Chapter 2 Math Guide
I can model multiplication comparisons
Molly has 5 stickers. Janet has 4 times as many stickers as Molly. How many
stickers does Janet have?
Molly
5
Janet
5
5
5
5
Start with Molly because we know how many stickers
she has. Draw one box and put that amount (5) inside. Janet has 4 times as many, so draw 4 boxes for
Janet. Each box always has the same number, so 5
goes into each of those boxes. Use the model and
problem to write a multiplication sentence.
5 (stickers )x 4 (times as many) = n (stickers)
n
5 x 4 = 20, so n = 20. Janet has 20 stickers
Logan has 3 times as many action figures as Chase. Logan has 9 action figures. How many action figures does Chase have?
Logan has 3 times as many, so draw three boxes for Logan. We know that Logan has 9, so those 3 boxes will
add up to 9. Add the 9 to your picture.
Chase
n
Logan
n
n
n
Draw one box for Chase. We don’t know how many
Chase has, so we use a letter to stand for the unknown
number of each box.
Use an equation to figure out the unknown number.
n (unknown) x 3 (boxes) = 9 (action figures)
9
I know 3 x 3 = 9, so n (unknown is equal to 3).
This means that Chase has 3 action figures.
Comparison Sentences
14 is 7 times as many as 2,
24 is 6 times as many as 4,
14 = 7 x 2
24 = 6 x 4
6 x 7 = 42
5 x 3 = 15
6 times as many as 7 is 42.
5 times as many as 3 is 15.
I can model multiplication comparisons
Online Resources:
*Cool Links —> Math: Multiplication Comparisons
Link: http://www.helpingwithmath.com/by_subject/equations_
expressions/equ_comparing01_4oa1.htm
*Cool Links —> Math: Multiplication Comparisons Practice
Link: https://www.khanacademy.org/math/arithmetic/multiplication-division/
mult-div-word-problems/e/comparing-with-multiplication
*Cool Links—> Math: Multiplication Comparisons Video
Link: https://www.youtube.com/watch?v=NEkRjZJGvnI
*Cool Links —> Math: Multiplication Comparison Statements
Link: http://mrnussbaum.com/grade_4_standards/multiplication_
statements/
Chapter 1 Math Guide
I can use a model to solve comparison problems
Alfred scored 5 times as many points as Sid. Together they scored a total of 30 points.
How many points did each boy score?
Alfred
n
n
n
n
Start off with what you know. Alfred scored 5
times as many so Alfred is going to have 5
boxes. The other person, Sid, will only have
one box.
n
30
n
Sid
Together they have 30, so the 30 goes on the
outside and includes both boys.
You don’t know how many each scored, so
use a letter in each box to show an unknown
number.
Now use the model to help you solve. There are 6 total boxes that equal 30. So, 6 times an
unknown number equals 30. Write an equation:
6 x n = 30
Now, solve for n. What times 6 equals 30? 5 x 6 = 30, so n=5
Use the value of n to find each boys’ points.
Sid = 5 points
Alfred has 5 boxes, so 5x5 = 25. Alfred scored 25 points
Online Resources:
*Cool Links—> Math: Multiplication Comparison Problem Solving Video
Link: https://www.youtube.com/watch?v=zJBJV5zbmLk
*Cool Links—> Math: Model Multiplication Comparison Problem Solving Lesson
Link: https://learnzillion.com/lesson_plans/5644-solve-multiplicativecomparison-word-problems-by-using-bar-models
*Cool Links —> Math: Multiplication Comparison Problem Solving
Link: http://www.mathplayground.com/tb_multiplication/thinking
_blocks_multiplication_division.html
*Cool Links —> Zondle —> Multiplication Comparison Problem Solving
Chapter 2 Math Guide
I can multiply tens, hundreds, and thousands
Strategy 1
8 x 600 =
8 x 6 hundreds
Break the 600 into it’s place
48 hundreds
Multiply the basic fact: 8x6 = 48
4,800
Change the 48 hundreds into it’s value
Strategy 2
8 x 600 = 4,800
Underline the basic fact and multiply: 8 x 6 = 48.
Add the two zeros from the problem to the answer
4 x 5,000 = 20,000
Underline the basic fact and multiply: 4 x 5 = 20
Add the three zeros from the problem to the answer.
