need to jump
between 3 and 4 jumps, which you can’t do so I said it
would take Flora about 4 jumps.
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).
Write the numerals 0 – 9 on the board and have students
find which numbers are symmetrical. 0, 1 (not in this
Grade 3 Math Expressions Check Your Understanding Questions 18 style below, but some ways you can write 1 would be
symmetrical), 3, 8
4
426
5
426
0 1 2 3 4 5 6 7 8 9
Draw 4 ways to show 45¢. Sample ways: 1. Q, D, D; 2.
Q, N, N, N, N; 3. 45 pennies; 4. D, D, D, D, N
If you were to estimate 42 + 67 + 88 + 55, what is the
best estimate- 230, 260, 270? 260
Grade 3 Math Expressions Check Your Understanding Questions 19 Check Your Understanding Questions
Unit 6- Patterns
Grade 3
Unit
Lesson
Activity
1
Page Number
434
Check Your Understanding
Draw this shape on the board. Then have students copy
the shape on their MathBoard and show what a flip of
that shape would look like. 1 possible flip is shown.
6
1
2
436
Draw this shape on the board. Then have students copy
the shape on their MathBoard and show what a slide
and a turn of that shape would look like.
sample slide
sample turn
1
440
Continue each repeating number pattern. 356356356
2
442
3 5 6 3 5 6 3 5 6 ______________
Draw the next figure in the pattern.
1
447
6
2
Write the missing number and the rule for each pattern.
88, 80; – 4
96, 92, _____, 84, _____, 76 Rule _________
6
2
447
Draw this growing pattern on the board and ask
students to decide what comes next.
3
448
Look at the table on Student Activity Book page 191.
Use this pattern to find out how many small triangles
will be in triangle number 20. 400
3
Grade 3 Math Expressions Check Your Understanding Questions 20 Check Your Understanding Questions
Unit 7- Multiplication and Division with 0–5, 9, and 10
Grade 3
Unit
7
7
Lesson
1
2
Activity
1
Page Number
460
2
462
3
463
4
N/A
1
468
2
470
3
471
Check Your Understanding
We learned how to relate multiplication and addition.
What is another way you can show
8 × 5 = 40?
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 40
What three symbols can you use to represent
multiplication? • ∗ ×
Fill in the blanks to make the statement true. factors,
product
In a multiplication equation, the numbers you
multiply are called __________. The answer or
total is called the _________.
N/A
What equation can you write to show 7 groups of 5? 7
× 5 = 35
The Fuzzy Friends pet store has 5 rabbit cages. There
are 4 rabbits in each cage. How many rabbits does the
store have in all? Use a simple math drawing and an
equation to solve.
5 × 4 = 20
The Fuzzy Friends pet store has 5 rabbit cages. There
are 4 rabbits in each cage. How many rabbits does the
store have in all? Use an Equal Shares Drawing and an
equation to solve.
20
4
4
4
4
4
5 × 4 = 20
7
7
1
2
N/A
479
3
482
4
484
1
2
N/A
3
4
N/A
Is there more than one way to make an array with a
total of 6 tiles? Yes, you can make a 1- by-6 array, a 6by-1 array, a 2-by-3 array, and a 3-by-2 array.
How can you use an array to solve 3 × 4 =
? The 3
represents the numbers of groups (the number of rows)
and the 4 represents the number in each group (the
number of columns). Altogether there would be 12 dots
in the array.
Fill in the blanks to make the statement true. factors,
product
The Commutative Property of Multiplication states
that you can switch the order of the ___________
without changing the ____________.
N/A
In this division equation, 30 ÷ 5 = 6, the number 30 is
called what? dividend The number 5? divisor The
number 6? quotient
Grade 3 Math Expressions Check Your Understanding Questions 21 3
494
4
496
What multiplication equation can you use to check that
your quotient is correct in the division equation 30 ÷ 5
=
? 6 × 5 = 30
Use a math drawing to help you solve this problem. 3
bird feeders
Loris counts 15 birds at the bird feeders in the
park. There are five birds at each feeder. How
many bird feeders are at the park?
7
7
5
1
2
N/A
501
3
505
4
N/A
1
2
3
N/A
N/A
511
4
513
5
514
6
N/A
List the 2s count-bys up to 20. 2, 4, 6, 8, 10, 12, 14, 16,
18, 20
Give an example of an even and an odd number.
