Big Ideas 4 - 6 Session 3

©Marian Small, 2011

Big Ideas 4 - 6Session 3


Continuing with..

• Tonight we will finish our work with number operations and go on to patterns and relations and statistics and probability.


Alternate algorithms

• We ended last time talking about the value of alternate strategies (or algorithms).


Would you…

• calculate 532 – 99 the same way you would calculate 532 – 111?

• Use a √ for yes and an x for no.


Would you…

• calculate 532 – 99 the same way you would calculate 532 – 111?

• Use a √ for yes and an x for no.

• Should students?


22 x 13• Here are two ways to represent 22 x 13.

22

x13

66

+220

286

Which one do you prefer?

Use √ for the left and x for the right.

20 2

10

3

200 20

60 6


What about division?

Let’s think about both

• what it means and

• how to calculate


Which representation?

• Which picture best shows what 72 ÷ 3 means? (You will vote soon.)


Which representation?

• Which picture best shows what 72 ÷ 3 means? (You will vote soon.)


Vote

• A for 1st picture

• B for 2nd picture

• C if you think they’re equally good

• D if you think neither is good

I will ask a few people to explain their thinking.


And what procedure?

• What do each of the procedures on the next screen help a student see better than the other ones?

• Vote A,B or C to tell me which you are willing to talk about in terms of what is good about it.

• I will call on people in each category.


115 ÷ 5 23 10 + 10 + 3

5 115 5 115 5 50 + 50 + 15

-100 - 50 10

15 65

- 15 - 50 10

0 15

- 15 3

0 23


What about estimating?

• Let’s think about estimating questions.

• It’s no longer just about rounding rules.

• Consider these questions.


I added….

• 3 numbers.

• One is little.

• One is close to double the other.

• The sum is 5000.

• What could the numbers be?

• Type your numbers on next empty screen.



I subtracted…

• a number from 3000.

• The result had the digits 3 and 4 in it.

• What could the subtraction have been?

• Write some numbers on next empty screen.



The product is..

• The product of two numbers is almost 400.

• What might the numbers be?

Raise your hand to respond.


I wonder..

• I divided []3[] by 4.

• The answer was a 3 digit number.

• Tell me anything about []3[] that you’re sure of.

Raise your hand to respond.



Patterns


WNCP Pattern Outcomes

• Grade 4- focus on identifying patterns and relationships in tables and charts

• Grade 5- focus on pattern rule to predict

• Grade 6- focus on table of value relationships


Here is a multiplication table

X 0 1 2 3 4 5 6 7 8 9

0 0 0 0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6 7 8 9

2 0 2 4 6 8 10 12 14 16 18

3 0 3 6 9 12 15 18 21 24 27

4 0 4 8 12 16 20 24 28 32 36

5 0 5 10 15 20 25 30 35 40 45

6 0 6 12 18 24 30 36 42 48 54

7 0 7 14 21 28 35 42 49 56 63

8 0 8 16 24 32 40 48 56 64 72

9 0 9 18 27 36 45 54 63 72 81



X 0 1 2 3 4 5 6 7 8 9

0 0 0 0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6 7 8 9

2 0 2 4 6 8 10 12 14 16 18

3 0 3 6 9 12 15 18 21 24 27

4 0 4 8 12 16 20 24 28 32 36

5 0 5 10 15 20 25 30 35 40 45

6 0 6 12 18 24 30 36 42 48 54

7 0 7 14 21 28 35 42 49 56 63

8 0 8 16 24 32 40 48 56 64 72

9 0 9 18 27 36 45 54 63 72 81


Big Idea



X 0 1 2 3 4 5 6 7 8 9

0 0 0 0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6 7 8 9

2 0 2 4 6 8 10 12 14 16 18

3 0 3 6 9 12 15 18 21 24 27

4 0 4 8 12 16 20 24 28 32 36

5 0 5 10 15 20 25 30 35 40 45

6 0 6 12 18 24 30 36 42 48 54

7 0 7 14 21 28 35 42 49 56 63

8 0 8 16 24 32 40 48 56 64 72

9 0 9 18 27 36 45 54 63 72 81


Big idea


Look at this

• To show the final digits of the multiples of 8:

01

2

3

45

6

7

8

9


Look at this

• To show the final digits of the multiples of 6. Someone take the pen.