*Remember, one of the zeros is from the basic fact of
4 x 5 = 20. That is why there are 4 zeros in the answer
Online Resources:
*Cool Links: —> Math: Multiply Tens, Hundreds, Thousands Video
Link: https://www.youtube.com/watch?v=0KkBYlMOUSU
*Cool Links —> Math: Multiply Tens, Hundreds, Thousands
Link: http://www.eduplace.com/kids/mw/practice/quiz.html?
qzid=hmm05_ep/gr4/0601&qseq=2,0,1,7,6,5,12,8,4,10&at=0&curq
=0&score=0&UNIT=3
*Cool Links —> Math: Multiply Tens, Hundreds, Thousands Video
*Cool Links—> Math: Multiply Tens, Hundreds, Thousands Practice
Link: http://www.mathgames.com/skill/4.48-multiply-two-numbers-up-to
-1000
Online Resources Continued
*Cool Links—> Math: Multiply Tens, Hundreds, Thousands Problem Solving
Link: http://www.mathgames.com/skill/4.80-multiplication-withoperands-up-to-100-iii
*Cool Links —> Zondle —> Multiply Tens, Hundreds, Thousands
Chapter 2 Math Guide
I can estimate products
Use Mental Math
5 x 841
5 x 800
Round the larger number to the greatest place
(underline the 8, look to the neighbor. It is a 4, so you let
it rest at 800)
5 x 800 = 4,000
Multiply basic fact 5 x 8 = 40. Add the two zeros
6 x 3948 =
3,948 is between 3,00 and 4,000. Find the product for each.
6 x 3,000 = 18,000
Multiply basic fact 6x3=18 and add three zeros.
6 x 4,000 = 24,000
Multiply basic fact 6x4-24 and add three zeros
Answer: Between 18,000 and 24,000
Online Resources:
*Think Central —> Animated Math Models —> Skills 6: Estimate Products
*Cool Links —> Math: Estimate Products by 1-digit
Link: https://www.ixl.com/math/grade-3/estimate-products
*Cool Links —> Math: Estimate Products by 1-Digit Pacman
Link: http://www.sheppardsoftware.com/mathgames/round/
mathman_round_multiplication.htm
Chapter 2 Math Guide
I can use the distributive property to multiply
7 x 19
10
9
1. Box out the full 7 rows and 19 columns.
7
2. Then, break apart the 19 columns. You
can break them apart in any way. The idea
is to make them EASIER to multiply, so tens
are a great way.
Yellow 10 x 7 = 70
Blue 9 x 7 = 63
70 + 63 = 133
3. Multiply each section you broke apart.
You can count the boxes to be sure.
4. Put the sections back together (add).
So…. 7 x 19 = 133
New Problem: 5 x 15
9
6
1. Box out the full 5 rows and 17 columns
5
2. Break apart the columns. This is just an
example, you can break them apart in ANY
way that add up to 17.
Yellow 9x5=45
Blue 6x 5=30
45 + 30 = 75
3. Multiply each section you broke apart.
4. Put the sections back together (add).
So…. 5 x 15 = 75
Online Resources:
*Cool Links—> Math: Multiply by 1-Digit Distributive Property Video
Link: https://learnzillion.com/lesson_plans/6025-solve-multiplicationproblems-using-distributive-property
*Cool Links—> Math: Multiply by 1-Digit Distributive Property
Link: https://www.ixl.com/math/grade-4/multiply-using-the-distributive
-property
*Cool Links—> Math: Multiplication Basketball (Use distributive property to
solve)
Link: http://www.funbrain.com/brain/MathBrain/Games/Title.html?
GameName=MathBasketball&Grade=4&Brain=math
*Cool Links—> Math: Multiplication by 1-Digit Practice (Use distributive property
to solve)
Link: http://www.mathplayground.com/multiplication04.html
*Cool Links—> Math: Multiplication by 1-Digit Practice 2 (Use distributive
property to solve)
Link: http://www.mathplayground.com/multiplication03.html
*Cool Links—> Math: Multiplication by 1-Digit Practice 3 (Use distributive
property to solve)