Sample answers: even- 8; odd- 17
N/A
N/A
N/A
List the 10s count-bys up to 100. 10, 20, 30, 40, 50, 60,
70, 80, 90, 100
What division equation is related to this multiplication
equation
7 × 10 = ? 70 ÷ 10 = 7
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?
7
7
1
2
N/A
518
3
523
1
2
3
N/A
N/A
529
4
531
7
8
N/A
List the 9s count-bys up to 90. 9, 18, 27, 36, 45, 54, 63,
72, 81, 90
What division equation is related to this multiplication
equation
6 × 9 = ? 54 ÷ 9 = 6
N/A
N/A
How are the 9s and 10s count-bys related to each other?
One group of 9 is one group of 10 minus; [1 times 9
equals 10 minus 1.] Two groups of 9, or 18, is two
groups of 10 (or 20) minus 2; [2 times 9 equals 20
minus 2]
Use a Fast-Array drawing to solve the problem.
Sanjay planted iris bulbs in an array with 7 rows and 9
columns. How many iris bulbs did he plant? 63 iris
bulbs
9
7
7
9
1
2
3
N/A
N/A
538
4
541
63
N/A
N/A
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
Grade 3 Math Expressions Check Your Understanding Questions 22 × 3? Multiply 5 times 3 first, which is 15, and then add
three more groups of 3, which is 9. 15 + 9 = 24.
7
7
1
2
3
N/A
N/A
549
N/A
N/A
Make a rectangular drawing to represent the
multiplication equation 4 × 3 = ?
4
550
How can you break up
the large rectangle to
help you find the area?
You can break up the
large rectangle into
8
two small rectangles.
Then you can find the
areas of the two
small rectangles and
3
add them together. For example. 5 × 3 = 15 and 3 × 3
= 9. 15 + 9 = 24.
1
2
3
N/A
N/A
555
N/A
N/A
Solve the problem and identify what type of problem it
is. 3 balloons; Repeated Groups Division
10
11
The clown brought 24 balloons to the party.
He divided the balloons equally among 8 children.
How many balloons did each child get?
7
12
1
2
N/A
560
3
563
1
2
3
N/A
N/A
570
N/A
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.
N/A
N/A
What are the 8 equations that go with this fast array
drawing?
6
3
7
7
13
18
4
5
N/A
N/A
3 × 6 = 18
6 × 3= 18
18 = 6 × 3
18 = 3 × 6
N/A
N/A
1
2
N/A
577
N/A
Complete the statement to make it true. 1
578
When any number is multiplied by _______, the result
is that number.
Complete the statement to make it true. 0
14
3
18 ÷ 3 = 6
18 ÷ 6 = 3
6 = 18 ÷ 3
3 = 18 ÷ 6
Grade 3 Math Expressions Check Your Understanding Questions 23 4
583
When any number is multiplied by _______, the result
is 0.
Give an example of each of these multiplication
properties:
Commutative Property of Multiplication: i.e. 5 × 7 =7 ×
5
Associative Property of Multiplication: i.e. (3 × 7) × 2
= 3 × (7 × 2)
Identity Property of Multiplication: 5 × 1 =5
Zero Property of Multiplication:
7
7
15
16
5 × 0 =0
1
2
3
N/A
N/A
N/A
N/A
N/A
N/A
1
2
3
N/A
N/A
595
N/A
N/A
Have students solve this problem. 14 miles
To get ready for the running race, Troy ran 2 miles
each day for an entire week. How many miles did he
run during the week?
7
1
600
2
601
3
602
4
602
17
5
602
What is a survey? Something used to collect
information and data.
Do you think it’s better to survey more or fewer people
in a survey? more people to get better results
When will you know when 5 is a factor of a number?
Make a generalization and test it. When the answer ends
in 0 (20, 30, 40, 50, 60, etc.); When the answer ends in
5 (15, 25, 35, 45, 55, etc.).
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?
Find the even numbers in this list. 22, 46, 89, 134, 157
22, 46, 134
Grade 3 Math Expressions Check Your Understanding Questions 24 Check Your Understanding Questions
Unit 8- Area and Perimeter
Grade 3
Unit
8
8
8
Lesson
1
2
Activity
1
Page Number
610
2
613
3
614
4
615
1
620
2
621
1
2
626
628
3
629
3
Check Your Understanding
What are you measuring when you measure the
perimeter? You are measuring the distance/length
around a shape.
Look at problem 8 on Student Activity Book page 286.
Why is the area not 4 sq cm? You cannot count the half
squares as whole squares, so 2 + ½ + ½ = 3, not 4.
