Grade 3 Patterning and Algebra

Unit ONE

Name:_____________

Ontario Mathematics Curriculum Grades 1 to 8, 1997Strand: Patterning and AlgebraGrade: 3

© Math Wizards, 2003All rights reservedDeveloped by T. TaskerMay be photocopied for classroom use. Further replication or commercial use is strictlyprohibited.

Overall Expectations:- recognize that patterning results from repetition- identify, extend, and create linear and non-linear geometric patterns, number and measurementpatterns, and patterns in their environment- create charts to display patterns- identify relationships between and among patterns

* All specific expectations are covered by this unit with the exception of:P7:use environmental data to create models of patterns (eg. Monday - sunny, Tuesday - rainy)and display the patterns on a chart which is covered in the daily mathematical routines.

Patterning & AlgebraOur Patterned Discoveries

As a class, let’s meet at the carpet with our patterned discoveries and read A Cloakfor the Dreamer written by Aileen Friedman and illustrated by Kim Howard. Afterreading the book we will share our patterned discoveries.

There are four attributes that can change in a pattern.Attribute Example

Colour

Size

Position

Shape

Draw your patterned discovery Describe the patterns in yourdiscovery:_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Describe some of Ivan’s (the oldest son) pattern choices in his cloak:______________________________________________________________________________________________________________________________________________________________________________________________________

Describe some of Alex’s (the middle son) pattern choices in his two cloaks:______________________________________________________________________________________________________________________________________________________________________________________________________

Describe Misha’s pattern choice:______________________________________________________________________________________________________________________________________________________________________________________________________

Why didn’t Misha’s pattern work?______________________________________________________________________________________________________________________________________________________________________________________________________

How did his father and brother fix his cloak?______________________________________________________________________________________________________________________________________________________________________________________________________Grade 3 PAactivity001 covers:P2:identify patterns in which at least two attributes change (eg. size, colour)P4:discuss the choice of a pattern rule© Math Wizards, 2003

Patterning & AlgebraPatterning Rules

The core of a pattern is the shortest string of objects that repeat. Let’s take a lookat the pattern below:

The core of this pattern is:

The core of the pattern is also given a name. Each DIFFERENT object in the coreof the pattern is given a letter. This pattern core is named ABCD.

Let’s try another example:

What is the core of the pattern?

What is the name of the pattern? _______________________________________

What attributes change in the pattern?______________________________________________________________________________________________________________________________________________________________________________________________________

On the next page, Merlin has started some patterns but could not finish them. Would you finish the patterns for Merlin? Be sure to also name the pattern coreand list the attributes that change.

Finish the Patterns for Merlin

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Name the pattern:______________How many attributes change?_____Name the attributes:________________________________________________________

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Name the pattern:______________How many attributes change?_____Name the attributes:_________________________________________________________

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Name the pattern:______________How many attributes change?_____Name the attributes:_________________________________________________________

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Name the pattern:______________How many attributes change?_____Name the attributes:_________________________________________________________

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Grade 3 PAactivity002 covers:P1:understand patterns in which operations are repeated (eg. multiplication), transformation are repeated, or multiple changes are made to attributesP2:identify patterns in which at least two attributes change (eg. size, colour)© Math Wizards, 2003

Patterning & AlgebraFinish the Pattern For Merlin

A pattern is ____________________________________.----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Name the pattern:______________How many attributes change?_____Name the attributes:________________________________________________________

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Name the pattern:______________How many attributes change?_____Name the attributes:_________________________________________________________

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Name the pattern:______________How many attributes change?_____Name the attributes:_________________________________________________________

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Name the pattern:______________How many attributes change?_____Name the attributes:_________________________________________________________

Merlin has a problem!

Merlin and Charlotte are racing up the TWELVE steps to the top of the tower. Charlotte lands on every second step and Merlin lands on every third step. Whichsteps will they both land on?

Grade 3 PAactivity003 covers:P1:understand patterns in which operations are repeated (eg. multiplication), transformations are repeated, or multiple changes are made toattributesP2:identify patterns in which at least two attributes change (eg. size, colour)© Math Wizards, 2003

Patterning & AlgebraThe longest pattern in the school

Merlin has a challenge for you. In groups of four, he is challenging you to makethe longest pattern possible. You may use any math manipulative, or you maymake your own pattern shapes with paper, pencils and scissors.

Our longest pattern information

The materials used:____________________________________________________________________________

A picture of our pattern:

The length:___________________

What attributes change:_________________________________________________________

How many attributeschange?___________________

The name of ourpattern:___________________

Why our group decided to choose this pattern:________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Grade 3 G3PAactivity004 covers:P3:create a pattern in which two or more attributes change (eg. size, colour, position)P4:discuss the choice of a pattern rule© Math Wizards, 2003

Patterning and AlgebraMake Your Own Pattern

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Name your pattern:_____________How many attributes change?_____Name the attributes:_________________________________________________________

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Name your pattern:_____________How many attributes change?_____Name the attributes:_________________________________________________________

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Name your pattern:_____________How many attributes change?_____Name the attributes:_________________________________________________________

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Name your pattern:_____________How many attributes change?_____Name the attributes:_________________________________________________________

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Merlin has a Problem!

On January 1st, Charlotte gave Merlin 5 bugs. On February 1st, she gave him 10bugs. If Charlotte were to keep following this pattern of giving Merlin twice asmany bugs as she gave him the month before, how many bugs would he have onJune 1st?

Grade 3 PAactivity005 covers:P3:create a pattern in which two or more attributes change (eg. size, colour, position)© Math Wizards, 2003

Patterning and AlgebraNumber Patterns with Adding

Charlotte loves playing number leap frog with Merlin. But Merlin needs your helpfiguring out Charlotte’s leaps. Help Merlin solve Charlotte’s number patterns andwrite down her pattern rule for Merlin.

