unit 10: patterns in number and...

Teacher GuideWestern Canadian

Unit 10: Patterns in Numberand Geometry

A D D I S O N W E S L E YA D D I S O N W E S L E Y Western

UNIT

“In Grades 3–5, students shouldinvestigate numerical andgeometric patterns and expressthem mathematically in wordsand symbols. They shouldanalyze the structure of thepattern and how it grows orchanges, organize thisinformation systematically, anduse their analysis to developgeneralizations about themathematical relationships inthe pattern.”

Principles and Standards for School

Mathematics, NCTM, 2000

Mathematics Background

What Are the Big Ideas?

• Patterns are a regular occurrence in mathematics, and they can beidentified, extended, and described.

• Patterns can be described using words, pictures, and pattern rules.

• A table displays positional relationships in patterns and is animportant early stage in the development of algebraic thinking andreasoning.

How Will the Concepts Develop?

Students explore different number patterns and demonstrateunderstanding by writing pattern rules, and completing or extendingpatterns in tables. Students identify, extend, and create geometricpatterns that show growth, using Pattern Blocks and Colour Tiles. Theycreate patterns by changing two, and then three attributes of figures.Students make and examine patterns on grids, and use a computer tocreate patterns.

Why Are These Concepts Important?

Active exploration of patterning helps students to develop effectivereasoning skills. As students gain experience in identifying, describing,extending, and creating patterns, they develop a foundation formeaningful mathematics learning in later grades. As students investigatepatterns, their work is closely connected with other mathematicalstrands, such as Number, and Shape and Space.

FOCUS STRANDPatterns and Relations

SUPPORTING STRANDSNumber: Number Operations,Shape and Space: 3-D Objectsand 2-D Shapes

ii Unit 10: Patterns in Number and Geometry

10 Patterns in Number and Geometry

Unit 10: Patterns in Number and Geometry iii

Lesson 1:Exploring Number PatternsLesson 2:Number Patterns in Tables

Curriculum Overview

General Outcome• Students investigate, establish and

communicate rules for numericalpatterns, including those found inthe home, and use these rules tomake predictions.

Specific Outcome• Students make predictions based on

addition and multiplication patterns.(PR3)

LaunchIndoor Recess!

Cluster 1: Number Patterns

General Outcome• Students investigate, establish and

communicate rules for numerical andnon-numerical patterns, includingthose found in the home, and usethese rules to make predictions.

Specific Outcomes• Students use objects and concrete

models to explain the rule for apattern, . . . (PR2)

• Students make predictions based onaddition and multiplication patterns.(PR3)

Cluster 2: Geometry PatternsLesson 3:Exploring Growing PatternsLesson 4:Strategies ToolkitLesson 5:Patterns with Two AttributesChangingLesson 6:Patterns with Three AttributesChangingLesson 7:Patterns on GridsTechnology:Patterns on a Computer

Show What You Know

Unit ProblemIndoor Recess!

iv Unit 10: Patterns in Number and Geometry

Curriculum across the Grades

Grade 2

Students identify anddescribe patterns,including numerical andnon-numerical patterns.

Students create, extend,and describe patternsincluding numerical andnon-numerical patterns.

Students translatepatterns from one modeto another: manipulatives,diagrams, charts,calculators, words,symbols.

Grade 3

Students use objects andconcrete models toexplain the rule of apattern, such as thosefound on addition andmultiplication charts.

Students make predictionsbased on addition andmultiplication patterns.

Grade 4

Students identify andexplain mathematicalrelationships andpatterns, usinggrids/tables, objects,Venn/Carroll/treediagrams, graphs, objectsor models, andtechnology.

Students make and justifypredictions, usingnumerical and non-numerical patterns.

Students use skipcounting (forward andbackward) to support anunderstanding of patternsin multiplication anddivision.

Materials for This Unit

Have marshmallows and toothpicks available for Explore in Lesson 4.

Roll and Go!For Extra Practice (Appropriate for use after Lesson 1)Materials: Roll and Go! (Master 10.6), number cubes

The work students do: Students work in pairs. Eachstudent chooses a number between 5 and 10. This is thestart of a number pattern. Each student then rolls thenumber cube. This is the number that is added eachtime. Students write the next 5 numbers in their pattern.Students trade patterns with their partner and find theirpartner’s pattern rule, making sure that all numbers fitthe pattern rule.

Take It Further: Students choose a number between31 and 40. This is the sixth number of a numberpattern. Students roll the number cube to find thenumber that was added each time. They work backwardto find the first 5 numbers in their pattern. Studentstrade patterns as above.

Mathematical/LogicalPartner Activity

Additional Activities

Missing BlocksFor Extra Practice (Appropriate for use after Lesson 5)Materials: Missing Blocks (Master 10.8), AttributeBlocks, cardboard divider

The work students do: Students work with a partner.Players sit facing each other, with a cardboard dividerbetween them. Each player uses 12 Attribute Blocks tomake a pattern with 2 attributes changing. Each playerremoves one block from his pattern and places it out ofhis opponent’s sight. The cardboard divider is removed.Each player tries to guess her or his opponent’s missingblock. If a player is correct, she gets 1 point. Playersrepeat, each time with a different pattern. The firstplayer to get 5 points wins.

Take It Further: Students repeat the activity, this timeremoving two blocks.

Visual/SpatialPartner Activity

Patterning Mix-UpFor Extra Practice (Appropriate for use after Lesson 3)Materials: Patterning Mix-Up (Master 10.7), 1-cm grid paper, scissors

The work students do: Students work in groups of4. Each student folds, and cuts, a sheet of grid paperinto 4 congruent rectangles. He writes a pattern rule fora growing pattern in section 1, uses squares to show thefirst 3 frames of the pattern in section 2, makes a tablefor the pattern in section 3, and writes the number ofsquares in the 5th frame in section 4. Each group putsall its sections together and mixes them up. Groupstrade sections, then sort the mixed up patterns. The firstgroup to correctly sort the patterns wins.

Take It Further: Groups use only section 4 cards.They trade these sections and try to find correspondingpattern rules.

Logical/Mathematical/SocialGroup Activity

Unit 10: Patterns in Number and Geometry v

Tower PowerFor Extension (Appropriate for use after Lesson 5)Materials: Tower Power (Master 10.9), Pattern Blocks

The work students do: Students work alone. Thestudent builds a hexagonal-shaped tower by stackingdifferent coloured Pattern Blocks on top of a yellowPattern Block. As the tower increases in height, each faceof the tower will show a colour pattern from the base up.The student tries to create repeating colour patterns thatare several layers in height. To do this, each time a yellowPattern Block is placed on top of the stack, the studentshould repeat the colour pattern below it. Student shouldrecord the colour pattern for each face of the tower.

Take It Further: Students predict the colours in the 10th and 20th layers.

Kinesthetic/Visual/SpatialIndividual Activity

vi Unit 10: Patterns in Number and Geometry

Planning for Unit 10

Planning for Instruction

Lesson Time Materials Program Support

Suggested Unit time: About 2–3 weeks

Unit 10: Patterns in Number and Geometry vii

Purpose Tools and Process Recording and Reporting

Planning for Assessment

2 Unit 10 • Launch • Student page 370

Indoor Recess!

LESSON ORGANIZER

Curriculum Focus: Activate prior learning about patterns innumber and geometry.Vocabulary: pattern

10 –15 min

L A U N C H

ASSUMED PRIOR KNOWLEDGE

Students can identify and describe patterns.✓

ACTIVATE PRIOR LEARNING

Engage students in a discussion about thethings they like to do during indoor recess.

Ask:• What is your favourite activity during

indoor recess?• Are there any patterns in this activity?

Invite students to examine the picture of theindoor recess in the Student Book.

Ask questions, such as:• Where do you see patterns in the picture?

(I can see a pattern in the checkerboard, in the frameof the bulletin board, in the bracelets, in the dominogame, in the window frames, in the floor, in thepicture on the wall, in one boy’s shirt, in one girl’stop, in the puzzle on the bulletin board, on thecomputer screen, in the building block structure, andin the circles the boy is tracing.)

• What pattern do you see in the checkerboard?(Alternate squares are red.) In the buildingblock structure? (There are 4 blocks in each layer,but the blocks get smaller as you go up.) In the window frame? (There are 4 rectangles of equal size in each row.)

• What kind of pattern is in the checkerboard?(A colour pattern)

• What patterns do you see in your classroom?(I see an alternating pattern in the floor. Every othertile is black. I see a pattern in the desks. The desksare arranged in groups, with 6 desks in each group.)

Tell students that, in this unit, they will learnabout number patterns and geometric patterns.They will display patterns in tables and grids.At the end of the unit, students will demonstratewhat they have learned by designing an activityfor children when recess is indoors.

LITERATURE CONNECTIONS FOR THE UNIT

Dave’s Down-to-Earth Rock Shop by Stuart J. Murphy.HarperCollins Children’s Books, 2000. ISBN 0060280190Young collectors will be fascinated by all there is to know aboutrocks and about classifying — sorting and organizing objects byattributes such as colour, shape, or size.