If you are finding out how many tiles you need to tile
the bottom of a pool, do you need to find the perimeter
or the area of the bottom of the pool? The area
Give students a sheet of centimeter grid paper (TRB
M31) and have them draw a star outline on their paper
and estimate the area of the unusual figure.
Measurements will vary depending on size of star.
What are some different rectangles that have a
perimeter of 10 centimeters? What is the area of each?
3 x 2 or 2 x 3 rectangle (A = 6 square centimeters); 1 x
4 or 4 x 1 rectangle (A = 4 square centimeters)
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);
What is the area formula for a rectangle? A = b x h
What is the perimeter formula for a rectangle?
P = 2 (b + h)
What is the area and perimeter formulas for a square?
A= s x s; P = 4 x s
Grade 3 Math Expressions Check Your Understanding Questions 25 Check Your Understanding Questions
Unit 9- Multiplication and Division with 6, 7, and 8 and Problem Solving
Grade 3
Unit
Lesson
9
1
9
Activity
1
Page Number
640
2
642
3
644
1
2
648
649
3
651
4
652
2
Check Your Understanding
List the 6s count-bys up to 60. 6, 12, 18, 24, 30, 36, 42,
48, 54, 60
What division equation is related to this multiplication
equation 6 × 10 = [ ]? 60 ÷ 10 = 6
How can you combine 2 multiplications you know to
multiply 7 x 6? Sample combinations: (4 x 6) + (3 x 6)
= 24 + 18 = 42
N/A
Have students solve this problem. 32 square feet
The bird pool at the park is shaped like a
rectangle with sides 8 feet long by 4 feet wide.
What is the area of the bird pool?
What two measurements do you measure to find the
area of a rectangle? The length and the width
Draw a picture to solve this problem. 90 sq in; Sample
drawing:
10
3
9
3
3
A sign is shaped like a rectangle. Evan draws lines in
the sign to make 3 equal rectangles. Each rectangle is
3 inches wide and 10 inches long. What is the area of
the sign?
9
1
2
656
657
3
661
4
661
3
N/A
List the 8s count-bys up to 80. 8, 16, 24, 32, 40, 48, 56,
64, 72, 80
How can you combine 2 multiplications you know to
multiply 6 x 8? Sample combinations: (4 x 8) + (2 x 8)
= 32 + 16 = 48
What are the 8 equations that go with this fast array
drawing?
8
3
3 × 8 = 24
8 × 3= 24
24 = 8 × 3
24 = 3 × 8
9
4
1
2
3
666
666
667
24
24 ÷ 3 = 8
24 ÷ 8 = 3
8 = 24 ÷ 3
3 = 24 ÷ 8
N/A
N/A
Have students solve this word problem and then tell the
type of word problem it is and what operation you use
to solve it. 48 roses; repeated groups; multiplication
Grade 3 Math Expressions Check Your Understanding Questions 26 9
4
669
1
2
674
675
3
678
4
679
There are 6 roses in each vase at the flower shop. If
there are 8 vases on display, how many roses are there?
What is a variable? A variable is a letter used to
represent an unknown number.
N/A
List the 7s count-bys up to 70. 7, 14, 21, 28, 35, 42, 49,
56, 63, 70
How can you combine 2 multiplications you know to
multiply 6 x 7? Sample combinations: (4 x 7) + (2 x 7)
= 28 + 14 = 42
What are the 8 equations that go with this fast array
drawing?
7
4
5
Problem
Solving
Strategy
680
1
2
3
684
684
685
28
4 × 7 = 28 28 ÷ 4 = 7
7 × 4= 28 28 ÷ 7 = 4
28 = 7 × 4 7 = 28 ÷ 4
28 = 4× 7 4 = 28 ÷ 7
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.
N/A
N/A
Make a math drawing to show this situation.
Ariel has 6 comic books. Pasqual has 12 comic books.
9
6
Ariel
Extension
690
Pasqual
What is a multiple? A multiple is the product of a
number and any other number.
1
2
694
695
N/A
Draw comparison bars to represent this situation.
Ariel has 24 comic books. Pasqual has 6 comic books.
Ariel
Pasqual
9
7
3
697
6
6
6
6
6
Use the bar graph on Student Activity Book page 329 to
answer this question. 6 times; 1/6
If there were only 2 orange shirts, how can you
compare them to blue shirts?
4
698
Shannon has ____ as many blue shirts as orange shirts.
