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BANSHO

Planning sheet for Multiplication and Division

November/December

Math Strategies – Mental and Traditional

Numeration: Multiplication

Strategies in order of efficiency:

Sorted in this order whenever work goes on board:

- repetitive addition (lvl 2)

- by 10’s and 1’s (lvl 2)

- by place value (lvl 3)

- (arrays) math squares (lvl 2, 3, 4)

- Traditional long (lvl 3)

- Traditional short (lvl 3, 4)

- Napier’s Bones (lvl3, 4)

1. Lesson 1 – introduction and review of tools

Focus on multiplication tools

Prior Knowledge/introduction:

Part 1: Explore the use of Finger Multiplication and a Multiplication Chart. Finger multiplication works for the 6 to 10 times tables.

Touch the 2 fingers you want to multiply (6 X 6). All the fingers touching and under are 10’s (add them… two thumbs = 20). The fingers above are multiplied together (4 fingers X 4 fingers = 16) and then added to the tens (16 + 20 = 36). Therefore 6X6=36

10 9 8 7 6 6 7 8 9 10

[pic] [pic]

Practice with a partner (or races, or quizzes, etc…).

Part 2: Hand out Multiplication Chart. Using jot notes, explain to someone who had never used a multiplication chart, how to use one. Place explanations on blackboard. Have students practice (races, partners, etc…)

Today’s Problem: none

Consolidation:

Focus on math vocabulary and clear explanations

HW: Practice at home (speed races using oral questions)

2. Lesson 2 – Repetitive Addition

Prior Knowledge/introduction:

On a single sheet of paper represent 5 X 3 in as many ways as you can. (Looking to highlight any repetitive additions)

Today’s Problem: (groups of 4)

You can bake 48 cookies in one batch which fit on a single cookie sheet. You are going to make six batches of cookies for the class party. How many cookies are you going to make. (Answer in at least 2 different ways including explanations and labeling)

Consolidation:

Look at the connection between addition and multiplication. Have students name strategy and post on back wall. Focus on clear explanations and math vocabulary. Review labeling and how it is used to clarify work.

HW: Math Quest page 249 # 1-10 using repetitive addition strategy.

Looking for: Repetitive addition strategy

|Method 1 |Method 2 |

| | |

|48 X 9 = |48 |

| |48 |

|48 (1) |48 |

|+48 (2) |48 |

|98 |48 |

|+48 (3) |+ 48 |

|144 |288 |

|+48 (4) | |

|192 | |

|+48 (5) | |

|240 | |

|+48 (6) | |

|288 | |

3. Lesson 3 – By 10’s and 1’s

Prior Knowledge/introduction:

Do some questions on the board, multiply by 1, 10 and 100.

Have students write a rule to teach someone how to multiply by 1’s, 10’s 100’s

(open discussion up to friendly numbers and easy numbers to multiply by).

(Mr. Wendler’s Magic Numbers: 1, 2, 5, 10, 100)

Today’s Problem: (groups of 3)

There are 39 beads used to make one necklace. You want to make 9 necklaces, one for each of your 9 friends. How many beads will you need?

(Answer in at least 2 different ways – explanations and labels required)

Consolidation:

Look at the connection splitting strategy and “by 1’s and 10’s” strategy.

HW: 10 random questions (2 digit by 1 digit and 3 digit by 1 digit) using 1’s and 10’s strategy, Teacher produced sheet (multiply by 100’s), Speedy Multiplication sheet 6.

Looking for: By 10’s and 1’s stragegy

39 X 9 =

10 10 10 9

10 X 9 = 90

10 X 9 = 90 270 + 81 = 351

10 X 9 = 90

9 X 9 = 81

4. Lesson – By Place Value

Prior Knowledge/introduction:

Using the number 128, how many ways can you break this number up using “Mr. Wendler’s Magic Numbers”.

Today’s Problem: (groups of 2)

Mr. Wendler is training for the tip-toe Olympics. He tip-toes 278 metres each recess. He has trained now for 8 recesses in a row. How far has Mr. Wendler tip-toed?

(Answer in at least 2 different ways – explanations and labels required)

Consolidation:

Look at the connection between jumping/add-on strategy and multiplication

HW: 10 random questions (two and three digit by one digit), and one practice sheet on multiplying by 10’s and 100’s.