Grandma’s Button Box by Linda Williams Aber. Kane Press, 2002.ISBN 1575651106When she spills her grandmother’s button box, Kelly and hercousins try to sort them by size, colour, and shape and they earnGrandma’s gratitude.

What’s Next, Nina? by Sue Kassirer. Kane Press, 2001.ISBN 1575651068Nina is invited to a party but the only dress that fits her is an“icky plain one.” To spruce it up, she borrows a necklace fromher sister without asking. When it breaks, she is left toreconstruct it with a friend at the bead store, and it is there thatthe pattern building begins.

DIAGNOSTIC ASSESSMENT

What to Look For

✔ Students can identifyand describepatterns.

What to Do

Extra Support:

Students who have difficulty identifying patterns may benefit from working in steps:• Which pattern do you see in the numbers?• Which pattern do you see in the figures?• Which pattern do you see in the colours?• Which pattern do you see that grows?Work on this skill during Lessons 1, 2, 3, 5, and 6.

Students who have difficulty describing a pattern may benefit from modelling thepattern with concrete materials. Students could model patterns with changingattributes, such as colour, shape, and size. They could use manipulatives to explorepatterns that use simple math operations.Work on this skill throughout the unit.

Unit 10 • Launch • Student page 371 3

Some students may benefit from using the virtualmanipulatives on the e-Tools CD-ROM.

The e-Tools appropriate for this unit include Geometry Shapesand Place-Value Blocks.

REACHING ALL LEARNERS

4 Unit 10 • Lesson 1 • Student page 372

Exploring NumberPatterns

LESSON ORGANIZER

Curriculum Focus: Identify, extend, and create numberpatterns. (PR3)Teacher Materials� overhead transparency of a hundred chart (PM 13)� overhead markersStudent Materials Optional� hundred charts (PM 13) � Step-by-Step 1 (Master 10.10)� calculators � Extra Practice 1 (Master 10.18)Vocabulary: pattern ruleAssessment: Master 10.2 Ongoing Observations: Patterns in Number and Geometry

40–50 min

L E S S O N 1

Key Math Learnings1. A pattern rule that describes a number pattern can be used

to extend it.2. The pattern rule for a number pattern may be stated more

than one way.

BEFORE Get S tar ted

Invite students to examine the hundred charton page 372 of the Student Book. Ask:• What pattern do you see?

(The number 20 is coloured. Then, every othernumber is coloured.)

• How can you describe the pattern? (Start at 20. Count on by 2s.)

• How can you describe the pattern in adifferent way? (Start at 20. Colour all even numbers.)

• What are the next three numbers in thepattern? (32, 34, 36) How do you know? (I counted on by 2s from 30.)

Before students begin Explore, they mustunderstand how to describe and extend apattern. Make sure students know they mustalways give the start number.

Present Explore. Have hundred charts available.

DURING Exp lore

Ongoing Assessment: Observe and Listen

As students work, ask questions, such as:• What is the pattern in the first set of

numbers? (Start at 2. Add 2 each time.) Thesecond set of numbers? (Start at 1. Write eachcounting number. After 2, write 1 between each pairof counting numbers.) The third set ofnumbers? (Start at 90. Subtract 4 each time.) Thefourth set of numbers? (Start at 1. Add 1. Thenumber you add goes up by 1 each time.)

Encourage students to use different startingnumbers for their own patterns and to createpatterns that contain addition as well assubtraction. When they use subtraction, theymust begin with a large number.

Ensure students understand they should writethe next three numbers in each of their ownpatterns on a separate sheet of paper beforethey trade patterns with a classmate.

32, 34, 36

12, 14, 161, 6, 1

70, 66, 6222, 29, 37

Unit 10 • Lesson 1 • Student page 373 5

Alternative ExploreStudents work in small groups to play the game, “Around theWorld.” Students form a circle. One student picks the startnumber for a number pattern. The student on her or his rightdecides on the pattern rule, then names the next number in thepattern. One student records the pattern. Play continues witheach student naming the next number in the pattern, until eachstudent has had 3 turns. Players then use the same first twonumbers to create a number pattern using a different pattern rule.

Early FinishersHave students write their own pattern rule, then write the first 5 numbers of their pattern. Encourage students to begin theirpatterns with numbers greater than 20.

Common Misconceptions➤Students forget to include the start number in their pattern rule.How to Help: Encourage students to create answer blanks to befilled in as they work: Start at _________._____________________________________.

ESL StrategiesHave students model number patterns pictorially, using a number line.


AFTER Connec t

Invite volunteers to share one of theirclassmate’s number patterns with the class.

Ask questions, such as:• What number pattern did your classmate

write? (3, 5, 8, 12, 17, ...)• What are the next three numbers in your

classmate’s pattern? (23, 30, 38)• How did you find these numbers?

(I used a pattern rule. The pattern rule is: Start at 3.Add 2. The number you add goes up by 1 each time.)

Use the pattern rules in Connect. Reinforce theidea that patterns can be described in differentways. Ensure students realize that a patternrule tells which numbers belong to the pattern,as well as which numbers do not.

Share how patterns can be used to predict. Forexample, every seventh day is a Monday. IfJune 3 is a Monday, so are June 10, 17, and 24.

Prac t i ce

Have hundred charts available for questions 1, 2, 3, 4, and 6. Question 5 requires acalculator.

Assessment Focus: Question 6

Remind students that they can use a singleoperation, such as addition or multiplication; acombination of operations, such as addition andsubtraction; and repeating or growing patterns.Students should demonstrate that numberpatterns may be described in different ways.

Students who need extra support to completeAssessment Focus questions may benefit fromthe Step-by-Step masters (Masters 10.10–10.15).

Sample Answers1. a) Start at 13. Add 5 each time.

b) Start at 22. Subtract 3 each time.2. a) Start at 5. Add 1. The number you add goes up by 1 each

time.b) Write each counting number. Start at 1. Write 1 between

1 and 2. Write 1, 1, between 2 and 3, and between eachfollowing pair of counting numbers.

4. a) 2, 4, 6, 8, 10, 12 b) 1, 4, 7, 10, 13, 16c) 50, 43, 36, 29, 22, 15

5. a) Use 4 as the start number: 4, 8, 16, 32, 64b) Use 5 as the start number. Multiply by 3 each time.5, 15, 45, 135, 405

6. Start at 2. Add 2 each time: 2, 4, 6, 8, 10, ...Start at 2. Multiply by 2 each time: 2, 4, 8, 16, 32, ...Start at 2. Add 2. The number you add goes up by 1 eachtime: 2, 4, 7, 11, 16, ...

REFLECT: I chose question 3a. Look at the first two numbers inthe pattern. What do you have to do to get from 41 to 45?You have to add 4. Check to see if adding 4 to each numbergives you the next number in the pattern: 49 + 4 = 53, 53 + 4 = 57, 57 + 4 = 61, 61 + 4 = 65, 65 + 4 = 69. Yes,adding 4 works. So, the pattern rule is: Start at 41. Add 4 each time.


ASSESSMENT FOR LEARNING

What to Look For

Understanding concepts ✔ Students understand that a pattern

rule can describe a number pattern.

✔ Students understand that a patternrule can be used to extend a pattern.

Applying procedures✔ Students can create a number pattern

from a given pattern rule.

What to Do

Extra Support: Students may benefit from modelling numberpatterns with counters.Students can use Step-by-Step 1 (Master 10.10) to completequestion 6.

Extra Practice: Students can do the Additional Activity, Rolland Go! (Master 10.6).Students can complete Extra Practice 1 (Master 10.18).

Extension: Have students use a calculator to investigate numberpatterns with multiplication and/or large numbers.

Recording and ReportingMaster 10.2 Ongoing Observations:Patterns in Number and Geometry

Numbers Every DayStudents need to be able to write number words to one hundred.Reinforce and repeat this activity throughout the year.

38 43 48 7 4 1

20 26 33

53 57

1 1

89 41

Sixty-threeEighty-nineTwenty-sixThirty-one


L E S S O N 2

Number Patterns inTables

Key Math Learnings1. A table can be used to identify and display a

number pattern.2. The patterns in a table can be used to extend the table.

LESSON ORGANIZER

Curriculum Focus: Display number patterns in tables. (PR3)Student Materials Optional� 2-column charts (PM 17) � hundred charts (PM 13)� 3-column charts (PM 18) � Step-by-Step 2 (Master 10.11)

� Extra Practice 1 (Master 10.18)Assessment: Master 10.2 Ongoing Observations: Patterns in Number and Geometry

40–50 min

Numbers Every DayFor 21 + 45, add 20 and 45 to get 65, and then add 1 to get66. For 35 + 99, add 35 and 100 to get 135, and thensubtract 1 to get 134. For 17 + 79, add 17 and 80 to get 97,and then subtract 1 to get 96. For 52 + 18, add 50 and 18 toget 68, and then add 2 to get 70. For 19 + 27, add 20 and27 to get 47, and then subtract 1 to get 46.