Shannon has ____ as many blue shirts as orange shirts.
If you see the words “as many as” or “as much as,”
Grade 3 Math Expressions Check Your Understanding Questions 27 which operations are you likely to use when solving the
word problem? Multiply or divide
9
9
9
9
9
8
9
10
11
12
1
2
3
702
702
703
N/A
N/A
When you multiply a number by the same number (i.e.
7 x 7) what type of an array is formed? A square
1
2
3
4
710
710
711
712
N/A
N/A
N/A
What is 11 x 9? 99
1
2
3
716
716
717
N/A
N/A
Have students read this problem and determine which
operation to use. Then write an equation to solve the
problem. Subtraction (6 – 3 = 3 ); multiplication 3 x [ ]
= 6 (2 times as many)
4
720
5
721
Problem
Solving
Strategy
722
1
2
726
726
3
728
Extension
730
1
2
3
734
734
736
Jung has 6 nephews. George has 3 nephews. How
many more nephews does Jung have than George?
How do you know that you can’t use a multiplication or
division based question in problem 16 on Student
Activity Book page 348? You are not dealing with
equal groups.
Write a word problem for this equation. Check
students’ word problems.
567 + [ ] = 845
Have students share their toy combinations from
problem 3 on Student Activity Book page 350 and have
the class check for accuracy. Answers will vary.
N/A
If parentheses are not written in an expression, what
operations are done first? Multiplication and division
are done before addition and subtraction.
Have students share the equation to solve problem 11
on Student Activity Book page 352. (6 x 8) +10 = 58
Multiply 16 x 4 using either the Expanded Notation
Method or the Rectangle Sections Method. 64
N/A
N/A
How can you make multiplication comparisons rather
than the fractional comparisons between the length of
the spiral and the length of the wire before the spiral?
The blue, red, and white wire lengths before spiral are
two times greater than the length of the spiral.
The blue, red, and white wire lengths before spiral are
two times greater than the length of the spiral.
The black, orange, and purple wire lengths before
spiral are three times greater than the length of the
spiral.
Grade 3 Math Expressions Check Your Understanding Questions 28 The green, silver, and gold wire lengths before spiral
are four times greater than the length of the spiral.
1
2
3
9
13
4
740
740
741
742
N/A
N/A
Add this second question to problem 1 on Student
Activity book page 365 and solve. 43 minutes
How many more minutes did Raul’s sister spend on her
homework?
Write the rule and then complete the function table.
Rule: Add 25
Input
15
20
25
30
9
1
746
2
747
3
748
4
748
5
748
14
Output
40
45
50
55
Can you use a line graph in problem 1 on Student
Activity Book page 369? No, because a line graph only
graphs change over time.
If you are using only multiplication to find the
perimeter of a shape, what shape are you measuring? A
square
Can you make the same statements about the result of
adding 3 odd numbers and 3 even numbers as you did
with adding 2 odd numbers and 2 even numbers? No; 3
+ 5 + 7 = 15; 1 + 3 + 5 = 9 - it seems that when you
add 3 odd numbers, your answer is odd; yes; 2 + 4 +
6= 12; 4 + 8 + 12 = 24- it seems that when you add 3
even numbers your answer is even.
Draw as many arrays to show 18. Possible arrays: 1 ×
18, 18 × 1, 2 × 9, 9 × 2, 3 × 6, 6 × 3.
Give an example of hidden information in a problem.
Week = 7 days
Grade 3 Math Expressions Check Your Understanding Questions 29 Check Your Understanding Questions
Unit 10- Time and Date
Grade 3
Unit
Lesson
10
1
10
10
2
3
Activity
1
Page Number
757
Check Your Understanding
Have students show 8:15 on their analog clock. Check
students’ clocks.
Have students show 6:27 on their analog clock. Check
students’ clocks.
Show 4:50 on the Time Poster and have students say
the time before and after the hour. The time is 50
minutes after 4 and 10 minutes before 5.
2
759
3
760
1
2
764
766
How many days are in one year? 365 days
How many hours have passed from 9:30 am to 11:00
am? 1 ½ hours
1
772
2
773
If the minute hand moves 30 minutes, how many
degrees has the minute hand rotated? 180 degrees
How many degrees does the minute rotate in 1 minute?