Link: http://www.mathplayground.com/ASB_Canoe_Penguins.html
Chapter 2 Math Guide
I can use expanded form to multiply
4 x 183
4
1. Break apart the 183 into each place value
(expanded form) 183 = 100 + 80 + 3
100
80
400
320
3
12
2. Multiply 4 by each of those place values.
(4 x 400) + (4 x 80) + (4 x 3)—Expanded Form
4x100= 400
4x80=320
4x3=12
3. Put each value back together (add)
400 + 320 + 12 = 732
3 x 234
200
30
4
1. Break apart the 234 into each place value
(expanded form) 234 = 200 + 30 + 4
2. Multiply each of those place values
3
600
90
12
(3 x 200) + (3 x 30) + (3 x 4) —Expanded Form
3x200=600
3x30=90
3x4=12
3. put each value back together (add)
600 + 90 + 12 = 702
Online Resources:
*Cool Links—> Math: Multiply by 1-Digit Expanded Form Video
Link: https://www.youtube.com/watch?v=fwWEA82vr70
*Cool Links—> Math: Multiplication Basketball (Use expanded form to solve)
Link: http://www.funbrain.com/brain/MathBrain/Games/Title.html?
GameName=MathBasketball&Grade=4&Brain=math
*Cool Links—> Math: Multiplication by 1-Digit Practice (Use expanded form to
solve)
Link: http://www.mathplayground.com/multiplication04.html
Online Resources Continued
*Cool Links—> Math: Multiplication by 1-Digit Practice 2 (Use expanded form
to solve)
Link: http://www.mathplayground.com/multiplication03.html
*Cool Links—> Math: Multiplication by 1-Digit Practice 3 (Use expanded form
to solve)
Link: http://www.mathplayground.com/ASB_Canoe_Penguins.html
*Cool Links—> Math: Multiply by 1-Digit Partial Products Video
Link: http://www.summithill.org/teacher_list/teacher_edit_cool_links.asp?
path=3798
*Cool Links—> Math: Multiply by 1-Digit Partial Products Video 2
Link: https://www.youtube.com/watch?v=u-yrXpd-j6k
Chapter 2 Math Guide
I can use partial products to multiply
183
4 x 183
4
100
80
400
320
x
4
12
320
400
732
3
12
+
*Start with the ones place
1. Multiply the bottom number by the
ones place. Put the whole answer at
the bottom 3 x 4 = 12
2. Multiply the bottom number by
the tens place. Put the whole
number at the bottom. 4 x 80 = 320
3. Multiply the bottom number by the
hundreds place. Put the whole number at the bottom. 4 x 100 = 400
4. Add the partial products to find
the total product
12 + 320 + 400 = 732
3 x 234
200
3
600
30
90
4
12
+
234
*Start with the ones place
x
1. Multiply the bottom number by the
ones place. Put the whole answer at
the bottom 3 x 4 = 12
3
12
90
600
702
2. Multiply the bottom number by
the tens place. Put the whole
number at the bottom. 3 x 30 = 90
3. Multiply the bottom number by the
hundreds place. Put the whole number at the bottom. 3 x 200 = 600
4. Add the partial products to find
the total product
12 + 90 + 600 = 702
Online Resources
*Cool Links—> Math: Multiplication Basketball (Use partial products to solve)
Link: http://www.funbrain.com/brain/MathBrain/Games/Title.html?
GameName=MathBasketball&Grade=4&Brain=math
*Cool Links—> Math: Multiplication by 1-Digit Practice (Use partial products to
solve)
Link: http://www.mathplayground.com/multiplication04.html
*Cool Links—> Math: Multiplication by 1-Digit Practice 2 (Use partial products
to solve)
Link: http://www.mathplayground.com/multiplication03.html
*Cool Links—> Math: Multiplication by 1-Digit Practice 3 (Use partial products
form to solve)
Link: http://www.mathplayground.com/ASB_Canoe_Penguins.html
Chapter 2 Math Guide
I can solve multi-step word problems involving multiplication
*You can draw a picture to make connections and visualize what you would
do in real life
Problem: Laura has a garden with 7 rows of 13 carrot plants and 5 rows of 16 onion plants.
How many vegetable plants does she have?
7 rows
13 plants
Carrot Plants
7 x 13 = 91 carrot plants
5 rows
16 plants
Onion Plants
5 x 16 = 80 onion plants
1. Carrot Plants: 7 rows of 13 plants.
Multiply 13 x 7 = 91 carrot plants
2. Onion Plants: 5 rows of 16 plants.
Multiply 16 x 5 = 80 onion plants
3. You are putting all the plants
together to find the total, so add
91 carrot plants + 80 onion plants.