= 66= 134= 96= 70= 46

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^


Draw a 2-column table on the board. Label thecolumn headings as shown. Have a student sayhow many fingers and thumbs are on 1 hand, 2 hands, 3 hands, and so on. Extend the table.

Ask:• What patterns do you see in the table?

(In the first column, the numbers start at 1 and goup by 1 each time. In the second column, thenumbers start at 5 and go up by 5 each time.)

• Why do you think numbers are written in a table? (A table is easier to read, and it makes iteasier to see number patterns.)

Present Explore. Have hundred charts available.

DURING Exp lore


Ask questions, such as:• How many sections can Sabina paint in

1 hour? (3) In 2 hours? (6) In 3 hours? (9) In 4 hours? (12) In 5 hours? (15)

• What is the pattern in the number of sections painted? (Add 3 for each hour Sabina paints.)

• How long will it take Sabina to paint 21 sections? (7 hours) How do you know? (I extended the table by continuing the pattern. I kept adding 3 for each hour added.)

Number of Number of fingershands and thumbs

1 5

2 10

3 15


Alternative ExploreMaterials: play money coins (PM 27); 2-column charts (PM 17)Have students choose 1 type of coin (not 1¢). Students create a2-column table, with columns labelled “Number of Coins” and“Total Amount.” Students use 1, 2, 3, and then 4 coins tocomplete the first 4 rows of the table, then examine their tablesto find a pattern rule. They use the pattern rule or extend thetable to find the total amount of 8 and 11 coins.

Early FinishersHave students use the tables in Explore or Connect to write wordproblems that can be solved using the table. Students tradeproblems with a classmate, and use the table to solve theirclassmate’s problems.


AFTER Connec t

Ask questions, such as:• How do you know if your results are correct?

(I coloured a hundred chart. The seventh colourednumber was 21.)

• How is a pattern in a table different from thepatterns in Lesson 1? (There are two columns ofnumbers. There can be a pattern in each column.)

Review Connect. Discuss the patterns in the table.Students can look at each column separately tosee that as the time increases by 1 hour, the litresof water lost increase by 2.

In later grades, students will investigate thepatterns that relate the columns in a table; that is,each number in the 2nd column is 2 times thecorresponding number in the 1st column.

Some students may see this relationship. Askthem to predict how much water will be lost in20 hours, then 24 hours; Ask how long it isbefore 50 L, then 100 L are lost. Have students

explain the strategies they used to find their answers.

Prac t i ce

Provide 2-column charts for questions 1 and 2.Provide 3-column charts for question 3. Havehundred charts available for all questions.

To save time, use a 3-column chart to fill in thedata in question 3. Photocopy this chart and give itto students who find copying tables difficult. Thatway, students have only to complete the table.


Students identify the pattern rule for the 2ndrow, then extend the pattern to find the outputnumber for 6 and the input number for 12.Students look at the rows separately to see that asthe input number increases by 1, the outputnumber also increases by 1. They could thenextend the table to include the required numbers.

18

365

4

32

Sample Answers1. a) First column: Start at 1. Add 1 each time.

Second column: Start at 6. Add 6 each time.b) First column: Start at 1. Add 1 each time.

Second column: Start at 1. Multiply by 2 each time.2. The pattern rule for the number of stars is: Start at 1. Add 1.

The number you add goes up by 1 each time. There will be 22 stars in Row 7.

3. There are 3 pattern rules:First column: Start at1. Add 1 each time.Second column: Start at 3. Add 3 each time.Third column: Start at 4. Add 4 each time.

4. a) For the “In” row: Start at 2. Add 1 each time.For the “Out” row: Start at 6. Add 1 each time.

b) 6 is the next number in the pattern in the “In” row. The next number in the “Out” row is 10. So, 10 comes out.

c) Extend the “Out” row until we reach 12.Out: 6, 7, 8, 9, 10, 11, 12This is the 7th number.Extend the “In” row until the 7th number.In: 2, 3, 4, 5, 6, 7, 8So, for 12 to come out, 8 must go in.

REFLECT: A table makes it easier to display data and to see,and then extend, number patterns. When I completed thetable for Sabina’s fence painting, it was easy to see thepattern; add 3 each hour. I could have figured it out without atable, but it would have taken me much longer.



What to Look For

Understanding concepts ✔ Students understand that a table can

be used to identify and displaynumber patterns.

✔ Students understand that the patternsin a table can be used to extend the table.

Applying procedures✔ Students can extend number patterns

in tables using a pattern rule.

What to Do

Extra Support: Have students who have difficulty identifyingnumber patterns in a table subtract consecutive pairs of numbersto find the increase (or decrease) each time.Students can use Step-by-Step 2 (Master 10.11) to completequestion 4.

Extra Practice: Have students use 2-column charts to maketables; for example, the number of wheels on 1 car, 2 cars, 3 cars, and so on; the number of sides in 1 triangle, 2 triangles, 3 triangles, and so on.Students can complete Extra Practice 1 (Master 10.18).

Extension: Have students use a given pattern rule to workbackward to create a corresponding table. They could thendescribe a real-life situation that fits their data.


567

12

47

111622

22

89

2427

30

12

28

3236

40

10

8


Exploring GrowingPatterns

Key Math Learnings1. A growing pattern is a pattern that grows in number from

one frame to the next.2. A pattern rule that describes a growing pattern can be used

to extend it.3. A table can be used to display and identify a growing pattern.

LESSON ORGANIZER

Curriculum Focus: Identify, extend, and create growingpatterns. (PR2, PR3)Teacher Materials� pennies� Pattern Blocks for the overhead projectorStudent Materials Optional� Pattern Blocks (PM 25) � triangular grid paper (PM 24)� Colour Tiles or congruent � Step-by-Step 3 (Master 10.12)

squares � Extra Practice 2 (Master 10.19)� 2-column charts (PM 17)� 1-cm grid paper (PM 20)Vocabulary: growing patternAssessment: Master 10.2 Ongoing Observations: Patterns in Number and Geometry

40–50 min

L E S S O N 3

TEACHING TIPAs students begin to create growingpatterns, keep the concept simple

by not involving colour in thepatterns. If you are not able to

provide a student withmanipulatives of the same colour,tell students to ignore the colours.Colour should only be introduced

once students have gainedexperience and confidence with

growing patterns. Note that we usethe word “frame” to describe each

picture in a growing pattern.


Invite students to examine the growing patternon page 378 of the Student Book.

Place a penny on the overhead projector. Tellstudents that this is the first frame of a growingpattern. Show students the second frame. Ask:• What happened from Frame 1 to Frame 2?

(One more penny was added.)

Show students the third frame. Ask:• What happened from Frame 2 to Frame 3?

(One more penny was added.)• What pattern do you see in the frames?

(Each frame has 1 more penny than the framebefore it.)

• Why do you think we call this pattern agrowing pattern? (It is called a growing pattern because it grows innumber from one frame to the next.)

Show students the fourth frame. Ask:• Does the pattern apply to this frame also?

(Yes, one more penny was added from Frame 3 toFrame 4.)

• How many pennies will be in Frame 5? (5)

Numbers Every DayFor 11, 13, 15, 17, ..., the pattern rule is: Start at 11. Add 2 each time. Enter on the TI-108 calculator, thenpress . For 67, 64, 61, 58, ..., the pattern rule is: Start at 67. Subtract 3 each time. Enter , then press

. For 111, 222, 333, 444, ..., the pattern rule is: Start at 111. Add 111 each time. Enter , then press

.==

=111+111

==

=3–67

==

=2+11


Alternative ExploreMaterials: toothpicksStudents use toothpicks to create growing patterns. Demonstrate how to create a triangle with 3 toothpicks, a squarewith 4 toothpicks, and a pentagon with 5 toothpicks. In this case, students can move from one frame to the next by adding 1 toothpick.

Early FinishersHave students use 1-cm grid paper to create a growing pattern.Students make a table to record their growing pattern.

Common Misconceptions➤Students keep adding to the original frame, rather than

showing the individual frames.How to Help: Fold a strip of paper into sections. Label thesections Frame 1, Frame 2, and so on. Students can construct orrecord a frame in each section.


Present Explore. Remind students that they are toshow the first five frames of each of theirgrowing patterns. They should save bothpatterns to show and share with another pair ofclassmates. If you do not have enough blocks toenable students to do this, have them sketchtheir patterns on square or triangular grid paper.

DURING Exp lore


Ask questions, such as:• Which Pattern Block did you choose?

(The orange square)• What happened to your pattern from Frame 1

to Frame 2? (We added 2 orange squares.)• How many orange squares are in Frame 5? (9)• What is your pattern rule?

(Start with 1 square. Add 2 squares each time.)• Do both of your patterns follow the same rule?