6 degrees
Grade 3 Math Expressions Check Your Understanding Questions 30 Check Your Understanding Questions
Unit 11- Exploring Fractions, Decimals, Probability, and Division with Remainders
Grade 3
Unit
11
11
11
Lesson
Activity
1
Page Number
782
2
784
3
787
1
2
792
793
How do you write three eighths as a fraction? 3/8
Draw this set of shapes. What fraction of the shapes are
triangles? 3/7
1
2
798
799
What is ¼ of 12? 3
Have students solve this problem and encourage
students to share different methods with the class. 5
lillies
1
2
3
3
800
Check Your Understanding
In the fraction ⅓, what does the top and bottom number
stand for? The 1 stands for the number of shaded parts
and the 3 stands for the total number of parts.
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.
Have students use a rectangle to show 4/10 on their
MathBoard. Sample drawing:
One fifth of the flowers in the vase are lillies. There are
25 flowers in the vase. How many flowers were lillies?
Write the equation in two other ways. 1/3 x 9 = 3;
9÷3=3
1/3 of 9 = 3
1
11
804
4
2
806
Have students make some comparison statements about
this situation. Sample comparison statements: Renaldo
has 6 more stuffed animals than Tran. Tran has 6 fewer
stuffed animals than Renaldo. 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.
Have students solve this word problem and write three
different equations for the problem. 14; 14 = ¼ of 56;
14 = ¼ × 56; 14 = 56 ÷ 4
Darlene’s father is 56 years old. Darlene is ¼ as old as
her father. How old is Darlene?
11
5
1
810
2
811
Write these two numbers on the board (6 and 3) and
have students do the comparison chant. 6 is 2 times as
many as 3; 3 is ½ as many as 6.
Have students solve this word problem and share their
solution methods. 15 DVDs; Observe students’
methods.
Grade 3 Math Expressions Check Your Understanding Questions 31 Raymond has 5 DVDs.
Marlene has 3 times as many DVDs as Raymond has.
How many DVDs does Marlene have?
11
11
6
1
816
2
818
3
819
Problem
Solving
Strategy
820
1
824
2
826
7
Write three different ways to find ¾ of 12. ¾ of 12 = 9;
¾ x 12 = 9; (12 ÷ 4) x 3 = 9
Have students solve this problem. 24 cookies
Carla baked 36 cookies. She gave 4/6 of the cookies
to her grandma. How many cookies did she give
to her grandma?
When you are finding a non-unit fraction of a set and
you need to multiply, do you multiply the denominator
or numerator? Give an example. Numerator; Possible
example: 2/3 of 12, (12 ÷ 3) x 2 = 8
When using the Act It Out strategy to solve word
problems, do you have to literally act out or recreate the
scene? No, you can use counters or other objects to
represent the things described in the word problem.
What does each section of a circle graph represent? a
fractional piece of the whole
When you look at the circle graph on Student Activity
Book page 412, how do you know that this answer is
reasonable? Even if you didn’t know about fractions
that equal each other, you can see that the two 1/8
fractional pieces of the pie are the same size as the ¼
fractional piece of the pie.
2/8 is equal to 1/4
11
1
830
2
834
3
835
4
837
8
Read aloud the following statement and have students
explain whether the event is impossible, unlikely,
equally likely, likely, or certain. Possible answers: The
event is likely as you may go to school, but you could
also be ill and not attend school. The event could also
be impossible if the “tomorrow” was a weekend day.
I will go to school tomorrow.
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.
What information can help you make predictions? You
can make predictions before analyzing data, but you
can make more accurate predictions if you do an
experiment once and see what the outcomes are before
predicting the results in further experiments.
What does the word “outcome” mean? Outcome means
the result of an experiment or what comes out.
11
9
1
844
How many twelfths are in one fourth? 3 twelfths
11
10
1
852
How many sixths are in two twelfths? 4 sixths
1
857
2
860
Write an equivalence chain beginning with 5/6. 5/6,
10/12, 15/18, 20/24, 25/30, etc.
Write an equivalence chain beginning with 3/4. ¾, 6/8,
9/12, 12/16, 15/20, etc.
11
11
Grade 3 Math Expressions Check Your Understanding Questions 32 11
11
11
11
12
13
14
1
864
2
866
1
870
2
872
1
876
2
880
1
886
2
888
15
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
Use multiplication to find an equivalent fraction for 3/4.
Sample equivalent fraction: 9/12; 3/4 = 3 x 3/ 4 x 3 =
9/12
Use division to find an equivalent fraction for 4/6.
Sample equivalent fraction: 2/3; 4/6 = 4 ÷ 2/ 6 ÷ 2 =
2/3
Use division to find an equivalent fraction for 9/12.