Looking for: Place Value stragegy

278 X 8 =

200 70 8

200 X 8 = 1600

70 X 8 = 560 2224

8 X 8 = 64

5. Lesson 5 – Magic Squares

Prior Knowledge/introduction:

Have children represent 4X3 using an array… (Discuss and work with elbow partner or table)

Review the idea of an array using teacher provided sheet (177) and base ten blocks on the overhead (12 X 14 and 23 X 11).

Draw base 10 blocks as magic square.

Discuss the connection between multiplication and area.

Bring up the ideas of area connected with magic numbers or 10’s and 1’s.

Today’s Problem: (groups of 2)

A bus can carry 32 students. Our school ordered 16 busses to take students to a hockey game. How many students can come on the trip?

(Answer in at least 2 different ways – explanations and labels required)

Consolidation:

Magic squares connected with place value (and 10’s and 1’s)

HW: Magic Square sheets provided by teacher. Practice sheet of multiplying 10’s and 100’s.

Looking for: Magic Square strategy 32 X 16 =

30 2

| | | |

|300 |20 |10 |

| | | |

|180 |12 |6 |

300 + 180 + 20 + 12 = 512

10 10 10 2

| | | | | |

|100 |100 |100 |20 |10 |

| | | | | |

|50 |50 |50 |10 |5 |

| | | | | |

|10 |10 |10 |2 |1 |

100 + 100 + 100 + 50 + 50 + 50 + 20 + 10 + 10 + 10 + 10 + 2 = 512

6. Lesson 6 – Practice strategies to far

Prior Knowledge/introduction:

Review Magic Square

Today’s Problem: (groups of 2, 3 or 4)

Mr. Wendler’s class had 23 students and each planted 25 seedlings. Ms. Sarte-Dance’s class had 32 students and each planted 20 seedlings. Which class planted more seedlings? How many more seedlings did they plant?

Consolidation:

Review strategies

HW: Random questions (2 digit by 2 digit, three digit by 1 digit and 3 digit by 2 digit)

7. Lesson 7 – Traditional long

Prior Knowledge/introduction:

Take up homework

Today’s Problem:

Ms. Boxer’s heart beats 72 times per minute. How many times will it beat in an hour and 5 minutes?

(Answer in at least 2 different ways – explanations and labels required)

Consolidation:

Look at the connection between magic squares, place value and traditional multiplication.

HW: Random questions (2digit by 1 digit and 2digit by 2digit)

Looking for: traditional long

72

X 65

10 (bottom ones X top ones = 5X2)

350 (bottom ones X top tens = 5X70)

120 (bottom tens X top ones = 60X2)

4200 (bottom tens X top tens = 60X70)

4680

The Clarkson hotel has to buy felt pads for the legs of their chairs and tables. There are 157 rooms and each has 2 chairs, a regular table and an end table. The hotel also has 3 recreation rooms, each room with 25 chairs and 3 large tables. Also there is a lobby with 3 rows of 8 chairs with a table at both ends of each row. How many felt pads does the hotel need to buy?

8. Lesson 8 – Traditional

Prior Knowledge/introduction:

Take up homework

Today’s Problem:

Ms. Hendry was building a patio. It was going to be the shape of a rectangle. The length was 83 patio stones and the width was 34 patio stones. How many patio stones would she need to make the patio?

(Answer in at least 2 different ways – explanations and labels required)

Consolidation:

Look at the connection between traditional long and traditional short multiplication.

HW: Random questions from math quest.

Looking for: traditional short

83

X 34

332 (bottom ones X top ones, carry the tens, then bottom ones X top tens)

2490 (bottom tens X top ones, carry the tens, then bottom tens X top tens)

2822

9. Lesson 8 – Traditional Practice

Prior Knowledge/introduction:

Take up homework

Today’s Problem:

Worksheets

10. Lesson 8 – Napier’s Bones

Prior Knowledge/introduction:

Take up homework

Teacher directed lesson

1 356 X 235 =

1 3 5 6

| |0 |0 |1 |1 |2 |

| |2 |6 |0 |2 | |

| |0 |0 |1 |1 |3 |

|3 |3 |9 |5 |8 | |

| |0 |1 |2 |3 |5 |

|1 |5 |5 |5 |0 | |

8 6 6 0

1 356 X 235 = 318 660

A few more good questions:

Ted’s dad drives 13 km one-way to work each day. One day a week he drives an additional 10 km round trip to a computer research company to do research. Based on a 5 day work week, how many km does he drive in four weeks?