Remember a pattern is a repeating core or a repeating operation.

Leap frog A2 4 6

The pattern rule:_____________________________________________________

Leap frog B5 8

The pattern rule:_____________________________________________________

Leap frog C2 6

The pattern rule:_____________________________________________________

Leap frog D3 5 7

The pattern rule:_____________________________________________________

Leap frog E21 23 25

The pattern rule:_____________________________________________________

Leap frog F13 17 21

The pattern rule:_____________________________________________________

Leap frog G5 10

The pattern rule:_____________________________________________________

2 + 2 = = = =

3 + 5 = = = =

4 + 9 = = = =

5 + 2 = = = =

6 + 7 = = = =

Calculators are a fun tool to use to explore patterns. Punch in an addition sentencelike (1 + 1 =). If you keep pressing the (=) button you can quickly build a numberpattern.What would be the pattern rule:_________________________________________

Explore the following number patterns with your calculator. Each time you pressthe (=) button write down the number you get.

Make up your own calculator patterns and record them below:

Grade 3 PAactivity006 covers:P1: understand patterns in which operations are repeated (eg. multiplication), transformation are repeated, or multiple changes are made toattributesP5:given a rule, extend a pattern and describe it in informal mathematical language (eg. starting at 3, add 3 to each number to create a pattern)P9:use a calculator and a computer application to explore patterns© Math Wizards, 2003

Patterning & AlgebraNumber Patterns with Subtraction

Charlotte loves playing number leap frog with Merlin. But Merlin needs your helpfiguring out Charlotte’s leaps. Solve Charlotte’s number patterns and write downher pattern rule for Merlin.

Remember a pattern is _______________________________________________.

Leap frog A24 22

The pattern rule:_____________________________________________________

Leap frog B73 70 67

The pattern rule:_____________________________________________________

Leap frog C19 18

The pattern rule:_____________________________________________________

Leap frog D17 17 17

The pattern rule:_____________________________________________________

Leap frog E210 200 190

The pattern rule:_____________________________________________________

Leap frog F84 80

The pattern rule:_____________________________________________________

Leap frog G65 60 55

The pattern rule:_____________________________________________________

- 333 ====

- ====4 55

7 - ==4 2 ==

8 7 - 4 ====

9 - ===2 6 =

Calculators are a fun tool to use to explore patterns. Punch in a subtractionsentence like (9 - 1=). If you keep pressing the (=) button you can quickly subtracta number pattern.What would be the pattern rule:_________________________________________

Explore the following number patterns with your calculator. Each time you pressthe (=) button write down the number you get.

Make up your own calculator patterns and record them below:

Grade 3 PAactivity007 covers:P1:understand patterns in which operations are repeated (eg. multiplication), transformations are repeated, or multiple changes are made toattributes.P5:given a rule, extend a pattern and describe it in informal mathematical language (eg. starting at 3, add 3 to each number to create a pattern)P9:use a calculator and a computer application to explore patterns© Math Wizards, 2003

Patterning and AlgebraThe Shape of Number Patterns

Merlin has some special patterns. Finish both patterns, describe the pattern ruleand “draw” the pattern on the graph paper.

2 4 6

The pattern rule:_____________________________________________________

The next pattern is a multiplication pattern. Each number doubles itself.

1 2 4

The pattern rule:_____________________________________________________

Draw it:

How are the two pattern graphs different?________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Grade 3 PAactivity008 covers:P5:given a rule, extend a pattern and describe it in informal mathematical language (eg. starting at 3, add 3 to each number to create a pattern)© Math Wizards, 2003

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Patterning & AlgebraPatterns in Hundreds Charts

Merlin loves finding patterns in hundreds charts. He is wondering if you can findyour own pattern.

Pick a number between 2 and 10. I pick _________________________________.

Colour that number in on the hundreds chart. Then skip count using the numberyou picked until 100 (for example: if you picked 2, you would colour 2 in thehundreds chart and then count by twos and colour in 4, 6, 8, . . . all the way up to100).

Describe the pattern you made in the hundreds chart__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Merlin has a Problem!

Merlin has a $10.00 roll of quarters for lunch money. Lunch costs 75 cents eachday. How many days will the roll of quarters last? Will there be any quarters leftover?

Grade 3 PAactivity009 covers:P6:use addition and subtraction facts to generate simple patterns in a hundreds chart© Math Wizards, 2003

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100

Multiplication Problems:6 x 1 = ________6 x 2 = ________6 x 3 = ________6 x 4 = ________6 x 5 = ________6 x 6 = ________6 x 7 = ________

Division Problems:36 x 4 = ________32 x 4 = ________28 x 4 = ________24 x 4 = ________20 x 4 = ________16 x 4 = ________12 x 4 = ________

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100

Patterning & AlgebraOperation Relations

Using the hundreds chart below, colour in the following addition pattern: startingwith 6 add 6 to each number. Afterwards, solve the multiplication problems to theright, using your calculator.

Describe the similarities between the addition pattern and the multiplicationproblems.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Using your coloured in hundreds chart, what do you think 6 x 14 would be? _____Why?____________________________________________________________________________________________________________________________________

Using the hundreds chart below, colour in the following subtraction pattern:starting with 100 subtract 4 to each number. Afterwards, solve the divisionproblems to the right using your calculator.

Describe the similarities between the subtraction pattern and the division problems.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Using your coloured in hundreds chart, what do you think 72 x 4 would be? _____Why?____________________________________________________________________________________________________________________________________Grade 3 PAactivity010 covers:P8:identify relationships between addition, subtraction, multiplication, and division© Math Wizards, 2003