Sample equivalent fraction: 3/4; 9/12 = 9 ÷ 3/ 12 ÷ 3 =
¾
Use fraction strips to add 3/10 and 4/10. 3/10 + 4/10 =
7/10
Use fraction strips to add ½ and 2/8. ½ = 4/8, 4/8 + 2/8
= 6/8
Use fraction strips to subtract 1/5 from 4/5. 4/5 – 1/5 =
3/5
Write these two fractions on the board and have
students compare them with the greater than, less than,
or equal to symbols.
4/5
11
1
894
2
896
16
>
Have students place point D at 2 ½ on the 11th number
line on Student Activity Book page 440. Check
students’ number lines.
Write these two fractions on the board and have
students use a number line to compare them with the
greater than, less than, or equal to symbols.
3/6 =
11
17
3/10
½
3
897
Use a number line to add 2/8 and 4/8. 4/8 + 2/8 = 6/8
1
902
2
3
4
905
907
909
How else could you describe 25/100, the 100 being 100
pennies or a dollar. ¼ as 4 quarters make up a dollar.
Write 0.36 as a fraction. 36/100
Write an equivalent decimal to 0.60. 0.6
Write these two decimals on the board and have
students compare them with the greater than, less than,
or equal to symbols.
0.8 = 0.80
11
1
915
2
916
18
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
+
3
917
+
How can we figure out that 3 2/6 equals 20/6? Possible
answer: 6/6 + 6/6 + 6/6 + 2/6 = 20/6
Grade 3 Math Expressions Check Your Understanding Questions 33 1
11
19
2
922
924
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?
Use standard notation to divide.
5
R6
8 46
– 40
6
1
929
Divide and express the remainder as a fraction. 6 2/6
6
11
11
11
2
930
Problem
Solving
Strategy
932
1
937
2
938
1
942
2
943
20
21
R2
6 38
– 36
2
There are three types of remainders. Explain the three
types of remainders.
1. left-over remainder: the remainder cannot be used in
the context of the problem.
2. another whole remainder: the remainder needs
another whole added to the whole number answer.
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.
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.
What operation can you use to check your division?
multiplication
Write the answer with a remainder and as a mixed
number. 3 R4; 3 4/6
22 ÷ 6
Have students share their house drawings. Then have
the rest of the class describe the geometric figures they
see (i.e. angles, shapes, properties, etc.). Houses will
vary. Observe students’ descriptions.
Have students create an unfair spinner where you’d
have more of a chance of landing on a B. Spinners will
vary. Sample spinner shown:
22
3
944
A
B
B
B
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:
Grade 3 Math Expressions Check Your Understanding Questions 34 4
944
5
944
There are 3 marbles in a bag. One marble is yellow,
one marble is blue, and one marble is green. You select
one marble at a time and place it back in the bag after
selecting it. How many ways can you choose 2 marbles
if the order doesn’t matter? List the ways. 6 ways; YY,
YB, YG, BB, BG, GG
Write this puzzle on the board for students to solve.
Possible answers: 62, 64, 66, 68, 70.
I am thinking of a number.
It is greater than 100 – 40.
It is less than 100 – 28.
It is an even number.
What number am I thinking of?
Grade 3 Math Expressions Check Your Understanding Questions 35 Check Your Understanding Questions
Unit 12- Three-Dimensional Figures
Grade 3
Unit
Lesson
Activity
1
Page Number
952
12
1
2
953
1
958
2
959
Math
Connection
962
Extension
964
1
968
2
969
1
2
974
975
3
976
1
981
2
982
12
12
12
12
2
3
Check Your Understanding
What is a net? A 2-D pattern that can be folded into a
3-D figure.
Look at Student Activity Book page 460C. Why do
you think all your cube nets are made from six separate
squares? A cube has 6 faces.
How many cubes are hidden in problem 5 on Student
Activity Book page 463? 2 cubes
What are the three different viewpoints that you can
look at a 3-D object from? Front, back, left, and right
views
What is the formula for finding the volume of a prism?
Volume = length × width × height
If you estimate the volume of the same box with
centimetre cubes instead of inch cubes, do you think
you would fit more or less centimeter cubes inside the
box? More, as they are smaller and take up less space.
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 many edges and vertices does a cylinder have? 0
edges; 0 vertices
What is the shape of a cone’s base? circle
Name figures that fit these sorting rules: cylinder and
cone
4
5
Solid figures that have circle bases.