(No, our second pattern rule is: Start at 3. Add 3 each time.)

AFTER Connec t

Have pairs of students use overhead PatternBlocks on an overhead projector to model theirgrowing patterns. Invite a volunteer to describeeach pattern and to state the pattern rule. Ask:• How is your growing pattern different from

your classmates’? (We had three Pattern Blocksin Frame 1. They had 1 Pattern Block in Frame 1.)

• What do you see when you count the PatternBlocks in each Frame? (There is a pattern. Twogreen triangles are added to each frame.)

• What is the pattern rule for that growingpattern? (Start at 1. Add 2 each time.)

Review Connect. Tell students that when theyexplore a growing pattern, they should look ateach frame and see how it differs from theprevious frame.

Sample Answers1. a)

b)

b), c)

c)

3. a), b) In each pattern, one congruent square is added to eachend of the previous frame. The frames keep the same basic shape. The pattern rules differ. The first pattern rule is: Start at 1. Add 4 each time. The second pattern rule is: Start at 4. Add 3 each time.

Frame 4 Frame 5 Frame 6

Frame 4 Frame 5 Frame 6

Frame 4 Frame 5

Frame 6

Ask:• How are Frames 1 and 2 different?

(Frame 2 has two more trapezoids than Frame 1.)• How are Frames 2 and 3 different?

(Frame 3 has two more trapezoids than Frame 2.)• What is the growing pattern?

(Start at 1. Add two trapezoids each time.)

It is important for students to realize that theycan model a growing pattern in a table. Tellstudents that a table makes it easier to identifyand extend a pattern. If they had to find thenumber of trapezoids in Frame 8 of the pattern,it would take much longer to build all 8 framesthan if they extended the pattern in the table.Also, they may not have enough trapezoids tobuild all 8 frames.

Prac t i ce

Have Pattern Blocks available for questions 1, 6, and 7. Have Colour Tiles or congruentsquares available for questions 3, 4, 5, and 7.Have 2-column charts available for questions 1, 3, 5, 6, and 7. Have 1-cm grid paperavailable for question 5.


Students should make a growing pattern thatfollows a pattern rule. Some students mightcreate a simple pattern while stronger mathstudents might create complex patterns.Students should describe their pattern, clearlyexplaining how it changes from one frame tothe next. A student who fully understands theconcepts of this lesson will explain the numberpatterns that are associated with the growingpattern.


Frame

123456

Numberof Blocks

123456

Frame

123456

Numberof Blocks

136

101521

` a) Start at 1. Add 1 each time.

b), c) Start at 1. Add 2. The number you add goes up by 1 each time.

5. c)

6. a), b)

By continuing the patterns,I extended the table and found that Frame 5 would have 15 green blocks, 10 blue blocks, and 5 yellow blocks.

7.

Frame 1 has one tile. In Frame 2, one tile is placed on eachedge of the first tile. In Frame 3, 1 tile is placed on eachoutside edge of Frame 2. In Frame 4, 1 tile is placed on eachoutside edge of Frame 3. The pattern rule for the number oftiles in a frame is: Start at 1. Add 4. The number you addgoes up by 4 each time.

REFLECT: A table makes it easier to see the number pattern that ispart of a growing pattern. By extending the table, I can tell howmany objects will be in a frame that is not shown. Otherwise, I would have to draw or model all the frames to find out.

Frame 1 Frame 2 Frame 3 Frame 4



What to Look For

Understanding concepts ✔ Students understand that a growing

pattern involves a number pattern.

Applying procedures✔ Students can use a table to identify

and extend a growing pattern.

✔ Students can apply a pattern rule toextend or create a growing pattern.

Communication✔ Students can explain how a pattern

progresses from frame to frame.

What to Do

Extra Support: Have students use Colour Tiles to create agrowing pattern that follows a simple pattern rule, such as “Start at 1. Add 1 each time.”Students can use Step-by-Step 3 (Master 10.12) to completequestion 7.

Extra Practice: Students can do the Additional Activity,Patterning Mix-up (Master 10.7).Students can complete Extra Practice 2 (Master 10.19).

Extensions: Students use Colour Tiles to make the first fourframes of a growing pattern. They show a classmate Frame 4, then Frame 3. They challenge their classmate to createFrame 2, then Frame 1. Students compare their frames with theoriginal first two frames.


Start at 8. Add 4 each time.

Frame

123456

Numberof Blocks

81216202428

Frame

12345

Numberof GreenBlocks

369

1215

Numberof BlueBlocks

2468

10

Numberof Yellow

Blocks12345


Strategies Toolkit

Key Math LearningYou can use a pattern to help solve a problem.

LESSON ORGANIZER

Curriculum Focus: Interpret a problem and select anappropriate strategy. (PR2, PR3)Student Materials Optional� toothpicks � Plasticine� marshmallows � straws� Pattern Blocks (PM 25)� 2-column charts (PM 17)� 3-column charts (PM 18)Assessment: PM 1 Inquiry Process Check List, PM 3 Self-Assessment: Problem Solving

40–50 min

L E S S O N 4


Present Explore. Ask questions, such as:• How many marshmallows and toothpicks

did Joe use to build Level 1? (8 marshmallows and 12 toothpicks)

• How many marshmallows and toothpicksdid Joe use to build the first 2 levels? (12 marshmallows and 20 toothpicks)

DURING Exp lore

Ongoing Observations: Observe and Listen

Ask questions, such as:• What strategy will you use?

(I will make a table.)• What pattern do you see in your table?

(For each level, 4 marshmallows and 8 toothpicksare added.)

• How many levels can Joe make with 30 marshmallows? (6; he would have 2 marshmallows left over.)

• Suppose Joe ate 3 marshmallows. Howwould this change the height of his tower?(He would only be able to build 5 levels.)

• How would your answer change if Joe onlyhad 30 toothpicks? (He would only be able to build 3 levels.)

AFTER Connec t

Present Connect. Ask:• What patterns do you see in the blocks?

(For the triangles: Start at 3. Add 3 each time. For the trapezoids: Start at 1. Add 1 each time.)

• How could you solve this problem anotherway? (I could use Pattern Blocks to model the problem.)

Prac t i ce

Have Pattern Blocks, 2-column charts, and 3-column charts available. Encourage studentsto refer to the Strategies list to assist inselecting an appropriate strategy.

7Yes; 2 triangles and8 trapezoids

6

Sample AnswersREFLECT: When I am solving a problem in which something

changes in a regular way, I can use a pattern to help me solvethe problem. I can model the first few frames of the pattern,then record the pattern in a table. The table makes it easy tosee the pattern. I can then extend the table to solve theproblem.



What to Look For

Problem solving✔ Students can select an appropriate

strategy to solve a problem.

✔ Students can justify their solutions.

Communicating✔ Students can describe their strategy

clearly, using appropriate language.

What to Do

Extra Support: In Connect, have students stack Pattern Blocksas indicated.

Extra Practice: Have students repeat Explore, but this timebuild a triangular tower that is a prism. (Answer: 9 levels)

Extension: Challenge students to write a problem similar toPractice question 1. Their towers should be built with 3 differenttypes of Pattern Blocks. Students should solve their own problems.

Recording and ReportingPM 1 Inquiry Process Check ListPM 3 Self-Assessment: Problem Solving

Common Misconceptions➤Students think that adding another level in Explore adds

8 more marshmallows.How to Help: Have students use marshmallows and toothpicksto build Level 1, and then add on Level 2.


10 squares and 15 hexagons

7


Patterns with TwoAttributes Changing

Key Math Learnings1. An attribute is used to describe an object.2. The core of a repeating pattern is the smallest part

that repeats.3. Repeating patterns can be extended by identifying,

then repeating, the core.

LESSON ORGANIZER

Curriculum Focus: Create patterns in which two attributeschange. (PR2)Teacher Materials� Attribute BlocksStudent Materials Optional� Attribute Blocks � triangular grid paper (PM 24)� Pattern Blocks (PM 25) � 1-cm grid paper (PM 20)

� 2-cm grid paper (PM 21)� Step-by-Step 5 (Master 10.13)� Extra Practice 2 (Master 10.19)

Vocabulary: repeating pattern, coreAssessment: Master 10.2 Ongoing Observations: Patterns in Number and Geometry

80–100 min

L E S S O N 5

TEACHING TIPA set of Attribute Blocks contains

only 1 of each type of block. Eachpair of students will need access toseveral sets of Attribute Blocks to

make one pattern. So, several pairsof students need to share severalsets of Attribute Blocks. If you donot have enough Attribute Blocks,students could use Pattern Blocksinstead, with attributes of shapeand position. Alternatively, you

could colour and cut out differentsize squares that students could

use, with attributes of size, colour,and position.


Invite students to examine the table on page 384 of the Student Book. Ask:• What does the term attribute mean?

(An attribute is a characteristic of a person or thing.)

