Multiplication and division; Page 82 lesson 1: Multiplier à l'aide du doublement

This is the first lesson of our new math unit on multipliction and division. In this first lesson students learn vocabulary related to multiplication as well as a strategy called doubling.

Key vocabulary

facteur - One of the numbers being multiplied in a multiplication.

produit - The answer to a multiplication question. For example the product of 2X3 is 6.

matrice - This is a way of laying out objects in even rows and columns. It is easy to find how many objects are in the matrice by multiplying the rows by the columns.

Le doublement

Le doublement is a strategy used to find the answer to multiplication questions that students are unfamiliar with. Students must double one of the factors to find the product. For example

4X6=24; In this multiplication the factors are 4 and 6 and the product is 24. I can use this equation to help me find the product of 8X6 by doubling one of the factors.

So...

I double the 4 to 8. Then I know that 24+24 is 48. So I know that 8X6=48. It may seem like a roundabout way to get the answer but this strategy helps to develop number sense by making students double and halve numbers.

Subtracting numbers mentally; lesson 9 page 62

Our textbook explains 3 strategies to subtract numbers mentally. I will explain the strategies below.

Strategy 1: Using easier numbers

In this strategy students are taught to change the numbers in the equation to easier to subtract numbers. For example:

516-299=

In this equation 299 becomes 300 and 516 becomes 517. I have added 1 to each of the numbers so my new equation is:

517-300=200

It is much easier to mentally subtract 300 from 517.

Strategy 2: Changing just one of the numbers in the equation

In this strategy students change just ONE of the numbers in the equation. For example:

347-195=

In this strategy students change just one of the numbers in the equation. So, 195 becomes 200. My new equation is:

347-200=147

Students must remember to add the 5 they added to the original equation so the answer is actually 152. I find this strategy to be quite tricky. I prefer the first strategy.

Strategy 3: Counting by intervals

In this strategy students count up by intervals starting from the smaller number. They must either count by tens, hundreds or thousands depending on the number. For example in the equation:

532-240=

Students must count by 100 starting at 240. So that is 340, 440. That makes 200.

Students then count by tens from 440, so that makes 450, 460, 470, 480, 490, 500, 510, 520, 530. That makes 90, which students then add to the 200 making 290.

Finally students count 2 (for the 532) By combining those numbers students should arrive at 292 as the answer for 532-240. This strategy seems tricky but I find it less tricky to use than strategy #2.

Five step Method for solving problems

I use this method when teaching problem solving to students. I feel it helps to organize the problem and figure out which strategy will work best. Students also receive credit for each individual step. The process is the important part. That is what I am marking.

Step 1; Ce qu'on cherche (What are we looking for)

In this step students must identify the question in the problem. They must write a sentence to explain the problem in their own words.

Step 2; Ta démarche (How will you solve the problem)

In this step students must state what they will do to solve the problem. For example, I will multiply 9 by 8 to get the answer.

Step 3; Phrase maths (The math equation)

In this step students write the equation then solve it. They must show their work

Step 4; La réponse (The answer)

In this step students write a sentence to give their answer. The answer must be directly linked to the first step. This is why the sentence is so important.

Step 5; Vérification (Students check their answer)

In this step students must check their answer. Sometimes I omit this step depending on whether or not it is possible. Usually if the problem involves an operation such as division or multiplication it is possible.

Lesson 5 p 49

This lesson is on mental addition strategies. In the lesson students are given 3 strategies to use when adding large numbers mentally. It is important that students familiarize themselves with all three strategies because they will be called upon to use them in different situations. If students are having difficulty they should return to the lesson and review the strategies. We went through them in class so students should be somewhat familiar with these concepts.

Strategy 1 (André)

Andre's strategy is called "Easy to use numbers". In this strategy he will change a number to an easier to add number. In the example Andre is trying to add 198+343. So he changes 198 to 200. The answer is 543, but Andre must remember to subtract the original 2 from when he changed 198 to 200. So the answer to 198+343 is 541.

This strategy works well when the numbers are close to an even number. I like this strategy best and I personally use it whenever I can.

Strategy 2 (Trang)

Trang's strategy is similar but a little bit more abstract. It is called "addition by intervals". You need to be able to visualize the numbers and their place value. Trang is trying to add 130+348. So he adds 170 to 300. This gives him 470. He then counts by TEN from 470. So that is 480, 490, 500, 510 + 8 makes 518.

Strategy 3 (Alexia)

Alexia's strategy is called "Adding in steps from left to right" She starts by adding the 100s then the 10s then the 1s. This is a bit tricky because when you are adding if you get a number higher than 10 you need to know what to do. In the example given Alexia runs into this problem and the explanation is not that clear but she does this.

353+260=

3 hundreds +2 hundreds = 500

5 tens +6 tens= 11 (here is the problem. Alexia has to add another 100 to the previous step.

3 ones + 0 ones=3

So her final answer is 613.

I found this strategy to be the trickiest however it is worth working through it to make sense of it. The exercises are designed to make the students select a strategy to complete the addition mentally. Students should not shy away from any particular strategy but should attempt to use all three of them.