What shape package would you put tennis balls in? a
cylinder
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.
How is a sphere different from a circle? A sphere is 3-D
and a circle is 2-D.
Grade 3 Math Expressions Check Your Understanding Questions 36 Check Your Understanding Questions
Unit 13- Measurement
Grade 3
Unit
13
Lesson
1
Activity
1
Page Number
990
2
992
3
993
4
994
Check Your Understanding
People used to say an inch was the size of a man’s
thumb. Why isn’t the thumb the best unit of measure?
Everyone’s thumb is a different size so an inch would
be different on everyone and everyone’s measurements
would be different.
Have students name as many tools as they can and
explain what those tools measure. Possible tools: scale
(weight); thermometer (temperature); ruler (length),
cup (capacity); clock (time)
What do the different lines on an inch ruler stand for?
Quarter inches, half inches, whole inches
How would your rectangle look different in problem 15
on Student Activity Book page 476 if the directions said
this:
Draw a rectangle that is 3 inches wide and 1 inch long.
13
13
13
13
2
3
4
5
1
2
998
1000
How many inches are in a foot? 12 inches
Which is the best unit you would use to measure the
distance between states? mile
1
2
3
1004
1006
1010
What does a centimeter measure? length
How many centimeters are in 2 meters? 200 cm
Which is the best unit you would use to measure the
distance between states? Kilometer
1
1014
2
1015
3
1016
4
1017
Can you make a square with a perimeter of 12 inches?
Yes, a 3 x 3 square (3 + 3 + 3 + 3 = 12 inches)
Have a student show one of their classroom objects and
have the class try and estimate the perimeter of the
figure using an inch or centimeter referent. Estimates
will vary.
Have a student find a classroom object and have the
class try and estimate the area of the figure using a
square inch or square centimeter referent. Estimates will
vary.
How do you add 2 ¼ in. + 1 ¼ in.? 3 ½ in.; Add the
whole numbers first (2 + 1) and then add the fractions
(1/4 + ¼ = ½)
1
2
3
1022
1024
1025
4
1027
Which holds more, a pint or a gallon? A gallon
How many quarts are in 3 gallons? 12 quarts
Which is the best unit you would use to measure how
much a fish tank can hold? quart or gallon
Which estimate is better? 2 cups of water
Grade 3 Math Expressions Check Your Understanding Questions 37 A bowl would hold 2 cups of water.
A bowl would hold 20 gallons of water.
13
1
1033
2
1035
Which is the best unit you would use to measure the
capacity of a milk jug? Liter
Which estimate is better? 2 cups of water
1036
A sink would hold 10 litres of water.
A sink would hold 10 milliliters of water.
Have students solve this problem. 1 ½ liters
6
3
A jug holds 500 ml of water. How many
liters will 3 bottles hold?
13
7
13
8
13
13
13
1
1040
2
1042
1
1048
How many yards is 5 feet? 5/3 = 1 2/3 yards
1
2
1053
1055
3
1057
Which weighs less, an ounce or a pound? An ounce
Would you measure a piece of paper in grams or in
kilograms? grams
Which estimate is better? 140 pounds
9
10
11
Math
Connection
1059
1
1064
2
1065
1
1070
2
1071
3
1072
4
5
1072
1072
What is an improper fraction? A fraction that is greater
than or equal to 1.
How can you write 10/4 inches as a mixed number? 2
2/4 in. or 2 1/2 in..
A horse weighs 140 pounds.
A horse weighs 14 ounces.
If you want to simplify a measurement, what do you
need to do to the units of measure? Make sure they are
the same units so you may need to convert.
What are the two units you can measure temperature in?
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 use a triangle pattern block to create a
tessellation. Check students’ tessellations.
If you used a meter stick instead of a yardstick, would
you still get similar results? Yes, just different
measurement units.
True or false, a triangle can have two right angles?
False, a triangle can only have one right angle.
How many squares make up a cube net? 6 squares
Have students solve this problem. 9 pages; When you
divide 88 by 10 you get 8 R8 so you need another page
for the 8 remaining stamps. 8 + 1 = 9 pages
Darla is putting stamps in her stamp album.
Each page can hold 10 stamps. Darla has 88 stamps.
How many pages will she need? Explain.