Remind students of the attributes they used tosort objects in Unit 5, Lessons 1 and 2. Tell themthat they will use the same attributes to makepatterns. Have students identify the attribute thatwas not in Unit 5 (position). Use an AttributeBlock on the overhead projector or draw it on theboard to illustrate how its position can change.

In this lesson and in Lesson 6, the attribute of position ismodelled in terms of rotations. Since your curriculumdoes not address rotations in Grade 3, you may wish tomodel other ways of describing position (for example, a rectangle lying down, a rectangle standing up).

Curr i cu lum Focus

Making ConnectionsArt: Have students look for patterns in which two attributeschange in books or magazines, and on wallpaper. Studentsshould describe the core of each pattern they find.


Show students a set of Attribute Blocks. Havevolunteers use these blocks to demonstrate allthe attributes shown in the table.

Present Explore. Remind students to record theirwork. Have square grid paper and triangulargrid paper available for students to do this.Have students suggest how they will draw toshow thick and thin.

DURING Exp lore


Ask questions, such as:• How did you make your pattern?

(I decided on the two attributes that I wanted tochange, and then I chose Attribute Blocks that had myattributes. I used these blocks to make my pattern.)

• What two attributes changed in yourpartner’s pattern? (Colour and shape)

• What is the smallest part of the pattern thatrepeats? (Two red triangles, one yellow square)

• How did you continue your partner’s pattern? (I found the smallest part of her pattern thatrepeated, then I added this part, in the same order,to the end of her pattern.)

• Why did you colour your picture? (Colour is one of the attributes I used. If I did notcolour my picture, you would not be able to see my pattern.)

AFTER Connec t

Invite students to share their patterns with theclass. Have volunteers identify the two attributesthat change. On the board, make a list of thedifferent pairs of attributes that were used.

Explain to students that the core of a repeatingpattern is the smallest part that repeats.Students must understand how to identify thecore, and then extend the pattern.

Early FinishersStudents work in pairs. Each pair needs Attribute Blocks, anumber cube, and the table on page 384 of the Student Book.Each number on the cube represents an attribute in the table.(For example, 1 is size, 2 is shape, ..., 6 is student choice.) One student rolls the cube twice to select two different attributes.If the student rolls the same number twice, he must roll again.The other student creates a pattern with these two attributeschanging. Students switch roles.

Common Misconceptions➤Students have difficulty changing two attributes at a time.How to Help: Have students create a pattern in which oneattribute changes (for example, shape: circle, square, circle,square). Below this pattern, have students create another patternin which a different attribute changes (for example, colour: redcircle, blue circle, red circle, blue circle). Have students combinethe patterns to make a pattern in which two attributes change(for example, red circle, blue square, red circle, blue square).


Sample Answers1. a) Size and thickness

b) Colour and positionc) Colour and shape

4. Pattern rule for dominoes: horizontal domino, with 2 dots onthe left and 4 dots on the right; vertical domino, with 1 dot onthe top and 5 dots on the bottomPattern rule for scissors: 2 red scissors pointing up, 2 purplescissors pointing down

6. a)

b)

Both patterns have the same two changing attributes, colourand shape. Both patterns are made of red squares and bluetriangles. The first pattern has a core of 2 red squares and 1 blue triangle. The second pattern has a core of 3 bluetriangles and 1 red square. So, even though the sameattributes are changing, the cores are different and thepatterns are not the same.

Blue Blue Blue Red Blue Blue BlueRed

Red RedBlue

Red RedBlue

Red RedBlue

Ask:• Can two patterns with the same two

attributes changing look different? How?(Yes. If the attributes are colour and size, onepattern could have the core: big red circle, little bluecircle, while the other pattern could have the core:little yellow triangle, 2 big red triangles.)

Have volunteers demonstrate patterns that have the same two attributes changing, butdifferent cores.

Review the examples in Connect. Have studentslook at the patterns they drew in Explore andidentify the core and the pattern rule for each pattern.

Have students look around the classroom forother objects they could use to make patterns.This relates to Practice questions 2 to 5, wherestudents identify and describe patterns that donot use Attribute Blocks.

Prac t i ce

Have Attribute Blocks and Pattern Blocksavailable for question 6.


Students should demonstrate their ability tocreate patterns in which two attributes change.Most students will create simple patterns,while some will create more complex patternsby rotating blocks or piling blocks on top ofeach other to change the thickness. Indescribing each pattern, students shouldinclude the two attributes used, the core of thepattern, and the pattern rule.


Red Purple PurpleRed

Numbers Every DayStudents could use related multiplication facts to divide. For 24 � 4, students could recall that 4 � 6 = 24, and so 24 � 4 is 6. Students could also use a counting-on strategy.For 35 � 5, students could count on by 5s until they reach 35.They would count on 7 times.



What to Look For

Understanding concepts ✔ Students understand that a repeating

pattern has a core.

Applying procedures✔ Students can create a pattern in which

two attributes change.

✔ Students can identify the changingattributes, the core, and the patternrule for a repeating pattern.

Communicating✔ Students use appropriate terminology

when identifying attributes anddescribing repeating patterns.

What to Do

Extra Support: Have students use Attribute Blocks to makepatterns in which one attribute changes, for example: big, small,big, small.Students can use Step-by-Step 5 (Master 10.13) to completequestion 6.

Extra Practice: Have students use Attribute Blocks to create onepattern for every possible pair of attributes. (For example, size andshape, size and colour, size and thickness, and so on. There are10 possible combinations.)Students can do the Additional Activity, Missing Blocks (Master 10.8).Students can complete Extra Practice 2 (Master 10.19).

Extension: Students can do the Additional Activity, Tower Power(Master 10.9).


7. Two attributes: size and positionPattern rule: 2 large green triangles, 1 small green triangleturned to the right.

REFLECT: The pattern I made in question 7 has the pattern rule: 2 large green triangles, 1 small green triangle turned to theright. All the objects are green triangles, but some are smalland some are large. The large triangles are pointing up, whilethe small triangles are pointing to the right. All the triangleshave the same thickness. So, two attributes change: size andposition.

G GG

G G G

= 6= 7= 6


Patterns with ThreeAttributes Changing

Key Math LearningA repeating pattern with three attributes that change can beextended by identifying, then repeating, the core.

LESSON ORGANIZER

Curriculum Focus: Create patterns in which three attributeschange. (PR2)Student Materials Optional� Attribute Blocks � Step-by-Step 6 (Master 10.14)

� Extra Practice 3 (Master 10.20)Assessment: Master 10.2 Ongoing Observations: Patterns in Number and Geometry

80–100 min

L E S S O N 6


Present Explore. Remind students that the coreof their patterns should repeat at least twotimes, and that students should draw picturesto record their work. Ensure studentsunderstand their patterns must have threeattributes changing.

DURING Exp lore


Ask questions, such as:• Which Attribute Block did you start with?

(The large red triangle)• Which block could you use next?

(The small blue square)• Which attributes change?

(Size, colour, and shape)• Which block will you put next?

(Small red triangle)

• Which attributes changed this time? (Colour and shape)

• What is the core of your pattern? (Large red triangle, small blue square, small red triangle)

• How many times does your core repeat? (2 times)

• How do you know that three attributeschange? (The size, colour, and shape change.)

AFTER Connec t

Invite students to share their patterns with theclass. Have volunteers identify the threeattributes that change. Ask questions, such as:• How did you decide which block to add at

each step? (I chose an Attribute Block to start mypattern. My partner added a second block. I decidedwhat attributes had changed. Colour and shape hadchanged. I then chose another block so that a differentattribute changed. I chose size. I now had the core ofmy pattern. I then kept repeating the core.)

$10$20$30

Numbers Every DayStudents should round $4.99 to $5. They could multiply thenumber of books by 5, or they could count on by 5s. Forexample, for 6 books, students could count on by 5s until theyhave counted 6 numbers: 5, 10, 15, 20, 25, 30. 6 � 5 = 30; 6 books would cost about $30.

• Can two patterns with the same threeattributes changing look different? How?(Yes. If the attributes are colour, shape, and size, onepattern could have the core: big red circle, small bluecircle, big red triangle, while the other pattern couldhave the core: small yellow triangle, 2 big redtriangles, 1 small blue circle.)

• What happens if you change the order of theblocks in each core? (The pattern rule changes and the pattern isdifferent.)

Have volunteers demonstrate patterns that havethe same three attributes changing, butdifferent cores.

Review the examples in Connect. Have studentslook at the pictures they drew in Explore andidentify the core and the pattern rule for eachpattern.

Prac t i ce

Have Attribute Blocks available for question 4.


Students should demonstrate their ability tocreate patterns in which three attributeschange. In describing each pattern, studentsshould include the three attributes used, thecore of the pattern, and the pattern rule.Encourage students to make as many differentpatterns as they can.