There are 171 total plants.
Problem: Laura has a large flower garden. The whole garden is 9 rows of 15 flowers. In
the middle is a small section of tulips. The tulips are 3 rows of 5 tulips. How many other
flowers are in the garden?
15 plants
9 rows
Total Plants 9 x 15 = 135
Tulips
3x5=15 tulips
135 total—15 tulips = 120 other flowers
1. Find the total flowers in the garden.
Multiply 9 x 15 = 135 total flowers.
2. Find the number of flowers that are
tulips. Multiply 3 x 5 = 15 tulips.
3. Subtract the tulips from the total
flowers to see how many are not tulips.
135—15 = 120 other flowers.
Online Resources:
*Cool Links —> Zondle —> Multi-Step Multiplication Word Problems
Chapter 2 Math Guide
I can use regrouping to multiply a 2-digit number by a 1-digit number
4
*Start with the ones place.
38
1. Multiply the bottom number by the ones place: 6 x 8 = 48. You
leave the 8 ones and regroup the 4 tens
x6
2. Multiply the bottom number by the tens place: 6 x 3 tens = 18 tens.
Add the 4 regrouped tens. 18 tens + 4 regrouped tens = 22 tens.
Since there are no other numbers to multiply. The 22 tens go at the
bottom.
228
2
47
x4
*Start with the ones place.
1. Multiply the bottom number by the ones place: 4 x 7 = 28. You
leave the 7 ones and regroup the 2 tens
2. Multiply the bottom number by the tens place: 4 x 4 tens = 16 tens.
Add the 2 regrouped tens. 16 tens + 2 regrouped tens = 18 tens.
Since there are no other numbers to multiply. The 18 tens go at the
bottom.
188
Online Resources:
*Cool Links—> Math: Multiplication Basketball (Use regrouping to solve)
Link: http://www.funbrain.com/brain/MathBrain/Games/Title.html?
GameName=MathBasketball&Grade=4&Brain=math
*Cool Links—> Math: Multiplication by 1-Digit Practice (Use regrouping to
solve)
Link: http://www.mathplayground.com/multiplication04.html
Online Resources Continued
*Cool Links—> Math: Multiplication by 1-Digit Practice 2 (Use regrouping to
solve)
Link: http://www.mathplayground.com/multiplication03.html
*Cool Links—> Math: Multiplication by 1-Digit Practice 3 (Use regrouping form
to solve)
Link: http://www.mathplayground.com/ASB_Canoe_Penguins.html
*Cool Link—> Math: Multiply 2-Digit by 1-Digit Regrouping Video
Link: https://www.khanacademy.org/math/arithmetic/multiplicationdivision/multi-digit-multiplication/v/2-digit-times-1-digit-example
Chapter 2 Math Guide
I can use regrouping to multiply a 3– and 4--digit number by a 1-digit number
2 4
638
x6
3828
2 1 2
1, 5 4 7
x4
6188
*Start with the ones place.
1. Multiply the bottom number by the ones place: 6 x 8 = 48. You leave
the 8 ones and regroup the 4 tens
2. Multiply the bottom number by the tens place: 6 x 3 tens = 18 tens. Add
the 4 regrouped tens. 18 tens + 4 regrouped tens = 22 tens. Leave the 2
tens and regroup the 20 tens/2 hundreds
3. Multiply the bottom number by the hundreds place: 6 x 6 hundreds = 36
hundreds. Add the 2 regrouped hundreds. 36 hundreds + 2 regrouped
hundreds = 38 hundreds. Since there are no other numbers to multiply, the
38 hundreds go at the bottom.
*Start with the ones place.
1. Multiply the bottom number by the ones place: 4 x 7 = 28. You leave the
7 ones and regroup the 2 tens
2. Multiply the bottom number by the tens place: 4 x 4 tens = 16 tens. Add
the 2 regrouped tens. 16 tens + 2 regrouped tens = 18 tens. Leave the 8 tens
and regroup the 10 tens/1 hundred.