Grade 3 Math Expressions Check Your Understanding Questions 38 Check Your Understanding Questions
Unit 14- Directions and Locations
Grade 3
Unit
Lesson
14
1
14
14
2
Activity
1
Page Number
1080
2
1082
1
1086
2
1088
1
1092
3
2
1093
Check Your Understanding
What is the shortest route from the recreation center to
the movie theater? 6 blocks
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.
What is located at 5, 1? Fire pit (Watch that students
don’t locate the cherry tree which is 1, 5.)
Pass out another Coordinate Grid (TRB M148) and
have students create a picture on the grid. Then have
volunteers give the ordered pairs to the class and see if
they can create the same picture. Check students’ work.
Look at problem 10 on Student Activity Book page 520
and complete this statement. vertex
Each ordered pair of the parallelogram is a _______ of
the parallelogram.
If a line segment has two endpoints at 1 and 4, why is
the length only 3 units, instead of 4 units? Although the
endpoint ends at 4, it’s 1 unit from 1 to 2, 1 unit from 2
to 3, and 1 unit from 3 to 4. That’s 3 units, not 4 units.
Grade 3 Math Expressions Check Your Understanding Questions 39 Unit
Lesson
Extension
1
Activity
1
Page Number
1102
2
1103
1
1108
Extension
2
2
1111
Extension
3
1
1116
2
1118
1
1122
Extension
4
Check Your Understanding
What is the value of the underlined digit? 6,000
56, 980
Write these two numbers on the board and have
students use place value to compare them with the
greater than or less than symbols.
5, 230
<
7, 803
What property tells you that 3 x 5 and 5 x 3 are the
same? Commutative Property
Write out the steps for finding 30 x 20 by factoring the
tens. 30 x 20 = (3 x 10) x (2 x 10) = (3 x 2) x (10 x 10)
= 6 x 100= 600
How is 30 x 40 similar to 3 x 4? 30 x 40 is 120 and 3 x
4 is 12
How is 60 x 40 similar to 6 x 4? 60 x 40 is 240 and 6 x
4 is 24
Use the Area Model to multiply 34 x 3 on your
MathBoard. 102
30
+
4
3
2
1124
5
1
1128
4 x 3= 12
(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 the Rectangle Sections Method to multiply 4 x 56.
224
50
+
6
4
Extension
30 x 3 = 90
50 × 4 = 200
6 × 4 = 24
Use the Expanded Notation Method to multiply 36 x 4.
144
36 =
30
+
6
4
4
30
Extension
6
2
1130
1
1134
+
6
36 = 30 + 6
× 4
4
4 x 30 = 120
4 x 6 = 24
144
Use the Algebraic Notation Method to multiply 36 x 4.
4 Ÿ 36 = 4 Ÿ (30 + 6)
= 120 + 24
= 144
Use the Shortcut Method to multiply 36 x 4.
Step 1
Step 2
2
2
36
36
Grade 3 Math Expressions Check Your Understanding Questions 40 ×
Extension
7
4
4
×
4
144
2
1136
Have students use any method they choose to multiply
78 x 6. 468; Check students’ methods.
1
1140
Use the Rectangle Sections Method to multiply 4 x 568.
2, 272
500
+
500 × 4 =
2,000
2
1142
60
+
8
8×4=
32
60 × 4 =
240
4
Use the Expanded Notation Method to multiply 568 x
4. 2,272
568 = 500
+
60
+ 8
4
4
500
+
60
+
8
568 = 500 + 60 + 8
× 4
4
4 x 500 = 2, 000
4 x 60 = 240
4x 8=
32
2, 272
Extension
8
1
1146
2
1147
Have students use any method they choose to multiply
587 x 3. 1, 761; Check students’ methods.
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
Extension
9
1
1152
Have students use any method they choose to divide
560 ÷ 4. 140; Check students’ methods.
Extension
10
1
2
1158
1160
Use rounding to estimate 62 x 4. 60 x 4 = 240
Use rounding to estimate 136 ÷ 7. 140 ÷ 7 = 20
Extension
11
1
1164
What are the three different ways you can model
multiplication and division? Equal groups, repeated
addition, multiplication equation; equal groups,
repeated subtraction, division equation or “house”
model
Extension
12
1
1170
2
1171
Look at the function table on Student Activity Book
page 549. If the pattern continued to 7 weeks. What
would the money amount be? $300
The function table on Student Activity Book page 549
measures the growth of money in a savings account.
This is an example of change over time and could be
displayed in a line graph. Does that mean the data in
every function table can be graphed in a line graph? No,
not all function tables display data that shows a change
over time.