Torie helped plan a family vacation to the Rocky Mountains. The car holds 125 litres of gasoline. It also can drive 56 km per litre of gasoline. Her father estimates it will take 3 tanks of gas to get to their destination. Gas costs $1.05 per litre. About how far will they travel? About how much will they spend on gasoline?

Samantha did 112 push-ups in 2 weeks. How many push ups could she do in 18 days?

Grade 4 – divide two-digit whole numbers by one-digit whole numbers

Grade 5 – divide three-digit whole numbers by one-digit whole numbers

Division

1. Lesson – Multiplication Chart

Prior Knowledge/introduction:

How many ways can you show 35 divided by 7?

Today’s Problem:

Using multiplication charts, in groups of 2, do quick problems. One person looks at a number in the square, runs the finger to the end number and says, (the number in the square) divided by (the end number). The other student answers.

Consolidation:

Discuss the connection between multiplication and division (and area).

HW:

Looking for:

2. Lesson 2 – Grouping

Prior Knowledge/introduction:

How many ways can you divide 1$ amongst 4 students?

Today’s Problem: (groups of 4)

Jamie’s grandmother brought home 128 shells from her beach vacation. She wants to divide the shells equally among her 4 grandchildren. How many shells does each grandchild receive?

Consolidation:

Students might think of 132 as 100 + 32. They may realize that 100 is four 25’s. The remaining 32, they may realize that 4 X 8 is 32, and divide the remaining shells. We are looking at friendly numbers and simple or common multiplications.

HW:

Looking for: Grouping

132 ÷ 4 =

25 25 25 25 = 100

5 5 5 5 = 20

3 3 3 3 = 12

33 33 33 33 132

3. Lesson 3 – Repetitive addition/subtraction

Prior Knowledge/introduction:

How many ways can you represent 20 divided by 4

Today’s Problem: (groups of 3)

144 baseballs are placed in trays for storage. Each tray holds 24 balls. How many trays are needed?

Consolidation:

One might repeatedly add from 0 to get to 144, or repeatedly subtract from 144 to get to 0. More advanced students will realize you can add or subtract in chunks.

HW:

Looking for: Repetitive addition /subtraction strategy

24 (1)

+ 24 (2)

48

+ 24 (3)

72

+ 24 (4) answer is 6 trays

96

+ 24 (5)

120

+ 24 (6)

144

4. Lesson 4 – Open Array (using area – magic squares)

Prior Knowledge/introduction:

A rectangle has an area of 20. One side has a length of 5. Draw the rectangle and figure out the length of the other side (think area/magic squares and multiplication)

Today’s Problem: (groups of 2)

There are 195 Ottawa 67’s hockey tickets to be distributed amongst 15 classes at ACES. The teachers will be using the tickets to motivate the students to do good work. How many tickets will each class get?

Consolidation:

Look for the connection between area, multiplication and division.

HW: Try 889 divided by 24

Looking for: use of open arrays

195 ÷ 15 =

| | |

|15 | |

| | |

|150 |10 |

| 45 |3 |

10 + 3 = 13

5. Lesson 5 – Understanding the algorithms

Prior Knowledge/introduction:

Today’s Problem: (groups of 3)

Lindsay has $387. She wants to buy pink sparkly tops (shirts). They are $17 each. How many shirts can she buy? How much money will she have left?

Consolidation:

Connect algorithm with repetitive subtraction and open array.

HW:

Looking for:

| 17 | 387 | |

| |- 170 |10 |

| | 217 | |

| |- 170 |10 |

| | 47 | |

| |- 34 |2 |

| | 13 |22 |

387 ÷ 17 = 22 R13

6. Lesson 6 – Understanding the algorithms

Prior Knowledge/introduction:

Today’s Problem: (groups of 2)

There are 904 km between Marcus’ house and their vacation destination. They are going to divide the trip into 4 sections with a pit stop in between each one. How many km is it between stops?

Consolidation:

Connect different strategies to algorithm

HW:

Looking for:

226

| 4 | 904 | |

| |- 8 | 8 means 800 |

| | 10 | |

| |- 8 | 8 means 80 |

| | 24 | |

| |- 24 | 24 means 24 |

| | 0 | |

7. Lesson 7 – Practice

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