3. Multiply the bottom number by the hundreds place. 4 x 5 hundreds = 20
hundreds. Add the 1 regrouped hundreds. 20 hundreds + 1 regrouped
hundreds = 21 hundreds. Leave the 1 hundred and regroup the
20 hundreds/2 thousands.
4. Multiply the bottom number by the thousands place. 4 x 1 thousand = 4
thousands. Add the 2 regrouped thousands. 4 thousands + 2 regrouped
thousands = 6 thousands. Since there are no other numbers to multiply and
it only one digit, the whole thing goes at the bottom.
Online Resources:
*Cool Links—> Math: Multiplication Basketball (Use regrouping to solve)
Link: http://www.funbrain.com/brain/MathBrain/Games/Title.html?
GameName=MathBasketball&Grade=4&Brain=math
*Cool Links—> Math: Multiplication by 1-Digit Practice (Use regrouping to
solve)
Link: http://www.mathplayground.com/multiplication04.html
Online Resources Continued
*Cool Links—> Math: Multiplication by 1-Digit Practice 2 (Use regrouping to
solve)
Link: http://www.mathplayground.com/multiplication03.html
*Cool Links—> Math: Multiplication by 1-Digit Practice 3 (Use regrouping form
to solve)
Link: http://www.mathplayground.com/ASB_Canoe_Penguins.html
*Cool Links—> Math: Multiply 3-Digit by 1-Digit Regrouping Video
Link: https://www.youtube.com/watch?v=bWA626YrdF0
Chapter 2 Math Guide
I can find the area of an object.
*Area = Square units that cover an object.
*You find the area of an object by multiplying the length times the
width.
15 cm
8 cm
*The length is 15 cm and the
width is 8 cm.
Multiply 15 x 8 = 120
*The area of the figure is
120 square cm
*The length is 36 cm and the
width is 4 cm.
Multiply 36 x 4 = 144
4 in
36 in
*The area of the figure is
144 square in
*Sometimes figures are not perfect squares or rectangles. These complex
figures still have an area. We find that area by breaking the complex figures
up into smaller rectangles and squares. You find the area of each smaller
piece and then add then put it back together by adding the areas.
12 cm
17 cm
9 cm
*Blue: Multiply 12 x 9 because
the 17 includes the length all the
way to the bottom. 12 x 9 = 108
14 cm
*Yellow: Multiply 8 x 26 = 208
8 cm
26 cm
*Add the yellow and blue areas
together
108 + 208 = 316 square cm
Chapter 2 Math Guide
I can find the area of an object.
*Sometimes figures are not perfect squares or rectangles. These complex
figures still have an area. We find that area by breaking the complex figures
up into smaller rectangles and squares. You find the area of each smaller
piece and then add then put it back together by adding the areas.
4 in
4 in
8 in
14 in
14 in
8 in
8 in
*Blue: 4 x 8 = 32 (not 14 because it
goes the entire height
*Red: 4 x 8 = 32 (not 14 because it
goes the entire height)
*Yellow: 16 x 6 = 96
16 in
The full height is 14 inches. The blue
and red boxes take up 8 of those 14
inches. 14-8=6. This means the
remaining 6 inches are in the yellow
box. So you multiply the 16 by 6.
*Add the blue, red, and yellow
areas together
32 + 32 + 96 = 160 square inches
Online Resources
*Cool Links —> Math: Area Complex Figures Video
Link: http://www.youtube.com/watch?v=Bchoz0Q2Rj8&sns=em
*Cool Links —> Math: Area & Perimeter Practice
Link: http://www.mathplayground.com/manipulatives/
AreaandPerimeter_secure.swf
*Cool Links —> Math: Area & Perimeter Zoo Design
Link: http://mrnussbaum.com/zoo/
*Cool Links —> Math: Area Complex Figures Practice
Link: https://www.ixl.com/math/grade-4/area-of-complex-figures-with-
Online Resources Continued
*Cool Links —> Math: Area Complex Figures Practice 2
Link: http://www.mathgames.com/skill/6.106-area-of-complex-figures
*Think Central —> Go Math! Animated Math Models —> Skill Numbers 55, 56,
57, and 58.
*Think Central —> Mega Math —> Ice Station Exploration —> Q. Area and R.
Area of Complex Figures
*Think Central —> Interactive Student Edition —> Chapter 13 —> Lesson 13.2
Area and Lesson 13.3 Area of Combined Rectangles