Alternative ExploreCreate a pattern, using students, in which three attributeschange. As a class, make a list of the different attributes that ashirt can have, such as colour, sleeve length, type of neck, fabric,and so on. Select one student to stand at the front of theclassroom to be the first person in the pattern. Have a volunteerchoose an attribute from the list. Have students stand if they thinkthey could be the next person in the pattern. Invite one of thesestudents to join the pattern. Repeat this process until you havethe core. Then, as a class, select students to repeat the core.

Early FinishersChallenge students to make a pattern in which three attributeschange by using “every day” objects from the classroom, ratherthan Attribute Blocks.

Common Misconceptions➤Students have difficulty keeping track of the changes in

attributes.How to Help: Encourage students to draw an arrow from one block to the next, and label the arrow with the attributes that change.

ESL StrategiesHave students bring in an object from their own culture thatshows a repeating pattern, to share with the class.


Making ConnectionsSocial Studies: Have students look on the Internet or in booksfor pictures of clothing worn by First Nations people. Havestudents identify any repeating patterns they find.

Sample Answers2. a) b)

3. a) Large pink heart, small blue heart turned to the right, largepink heart, small blue heart turned upside down, large pinkheart, small blue heart turned to the left

b) Small white square, small white circle, large white square,small green square, small green circle, large green square

4. Student chooses 4 large blue rectangles, 4 large blue triangles,and 4 small yellow circles. Student may create patterns like these:

Using the same 12 Attribute Blocks, I was able to create manydifferent patterns. Sometimes I was only able to repeat thecore once because I ran out of blocks. In each case, the coreof the pattern and its pattern rule were different. The numberof blocks in the core was not always the same.

REFLECT: The first thing I do is find the core of the pattern. I lookat the first two blocks, and write the attributes that change. Ido the same with blocks two and three. I continue to do thisfor the rest of the core. I then count how many differentattributes change.

blue blue blue yellow yellow blue blue blue yellow yellow

yellow blue yellow blue yellow blue yellow blue

core

core

green green whiteblue pink blue



What to Look For

Understanding concepts ✔ Students can identify the changing

attributes, the core, and the patternrule for a repeating pattern.

Applying procedures✔ Students can create a pattern in which

three attributes change.

Communicating✔ Students use appropriate terminology

when identifying attributes anddescribing repeating patterns.

What to Do

Extra Support: Have students list the three attributes on asheet of paper. Students can check off the attributes as theychange in their patterns to ensure that they have three attributeschanging.Students can use Step-by-Step 6 (Master 10.14) to completequestion 4.

Extra Practice: Students can complete Extra Practice 3 (Master 10.20).

Extension: Students work in pairs. Each student creates apattern in which three attributes change. Students cover severalobjects in their pattern. Students determine their partner’s hiddenobjects, then identify the core and the pattern rule.


Position,size, andthickness

Position,colour,and shape

Size, colour, and shape


L E S S O N 7

Patterns on Grids

Key Math Learnings1. A pattern can be made on a grid.2. A pattern can be identified by looking across the rows,

down the columns, and along the diagonals of a grid.

LESSON ORGANIZER

Curriculum Focus: Identify, create, and extend patterns ongrids. (PR2)Teacher Materials� 1-cm grid transparency (PM 20)Student Materials Optional� Colour Tiles or coloured � Step-by-Step 7 (Master 10.15)

congruent squares � Extra Practice 3 (Master 10.20)� 1-cm grid paper (PM 20)� 2-cm grid paper (PM 21)� Pattern Blocks (PM 25)� triangular grid paper (PM 24)Assessment: Master 10.2 Ongoing Observations: Patterns inNumber and Geometry

40–50 min


Invite students to examine the patterns on thegrids on page 391 of the Student Book.

Ask:• How do you know that both grids show

a pattern? (The same squares appear in the same order, butdifferent positions, in different rows.)

• How could you describe the pattern on thefirst grid? (The squares alternate between white and black.The first, third, and fifth rows start with a whitesquare. The other rows start with a black square.)

• How could you describe the pattern on thesecond grid? (In each row, the flower colours are white, pink,dark pink. Diagonals from top left to bottom righthave the same colours.)

• Where else might you see patterns like these? (In a tile floor and in a garden centre)

Engage students in a discussion about wherethey might find other patterns on grids. Recordstudents’ answers on the board. (Chess board, bathroom tiles, checkered shirt)

Present Explore. Tell students to make theirpattern cover part of their table. Review withstudents the meanings of the terms row, column,and diagonal. Make sure students know they areto record their work on grid paper and writeabout the different patterns they see.

DURING Exp lore


Ask questions, such as:• How did you make your pattern?

(I used these six squares: red, blue, red, green, red,yellow, and kept repeating them. My grid had9 squares in each row, so when I reached the end ofthe row I started the next row. It was like breaking upa very long repeating pattern to fit the rows on a grid.)

Numbers Every DayStudents should recognize that in the first 3 products, the first factorremains the same, the second factor increases by 2 each time, andthe product increases by 4 each time. In the second 3 products, thefirst factor remains the same, the second factor increases by 2 eachtime, and the product increases by 10 each time.


• What patterns do you see on your grid?(Every other row is the same. Every other diagonalhas only red squares in it.)

AFTER Connec t

Invite a pair of students to share their patternon a grid by recording it on an overheadtransparency of 1-cm grid paper. Have anotherpair of students record their pattern on thesame transparency. Have volunteers describethe patterns they see on the grids.

Ask:• How are these two grids the same?

(Both of them use the same colours and the samenumber of squares. Both have patterns across therows, down the columns, and along the diagonals.)

• How are these two grids different? (The first grid has a pattern of 4 squares in a row.The second grid has a pattern of 6 squares in a row.)

• How could you extend the patterns? (We could add squares to each row or squares to eachcolumn, keeping the order of the colours the same.)

Review Connect. Compare the pattern in Connectwith the patterns recorded on the overheadtransparency. Discuss how students couldextend these patterns.

Ensure students understand that the first rowor column of their patterns can be of anymanageable length. The patterns in thediagonals will depend on these lengths.

Tell students that a pattern does not have to beon a square grid. Use a transparency oftriangular grid paper and overhead PatternBlocks to demonstrate a pattern on a triangulargrid. Have students create other patterns on atriangular grid on the overhead projector. Invitea volunteer to describe each pattern.

Early FinishersChallenge students to use grid paper and coloured pencils tocreate a pattern that has 2 lines of symmetry.

Common Misconceptions➤Students have difficulty seeing patterns on a grid.How to Help: Have students use a ruler to cover all rows exceptthe first row. Students then read out or write down the colours inthat row, until they see a pattern. If necessary, continue to read orwrite the colours in the next row, until a pattern becomes clear.

ESL StrategiesHave students who are struggling with the terms row and columnmake a reference card. Have them add vertical lines to a ruledindex card to make a grid. They colour one row red and label it“row,” and one column blue and label it “column.”


= 4= 8= 12

= 10= 20= 30

Sample Answers1.

2. My name is 6 letters long. I wrote my name4 times. My classmate’s name is Jodi. Shewrote her name 6 times. Both of us haveone extra letter at the end.

3. I repeated: sun, moon, sun, starIn the diagonals that run from top left tobottom right, the objects in eachdiagonal are the same. In the diagonalsthat run from top right to bottom left,every other diagonal is all suns, and theother diagonals have an alternatingpattern (moon, star, moon, star).

4. a), b)

c) Rows 1 and 7; columns 1 and 7d) In my pattern, I repeated: cherry,

cherry, banana, banana, grapes,orange. The diagonals from top rightto bottom left show the same fruitrepeated. The diagonals from top leftto bottom right have the patterngrapes, cherry, banana, or banana,orange, cherry.

D

E

N

H

P

A

D

E

N

H

P

A

D

E

N

H

P

A

D

E

N

H

P

A

D

G

G

GG

G

GG

G

G

G

GG

R G

G

G

Y Y

Y Y

R

R

R

R

R

R

R

G

Ask questions, such as:

• What pattern do you see? (In the first row of the pattern, there are 2 green triangles to the left of a yellow hexagon, then a blue rhombus, and then 2 more green triangles. This pattern is repeated.)

Students may find it more challenging todescribe a pattern when the pattern is on atriangular grid. They may find it easier to circlethe part that repeats on the grid.

Prac t i ce

Have 1-cm and 2-cm grid paper available for allquestions. Have Pattern Blocks and triangulargrid paper available for question 1. Forquestion 2, ensure students understand they areto write their name over and over again, untilall squares are filled. For question 6, ensurestudents can identify the daisy and the rose.


Patterns will show a range of complexity.Students should use appropriate mathematicalterminology to describe their patterns, usingwords such as row, column, and diagonal.


5. a) The leaves are repeated in the same order across the rowsand down the columns. All the leaves in each diagonalthat runs from top left to bottom right are the same. In thediagonals that run from top right to bottom left, everyother diagonal is all maple leaves, and the other diagonalshave an alternating pattern (birch leaf, oak leaf, birch leaf,oak leaf).

b) 1 and 5, 2 and 6, 3 and 7, 4 and 8c) 1 and 5, 2 and 6, 3 and 7d) I looked at the pattern in part a. To get from one row to the

next row that is the same, add 4 to the row number. So, 4 + 7 = 11; row 11 is the same as row 7.

