Download MATH - UNIT 1 Number Patterns - study guide

Problem Solving Steps
Step 1.
Step 2.
Step 3
Step 4
Step 5
Step 6
Read information carefully
Understand what the question is asking you do to.
Use information from the question to find your answer
Decide on a strategy to use.
Show your thinking
Write a final statement (sentence)
Strategies
 Use a pattern
 Use logic
 Work backwards
 Make a picture or a table
 Draw a chart or a graph
 Use a model
 Make an organized list
 Solve a simpler problem
 MATH UNIT 1 – NUMBER PATTERNS
Learning Goals (gr. 5)
I can find a pattern rule for a number
pattern
I can identify, extend, and create
patterns
I use patterns to pose and solve
problems
Learning Goals (gr. 6)
I can write a pattern rule for a number
pattern
I can identify, extend, and create
patterns
I use patterns to pose and solve
problems
I can describe and model patterns
I use patterns in a table to make
predictions
I use patterns to explore divisibility
rules
I can find the value of a missing
number in an equation
I use patterns to explore integers
Patterning Vocabulary
REPEATING PATTERN = a pattern that repeats  e.g. 4, 8, 4, 8, 4, 8
PATTERN CORE = the part of the pattern that repeats  e.g. 4, 6, 4, 6, 4, 6, 4,6 
4,6 is the core.
GROWING PATTERN = a pattern that gets bigger  e.g. 2, 4, 6, 8, 10
SHRINKING PATTERN = a pattern that gets smaller  e.g. 50, 45, 40, 35, 30
PATTERNING RULE = the math function (+, -, x, / ) to follow. To follow the pattern.
Start at ___________________. Add _____________ each time.
Increase (UP)
the number you add (+)
by ____________ each time
Decrease (DOWN) the number you subtract (-) by ____________ each time
Alternately – switch back and forth e.g. add 1, subtract 2, each time.
Number Patterns and Pattern Rules - strategies
To identify the pattern rule,
I find the difference between pairs of consecutive numbers in the pattern.
5 (+1) 6 (+2) 8 (+3) 11 (+4) 15
The pattern rule is: Start at 5. Add 1. Increase the number you add by 1 each time.
 To get the next 5 terms, continue to increase the number you add by 1 each time.
5,6,8,11,15,20,26,33,41,50…
2 (+3) 5 (+4) 9 (+3) 12 (+4) 16
The pattern rule is: Start at 2. Alternately add 3, then add 4.
 To get the next 5 terms, continue to add 3, then add 4.  2,5,9,12,16,19,23,26,30,33…
10 (-4) 6 (+5) 11 (-4) 7 (+5) 12
The pattern rule is: Start at 10. Alternately subtract 4, then add 5.
 To get the next 5 terms, continue to subtract 4, then add 5.  10,6,11,7,12,8,13,9,14,10…
Patterning vocabulary and definitions
Input/Output Machine  performs an operation (=add/subtract/divide by/multiply by) on a
number (the input) to produce another number (the output).
An operation is add, subtract, multiply or divide.
This input/output machine multiplies the input by 2.
Input
operation
6
X2
output
 12
What are multiples?  Start at a number, then count on by that number to get the
multiples of that number. To get the multiples of 3, start at 3 and count on by 3. 
3,6,9,12,15,…
Patterning vocabulary and definitions
(gr. 6) This input/output machine doubles each input, then adds 6. When the input is 1,
the output is 8. When the input is 4, the output is 14.

Input
operation
operation
Output
1
X2
2
+6
8
4
X2
8
+6
14
 I check all the inputs to make sure I have found the correct numbers and the
correct operations!!!
(Gr. 6) What is a recursive pattern?  In a recursive pattern, each term can be foundby
applying the pattern rule to the previous term.
Ex. Write the first 5 terms for a recursive pattern that starts at 7.
A pattern rule is: Start at 7. Multiply by 2, then add 1 each time.
7 x 2 + 1 = 15
15 x 2 + 1 = 31 31 x 2 + 1 = 63 63 x2 + 1 = 127
The first 5 terms of the pattern are: 7, 15, 31, 63, 127
Here is a recursive pattern: 1, 6, 11, 16, 21
To find the pattern rule, find the difference between each pair of consecutive terms.
The difference between each pair of consecutive terms is 5. Add 5 to each term to find
the next term.
1 (6-1=5) 6 (11-6=5) 11 (16-11=5) 16 (21-16=5) 21
Patterning vocabulary and definitions
(gr. 6) Number Patterns
Divisibility Rules: A whole number is divisible by:
2 = if it is an even number
3 sum of digits is divisible by 3 (The numbers that are divisible by 3 are multiples of 3)
4 if the number represented by the tens and ones digits is divisible by 4 (every multiple of 4 is divisible by 4)
5 last digit (the ones digit) is 0 or 5
6 if the number is divisible by 2 and by 3
8 if the number represented by the hundreds, tens, and ones digits is divisible by 8
9 if the sum of the digits is divisible by 9
10 if the ones digit is o
Patterning vocabulary and definitions
(Gr. 6) An equation is a statement that two things are equal.
e.g. 7 x 3 = 21
19 = 25-6
You solve an equation when you find the value of a missing number in an equation.
e.g. 163 = ? + 49
You can use an inverse operation to find the missing number  163 – 49 = ? (?=114)
e.g. ? divided by 6 = 144
The inverse operation here is multiplication. The number that is divided by 6 to get 144
= 144 x 6 = 864. This means that your answer is 864 divided by 6 = 144. Your solution is
864.
Multiplication and division are inverse operations. Addition and subtraction are also
inverse operations.
Patterning vocabulary and definitions
(gr. 6)
Numbers such as 24 and -18 are integers.
 You can represent integers on a number line. The number line may be vertical (as in
a thermometer) or horizontal (the number line to the left of 0 shows negative
numbers).
 You use integers to represent quantities that have both size and direction.
Hilde spent $ 25.00. This can be represented as - $ 25.
Tammy walked 5 steps forward. This can be represented at + 5 steps, or 5 steps.
Shannon swam to a depth of 50 m. This can be represented as - 50 m.
NOTE: If no sign is written, the integer is positive!
Strategies to use when you are stuck on a math problem
Prepare for success!!!!
GET UNSTUCK!  HOW???
 Represent the information in another way.
Rewrite the question in your own words. Reorganize the information. Draw a diagram or
use a table.
 Think about what you already know. Ask yourself:
 What facts am I given?
 What other problem have I done like this one?
 What do I know how to do that might help?
 What possible answers can I eliminate?
 Try a problem-solving strategy  draw a diagram/make a table/use a
pattern
 Collaborate (ask two friends or Madame Acx) – unless it is a test, of course!