I have put a link to a mental math page at the bottom of this page. There are also links to explore on the course outline page.

Lesson 3 page 44-45 Venn Diagrams

Check out the link on Venn diagrams at the bottom of this page. November 5

Page 40, 41

This lesson continues to build on and review place value concepts. Students must be familiar with the following vocabulary.

• Ordonner: To put in the correct order. Either from smallest to biggest or biggest to smallest.
• Comparer: To compare numbers. Sometimes using < or > or =

P. 32 - 33 À ton tour

1. Write 5236 in words in French. Par example. 23 - vingt-trois.

2. Dessine le nombre en utilisant le matériel base 10. Souviens toi. Un gros cube=1000. Une plaque = 100, Un batôn = 10, un petit cube = 1

3. Forme décomposé = 3000+200+60+3 fait 3263. Alors écris 5955 en forme décomposé.

4. Écris sous forme symbolique la représentation. Forme symbolique = 2345. Or, the regular way we write numbers. Alors écris le nombre représenté par les dessins de matériel base 10.

5. Write the numbers from question 4 in words. Important note, writing numbers in French is very tricky. Use the Robert Junior or be prepared to check your work tomorrow.

6. Write the numbers the normal way.

7. Write each number the regular way and "sous forme décomposé". You should know at this point what "décomposé" means.

If you have come this far. Relax, take a break. You will have time to finish tomorrow.

October 30, 2008

Hello everyone. Here are some explanations for pages 36 and 37 which are due tomorrow.

8. Write these numbers in "forme décomposé"

9. Represent or draw the numbers using base ten material.

10. Write each number from question 8 in words. (watch the spelling) Click on this link to go to my page on writing French numbers.

How to write French numbers

11. a) I had quite a few questions about question 11. You need a calculator to do it. You simply punch in the number 578. Then explain how you did it. The point is to make students reflect on the use of a calculator. It seems simple but students must be able to make the link between place value and the calculator.

b) Explain how to get the target number. Hint, you have to use one of the for operations. The bottom number in the chart is the target number.

12. Explain Thomas mistake.

13. You must use base ten material. We will do this activity in class together.

14. Use a place value chart to represent the numbers. You can find an example of the place value chart on page 35.

15. What is the place value of each of the underlined numbers.

16. Explain the error the student made.

Page 28-29 Montre ce que tu sais: This assignment is your best preparation for the test on Wednesday. If you do not understand something from this assignment and you just cannot seem to get it come and see me at lunch recess.

1. Copy the table and fill in the missing numbers by looking at the pattern.

2. Find the mistakes in the addition table. Explain what you did to find each error. Copy the table and correct the errors.

3. The pyramid has 7 levels. The top level has one cube, the next one down has 4 and so on.

a) make a table to note the pattern.
b) How many cubes will there be on the 7th level.
c) Is it possible to have a level with 20 cubes? How do you know?

4. The length of the side of a hexagon is 1 unit. The perimeter of each unit is in the table and the pattern is extended.

a) Copy and complete the table.
b) Write a rule for the pattern.
c) Use the pattern to predict the perimeter of the figure forming 8 hexagons.
d) What is the perimeter of the figure formed with 15 hexagons.
e) Is it possible for a figure to have a perimeter of 30 units? What about 40 units. Explain how you know.

5.

a) Represent this pattern with tokens.
b) Write a rule for this pattern.
c) How many objects form the 7th figure.
d) Is it possible for a figure to be made of 15 objects.

6. For each equation:

• Explain what it means.
• Solve the equation. Use a different method each time.
• Write a word problem that could be solved using the equation.

a) Write an equation which could be used to find out how many marguerites Theresa has.
b) How many marguerites are there?

8. Mahmood has 15 small vehicles. He places them on 3 shelves so that there is the same number of vehicles on each shelf.

a) Write 2 equations that you can solve to find the number of vehicles on each shelf.
b) Solve each equation. How many cars on each shelf.
Lesson 5, page 24

Hint: Use your times tables at the back of your agenda if you do not know them by heart.

1. Students must write an multiplication equation based on the matrix in the picture. Students must be careful to use the correct numbers.

2. Write a division equation based on the matrix.

3. Explain what each equation means. For example the first equation could have an explanation such as:

Something multiplied by 3 equals 9.

Afterward solve the equation.

4. For the four equations in number 3 students must create a word problem based on that equation and then solve it.

5. Students must select the equation that would solve the problem.

"Sholeh, Marc, Tasha, and Cedric are training for a relay race. Sholeh went around the track twice and passed the baton to Cedriv. Cedric went around twice and passed the baton to Marc. Marc went around the track twice and passed the baton to Tasha. Which equation could you use to find out the total number of times around the track." Explain why you chose that equation.

6. Use these numbers and some of the symbols to.

a) Write one equation, how many different equations can you make?

b) Solve each equation and use a different method for each one. See page 23 for the different methods.

c) Write a problem for each equation.

Nb. Minimum 3 equations and 3 problems for #6.

7. Salim has 7 friends. Each friend has 12 books.

a) Write an equation which represents the total number of books for Salim's friends.

b) Solve the problem.