6. Brian plants 2 daisies, then 1 rose, 2 daises, then 1 rose, andso on. From the grid, I can see that when Brian has planted 5 roses, he has planted 10 daisies. If I continue this pattern orextend the grid, Brian will have planted 10 roses after he hasplanted 20 daisies.

REFLECT: A pattern on a grid is like a pattern in a very long linethat is broken and arranged in a grid. The same squares arerepeated in the same order. There are several patterns in agrid: in rows, in columns, and in diagonals. There is only onepattern in a line.



What to Look For

Understanding concepts ✔ Students understand that patterns on

a grid result from repetition.

Applying procedures✔ Students can identify, create, and

extend patterns on a grid.

Communicating✔ Students use appropriate

mathematical terminology to describepatterns on a grid.

What to Do

Extra Support: Have students begin by covering a surface with only 2 colours of squares, then recording the pattern on 2-cm grid paper.Students can use Step-by-Step 7 (Master 10.15) to completequestion 4.

Extra Practice: Students can complete Extra Practice 3 (Master 10.20).

Extension: Have students make as many different patterns as theycan with only 2 colours of squares on a 5 by 5 grid.


Row 11

20

Unit 10 • Technology • Student page 395 27

T E C H N O L O G Y

Patterns on aComputer

Key Math LearningComputers can be used to create patterns.

LESSON ORGANIZER

Curriculum Focus: Use a computer to create patterns.Student Materials� computer with AppleWorks or Microsoft Word

optional

BEFORE

Explain to students that they will use acomputer to create a pattern.

Students will have a wide range of comfort,experience, and ability using a computer. Ifnecessary, spend some time reviewing basiccomputer skills. Tell students that the computerprogram will make it easy to create and copyfigures, and to move the figures on the screento make repeating patterns.

DURING


Watch to ensure that students read and followthe instructions carefully.

Instructions for creating a pattern usingMicrosoft Word:

1. Open a new document in Microsoft Word.

2. To set the measurement units to centimetres:Click Tools.Click Options. Click the tab labelled General. Look for Measurement units. Click .Click Centimeters.Click OK.

3. To display the Drawing toolbar:Click View.Click Toolbars. Drawing should have a check mark besideit. If not, click Drawing.

4. To select grid settings:Click Draw in the Drawing toolbar. Click Grid.

The content of this lesson is not required by yourcurriculum. If you choose to complete this lesson, allow40–50 minutes.

Curr i cu lum Focus

The box next to Snap objects to gridshould have a check mark in it. If not, clickon the box.

Grid Settings should be:Horizontal spacing: 1 cmVertical spacing: 1 cmIf not, click in each box and enter 1 cm.

The box next to Display gridlines onscreen should have a check mark in it. Ifnot, click on the box.Click OK.

5. To draw, click AutoShapes in the Drawingtoolbar.Click Basic Shapes, Block Arrows, orStars and Banners.Click on the figure you want to draw.The cursor will look like this: +Click and hold down the mouse button.Drag the cursor until the figure is the sizeyou want.

Release the mouse button.

If you are making a circle or a square, holddown the Shift key while you click anddrag an oval or a rectangle.

6. To change the size of a figure, double-clickon the figure. Click the tab labelled Size. Enter the height and width you want. Click OK.

7. To move a figure, put the cursor inside thefigure.Click and hold down the mouse button.Drag the figure to where you want it.Release the mouse button.

8. To colour a figure, double-click on the figure. Click on the tab labelled Colors and Lines.Click next to Fill. Click on a colour.Click OK.

28 Unit 10 • Technology • Student page 396

Early FinishersHave students use a computer to make a growing pattern and apattern on a grid. Have students describe what they did toproduce each pattern.

Common Misconceptions➤Students have difficulty clicking, holding, and dragging the

mouse at the same time.How to Help: Have students click on a figure to select it, thenuse the arrow keys to move the figure on the screen.


Sample Answers12.

REFLECT: My pattern is a repeating pattern with 3 attributeschanging. In my pattern, colour, shape, and position change.The core of the pattern is: red star, red star, green heart,green heart turned a �

12

� turn. My core repeats two times.

red red greengreen red red greengreen red red greengreen

Unit 10 • Technology • Student page 397 29

9. To flip or turn a figure, click the figure. Click Draw in the Drawing toolbar.Click Rotate or Flip. Click Free Rotate.Put the cursor on one of the green dots onthe edge of the figure.Click, hold down the mouse button, anddrag the figure until it is in the position you want.

10. To copy a figure, click the figure.Click Edit.Click Copy.Click Edit.Click Paste.Click and drag the copy to where you want it.

11. Use Steps 5 to 10 to create a repeatingpattern.

12. Save your pattern.Click File.Click Save As.Name your file, then click Save.

13. Print your pattern.Click File.Click Print.Click OK.

AFTER

Students should share their patterns withclassmates. They should explain how theycreated their patterns.

30 Unit 10 • Show What You Know • Student page 398

LESSON ORGANIZER

Student Materials� hundred charts (PM 13)� 1-cm grid paper (PM 20)� Pattern Blocks (PM 25)� Attribute Blocks� calculatorsAssessment: Masters 10.1 Unit Rubric: Patterns in Numberand Geometry, 10.4 Unit Summary: Patterns in Number andGeometry

40–50 min

S H O W W H AT Y O U K N O W

Sample Answers1. c) Start at 9. Add 7 each time.

The number pattern is: 9, 16, 23, 30, 37, ...2. a) The number of cars starts at 1 and increases by

1 each time.The number of people starts at 4 and increases by 4 each time.The number of tickets starts at 12 and increases by 12 each time.The number of people is the number of cars multipliedby 4.The number of tickets is the number of cars multipliedby 12.The number of tickets is the number of peoplemultiplied by 3.

c) The number of people starts at 4 and increases by 4 each time. The number of people in 5 cars would be16 + 4 = 20. The number of people in 6 cars wouldbe 20 + 4 = 24.

d) Twelve tickets are collected per car. 12 � 8 = 96; 96 tickets were collected.

4. a) Small pink butterfly, large orange butterfly

b) Small blue arrow pointing up, large yellow arrowpointing up, large blue arrow pointing down, smallyellow arrow pointing down

5.

Pattern rule: Two large blue thin squares, 1 small thinyellow square, 1 small thick yellow square

blue blue blueblueyellow yellowyellow yellow

blue blueyellow

orange orangepink

Start at 18. Add 7 each time.53, 60, 67

3 tickets24 people

6 squares and 12 rhombuses

6. a)

b) The pattern that goes across the rows is: B, B, R, R, L.The pattern that goes down the columns is: B, B, R, R, L.All the wildflowers in each diagonal that runs from topright to bottom left are the same. There are pairs ofdiagonals that are the same from top left to bottom right.One diagonal is: B, R, L, B, R, B. Two diagonals are: B, R,B, R, L. Two diagonals are: R, L, B, R. Two diagonals are:R, B, R. Two diagonals are: L, B.

c) I can add rows and columns to the garden by repeating thepattern B, B, R, R, L, continuing from the previous row orcolumn, making sure I start at the right flower.

B

B

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Unit 10 • Show What You Know • Student page 399 31


What to Look For

Reasoning; Applying concepts✔ Questions 1 and 3: Student understands pattern rules and how to extend a pattern.

Accuracy of procedures✔ Question 4: Student can identify a repeating pattern and find missing parts of the pattern.

✔ Question 5: Student can create patterns in which three attributes change.

✔ Question 6: Student can identify, create, and extend a pattern on a grid.

Problem solving✔ Question 2: Student can identify and extend patterns in a table to solve a problem.

Recording and ReportingMaster 10.1 Unit Rubric: Patterns in Number and GeometryMaster 10.4 Unit Summary: Patterns in Number and Geometry

Have students turn to the Unit Launch on pages370 and 371 of the Student Book.

Review the Learning Goals of the unit anddiscuss the meanings of the Key Words. Tellstudents they will use these skills and conceptsas they complete the Unit Problem.

Have a variety of materials, such as grid paper,pencil crayons, markers, coloured paper,Pattern Blocks, Attribute Blocks, and othermanipulatives available.

Present the Unit Problem. Invite volunteers toread the guidelines and instructions for theproblem aloud. Ensure students understandwhat they are expected to do.

Have one student read the Check List aloud.Remind students to use the Check List to assesstheir work before handing it in.

You may also wish to provide students withcopies of Master 10.3 Performance AssessmentRubric: Indoor Recess! so they will know howtheir work will be assessed.

Before students begin, ask volunteers toexplain a repeating pattern, a growing pattern,and a pattern on a grid. Ensure students knowthey are to record each pattern they make, andthey must include clear instructions on how tocomplete their indoor recess activity. Encouragestudents to use their imagination and come upwith new, fun, and interesting activities.

