Patterning Unit

What is the relationship between the number of shapes and the perimeter of the combined shapes?

e.g. 1 triangle = 3; 2 triangles = 4; 3 triangles = 5 and so on. The rule is n+2.

Do this for three types of shapes. What do you find?

Extension:

Activity – find the relationship between the number of frogs and the number of moves to get across to the other side of the swamp.

1. Chart the growth2. Graph the growth3. How many squares in the 8th figure4. How many in the nth?5. What kind of pattern is this?

Activity:

1. Create a chart up to the 5th term for the following rules:a) 2n + 1b) 3n – 1c) 12 – 2n

2. What do you notice is different about c?

3. What is the pattern rule for the following?

a)

1 2 3 414 10 6 2

b)

1 2 3 43 7 11 15

Show how to find a pattern for fractions (ex. 1/5, 2/15, 3/ 25…

Minds on

Write an expression for the nth term.

1. 1, 3, 5, 7…2. 1/1, ½, 1/3, ¼, 1/5…3. ½, 2/3, ¾, 4/5…

Activity:

Here is the beginning of a number pattern: 10, 20…

Extend the pattern in two different ways.

Represent each pattern in at least 4 different ways

Homework

Find the 60th term for the following patterns:

2, 4, 6, 8, 10

6, 9, 12, 15, 18

3, 7, 11, 15, 19

10, 15, 20, 25, 30

60, 55, 50, 45, 40

State the Rules for the patterns below.

1. Chart the growth2. Graph the growth3. How many small triangles in the 8th figure4. How many in the nth?5. What kind of pattern is this?

Activity

Is it better to receive one penny doubled every day for a month or a million dollars? Show how you know.

Minds on

What could the missing numbers be? How do you know? What is the rule for each?

1, ___, 3, ____, 5, 6…

1, ___, ____, 13, 17…

60, ___, ____, ____, _____, 10….

Word Problems

Phone Bill Budget The Aztec Cell Phone company charges $50 per month plus 15 cents per minute. The Southern Cell Phone Company charges no monthly fee but 25 cents per minute. Susan is trying to determine which company’s phone is right for her. Her budget is $60 a month. Which should she choose and why?

Graph and find the rule for:

Graph and find the rule for:

Solve the following in pairs