Patterns and Relations

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Grade 7: The Learning Equation Math

21.01 Patterns and Relations

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Patterns

Refresher pp 44-5

Learning Outcomes:

The student will:

predict and justify possible nth values of a number pattern.

Number Sequences

Look at each sequence below. Click the answer button to see the correct answer.

1,2,4,7,11,____,____,____,.
1,3,2,4,3,____,____,____,.
2,6,14,30,____,____,____,
3, 5, 9, 17,____,____,____,
4, 7,___, 25,____ , 97.

Source of sequences: Advantages of a Pattern-Based Curriculum

Make a Table

4 volleyball teams are playing in a round robin tournament where each team plays each other once. How many rounds will it take. A table helps organize the information for each game in each round needed.

Round/Game	Game 1	Game 2
Round 1	1 vs 2	3 vs 4
Round 2	1 vs 3	2 vs 4
Round 3	1 vs 4	2 vs 3

3 rounds are needed for the four team round robin.

Use a Diagram or Model

Sometimes a diagram makes it easier to see the next number in a series. Take the following:

1 3 6 10 15

Organizing the diagram gives:

	o	o oo	o oo ooo	o oo ooo oooo	o oo ooo oooo ooooo
Total	1	3	6	10	15
# Added:	1	2	3	4	5
	1st term	2nd term	3rd term	4th term	5th term	6th term	nth term

The 6th term will be 1 + 2 + 3 + 4 + 5 + 6 = 21

The 10th term will be 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 =55

The nth terms will be 1 + 2 + 3 + 4 + ..... + n

Find the nth Term

For each of the following sequences, write the mathematical expression that allows you to find the nth term.

Series	1, 2, 3, 4, 5, ...	1, 4, 9, 16, 25, ...
6 th term	6	36
10th term	10	100
nth term	n	n²

use patterns and relations to represent simple oral and written expressions as mathematical symbols, and vice versa.

Subtraction	Words for Operations
	minus	"a number minus 2"	x – 2
	difference between	"the difference between a number and 8"	x – 8
	from	"2 from a number"	n – 2
	less	"a number less 3"	n – 3
	less than	"3 less than a number"	y – 3
	fewer than	"2 fewer than a number"	y – 2
	decreased by	"a number decreased by 2"	x – 2
	take away	"a number take away 2"	x – 2
Addition	plus	"a number plus 2"	x + 2
	and	"3 and a number"	3 + n
	added to	"8 added to a number"	x + 8
	greater than	"3 greater than a number"	n + 3
	more than	"3 more than a number"	y + 3
	increased by	"a number increased by 2"	y + 2
	total	"the total length"	l ₁ + l ₂ + ź
	sum of	"The sum of the length and width"	l + w
Multiplication	times	"5 times a number"	5n
	product	"The product of 3 and a number"	3y
	at	"3 at 1.59"	3 ˇ 1.59
	double, triple, etc.	"double a number"	2x
	twice	"twice a number"	2y
	of (fractions of)	"three-fourths of a number"	(ž)y
Division	quotient of	"The quotient of 5 and a number"	5 ÷ n or 5/n
	Half of	"half of a number"	n/2
	goes into	"a number goes into 6 twice"	6/n = 2
	per	"The price is $8 per 50"	P = 8/50
Equals	Is, is the same as, gives, will be, was, is equivalent to