01

2

3

45

6

7

8

9


Another big idea


Or another pattern

X 0 1 2 3 4 5 6 7 8 9

0 0 0 0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6 7 8 9

2 0 2 4 6 8 10 12 14 16 18

3 0 3 6 9 12 15 18 21 24 27

4 0 4 8 12 16 20 24 28 32 36

5 0 5 10 15 20 25 30 35 40 45

6 0 6 12 18 24 30 36 42 48 54

7 0 7 14 21 28 35 42 49 56 63

8 0 8 16 24 32 40 48 56 64 72

9 0 9 18 27 36 45 54 63 72 81


1 x 2 + 2 x 3 1 x 3 + 2 x 3

3 x 1 + 4 x 2 3 x 2+ 4 x 1


Move objects to compare 3 x 3 + 4 x 4 to 3 x 4 + 4 x 3


Picture a 100 chart

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100


Big Idea


How else could you…

• represent the pattern 2, 5, 8, 11,….









• What pattern do you see?

Term number Term value

1 2

2 5

3 8

4 11



• What pattern do you see?

Term number Term value Related pattern

1 2 3

2 5 6

3 8 9

4 11 12


Variables and equations

• Grade 4- problems as equations with unknowns; solve one-step equations

• Grade 5- single-variable, one-step equations

• Grade 6- generalizations written using variables; model equality preservation


Algebra big ideas


Try this

• What situation might 2w describe?

• Type some possibilities on the next screen.



Try this

• Jeff got $12 in allowance every week.

• What does 6 x w tell about the situation?

A: his allowance

B: his allowance in w weeks

C: his allowance in 2 xw weeks

D: his allowance in w ÷ 2 weeks


Try this

• Jeff got $12 in allowance every week.

• What does 12w tell about the situation?

• What equation would you solve to find out how many weeks until he had $156?


The solution is…

• The solution to an equation is x = 2.

• What might the equation have been?

• Type some possibilities on the next screen.



Respond by raising your hand


Data

• Grade 4- many-to-one correspondence for

pictographs and bar graphs

• Grade 5- double bar graphs

• Grade 6- line graphs


What’s going on?

• Vote for A or B in terms of which makes it easier for you to tell what’s going on?


A

• Kids who like chocolate chip cookies most: Jane, Kyle, Ravi, Shilpa, Elaine, Jar-Ye, Sindy, Amy, Liam

• Kids who like oatmeal cookies most: Aaron, Amanda, Diana, Carolyn, Geoffrey, Suhana, Jeremy, Terry-Lynn


B

Chocolate Chip

Oatmeal


B

Chocolate Chip

Oatmeal


Which graph would you use?

• Vote:

• A for bar graph with scale of 2

• B for bar graph with scale of 5

• C for pictograph with scale of 2

• D for pictograph with scale of 5


Let’s compare bar graphs

• Do the two graphs on the next two slides give you the same impression about the following data?

• Use √ for yes and x for no.

Favourite Pets

Dog 20

Cat 15

Rat 2


You choose


You choose


You choose


How do these differ in the impression they give? Raise

your hand.


What will happen

• I will show you a graph.

• I will mention some things you might think it shows well.

• If you think it is easy to see, click a happy face.

• If not, click a thumbs down.


What does this graph about how I divide my day show?


The big idea


Other important big ideas

• Pictographs and bar graphs are particularly useful for comparing frequency of data in different categories.

• Line graphs are particularly useful for showing relationships between quantities and trends.


Probability

• Grade 5- verbal comparisons of likelihood

• Grade 6- experimental/theoretical probability


Using probability language

• Choose which is most likely about a new kid joining a Grade 5 class:

• A: It’s a boy.

• B: The student is the same age as lots of other kids in the class.

• C: The student lives in the area.

• D: The student is human.


Now…

• You write a phrase that is:

• Almost certain

• Impossible

• Very likely

• Very unlikely


A Big Idea


You just flipped a coin and…

• You got

• H H H H H H H H H

Vote:

√ if you think a H next time

X if you think a T next time


Experimental probability

• You are going to create an experiment using ONE die.

• The result you want should happen about three-fourths of the time.

• What would you choose for your result?

• Some choices are on the next screen.


Choices

• A: an even number

• B: a number more than 2

• C: anything but 1

• D: a number less than 5


Big Ideas


Sharing Time

• I hope some of you have stories to share.


I am hoping that :

• you will try out one of the questions we discussed or, even better, your own question to bring out a big idea in number.

• We’ll talk about the results next time.

Big Ideas 4 - 6 Session 3

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