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