Set a reasonable time for the completion of thetasks. Allow 10 minutes for Parts 1 and 2, andabout 30 minutes for Part 3. If there is time,allow students to try each other’s activities. Thebetter activities could be used during the nextindoor recess.

32 Unit 10 • Unit Problem • Student page 400

Indoor Recess!

Sample ResponseStudent work should include a picture of each pattern studentsmade, a description of how they made the patterns, and anexplanation of how they extended their growing pattern. Theiractivity should be accompanied with clear instructions, usingappropriate language. For example:

Part 1

I chose the attributes colour and size. I chose the large redtriangle and the small blue triangle. The core of my pattern is:2 large red triangles, 1 small blue triangle.

LESSON ORGANIZER

Student Grouping: 3Student Materials� 1-cm grid paper (PM 20)� 2-cm grid paper (PM 21)� Pattern Blocks (PM 25)� Attribute BlocksAssessment: Masters 10.3 Performance Assessment Rubric:Indoor Recess!, 10.4 Unit Summary: Patterns in Number andGeometry

40–50 min

U N I T P R O B L E M

R R B R R B

Part 2

I started with 3 circles in Frame 1.I added 2 circles each time.The pattern rule is: Start at 3.Add 2 each time. To extend mypattern, I used a table.

Part 3

I chose to make a game. I took a sheet of 2-cm grid paper andcut out an 8-square by 8-square piece. I glued it onto a piece ofcardboard. I coloured the squares. My pattern on the grid is: red,green, yellow, yellow, green, yellow. I repeated these coloursacross the rows from left to right until all squares were coloured. I then glued a small piece of paper onto each face of a cube.There are 6 faces. On 2 faces, I drew 1 red dot. On 2 otherfaces, I drew 1 green dot. On 2 other faces, I drew 1 yellow dot.How to play:Play in pairs. You need 1 number cube, 1 colour cube, and 2 game pieces. Placeyour pieces on the first square. Player A rollsthe cubes. For example, if a 4 and a red dotare rolled, move to the 4th red square. Moveacross the rows from left to right, then rightto left, and so on. Players take turns. The player who first reaches the last square wins.

Reflect on the UnitMy favourite pattern is a growing pattern that makes an “X”shape. I start with one square in Frame 1 and add 4 squareseach time. My “X” gets larger as I add new squares to thecorners. The pattern rule is: Start at 1. Add 4 each time.

R

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Frame 1

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Unit 10 • Unit Problem • Student page 401 33


What to Look For

Understanding concepts ✔ Students understand that patterns

result from repetition.

✔ Students identify patterns in which twoattributes change.

Applying procedures✔ Students apply a pattern rule to create

and extend a growing pattern.

Communicating✔ Students use language effectively to

describe patterns, to discuss theirchoice of a pattern rule, and toexplain how patterns can beextended.

What to Do

Extra Support: Make the problem accessible.

Some students may have difficulty recognizing and extendingpatterns. These students may benefit from having each step of theUnit Problem structured, using tables and manipulatives.

Other students may have difficulty describing their patterns andexplaining their activity in writing. Assess these students verbally.Are they able to communicate their ideas orally, usingappropriate mathematical language?

Some students may have difficulty creating an activity. Brainstorma list of potential activities with the class. Record the list on theboard for all students to refer to.

Recording and ReportingMaster 10.3 Performance Assessment Rubric: Indoor Recess!Master 10.4 Unit Summary: Patterns in Number and Geometry

Copyright © 2005 Pearson Education Canada Inc. 34

Evaluating Student Learning: Preparing to Report: Unit 10 Patterns in Number and Geometry This unit provides an opportunity to report on the Patterns and Relations strand. Master 10.4: Unit Summary: Patterns in Number and Geometry provides a comprehensive format for recording and summarizing evidence collected.

Here is an example of a completed summary chart for this Unit: Key: 1 = Not Yet Adequate 2 = Adequate 3 = Proficient 4 = Excellent

Strand: Patterns and Relations

Reasoning; Applying concepts

Accuracy of procedures

Problem solving

Communication Overall

Ongoing Observations 3 2 2 3 2/3 Strategies Toolkit 3 3 Work samples or portfolios; conferences

3 3 2 3 3

Show What You Know 3 3 3 3 3 Unit Test 3 2 2 3 2/3 Unit Problem Indoor Recess!

3 2 3 3 3

Achievement Level for reporting 3

Recording How to Report Ongoing Observations

Use Master 10.2 Ongoing Observations: Patterns in Number and Geometry to determine the most consistent level achieved in each category. Enter it in the chart. Choose to summarize by achievement category, or simply to enter an overall level. Observations from late in the unit should be most heavily weighted.

Strategies Toolkit (problem solving)

Use PM 1: Inquiry Process Check List with the Strategies Toolkit (Lesson 4). Transfer results to the summary form. Teachers may choose to enter a level in the Problem solving column and/or Communication.

Portfolios or collections of work samples; conferences or interviews

Use Master 10.1 Unit Rubric: Patterns in Number and Geometry to guide evaluation of collections of work and information gathered in conferences. Teachers may choose to focus particular attention on the Assessment Focus questions. Work from late in the unit should be most heavily weighted.

Show What You Know Master 10.1 Unit Rubric: Patterns in Number and Geometry may be helpful in determining levels of achievement. #1 and 3 provide evidence of Reasoning; Applying concepts; #4, 5, and 6 provide evidence of Accuracy of procedures; #2 provides evidence of Problem solving; all provide evidence of Communication.

Unit Test Master 10.1 Unit Rubric: Patterns in Number and Geometry may be helpful in determining levels of achievement. Part A provides evidence of Accuracy of procedures, Part B provides evidence of Reasoning; Applying concepts; Part C provides evidence of Problem solving; all parts provide evidence of Communication.

Unit performance task Use Master 10.3 Performance Assessment Rubric: Indoor Recess! The Unit Problem offers a snapshot of students’ achievement. In particular, it shows their ability to synthesize and apply what they have learned.

Student Self-Assessment Note students’ perceptions of their own progress. This may take the form of an oral or written comment, or a self-rating.

Comments Analyse the pattern of achievement to identify strengths and needs. In some cases, specific actions may need to be planned to support the learner.

Learning Skills

PM 4: Learning Skills Check List Use to record and report throughout a reporting period, rather than for each unit and/or strand.

Ongoing Records

PM 10: Summary Class Records: Strands PM 11: Summary Class Records: Achievement Categories PM 12: Summary Record: Individual Use to record and report evaluations of student achievement over several clusters, a reporting period, or a school year. These can also be used in place of the Unit Summary.


Name Date

Unit Rubric: Patterns in Number and Geometry Not Yet

Adequate Adequate Proficient Excellent


• shows understanding by: – explaining and

using models to explain pattern rules

– making predictions based on patterns

– recognizing patterns in the environment

may be unable to apply concepts of patterning to: – explain pattern

rules – make predictions

based on patterns – recognize patterns

in the environment

partially able to apply concepts of patterning to: – explain pattern



in the environment

able to apply concepts of patterning to: – explain pattern



in the environment

in various contexts, appropriately applies concepts of patterning to: – explain pattern



in the environment


• accurately identifies and extends repeating and growing patterns

limited accuracy; omissions or major errors in identifying or extending patterns

partially accurate; omissions or frequent minor errors in identifying or extending patterns

generally accurate; few errors in identifying or extending patterns

accurate; no errors in identifying or extending patterns

Problem-solving strategies

• chooses and carries out a range of strategies (e.g., using objects, drawing, using a grid, creating a chart or table, using a computer or calculator) to solve and create problems involving patterns

may be unable to use appropriate strategies to solve and create problems involving patterns

with limited help, uses some appropriate strategies to solve and create problems involving patterns; partially successful

uses appropriate strategies to solve and create problems involving patterns successfully

uses appropriate, often innovative, strategies to solve and create problems involving patterns successfully

Communication

• explains reasoning and procedures clearly, including appropriate terminology

unable to explain reasoning and procedures clearly

partially explains reasoning and procedures

explains reasoning and procedures clearly

explains reasoning and procedures clearly, precisely, and confidently

• presents work clearly

work is often unclear presents work with some clarity

presents work clearly presents work clearly and precisely

Master 10.1


Name Date

Ongoing Observations: Patterns in Number and Geometry

The behaviours described under each heading are examples; they are not intended to be an exhaustive list of all that might be observed. More detailed descriptions are provided in each lesson under Assessment for Learning.

STUDENT ACHIEVEMENT: Patterns in Number and Geometry* Student Reasoning; Applying

concepts Accuracy of procedures

Problem solving Communication

Explains and applies concepts related to patterns Makes predictions

based on patterns Recognizes patterns

in the environment

Accurately identifies and extends repeating and growing patterns

Uses appropriate strategies to solve and create problems involving patterns

Presents work clearly Explains reasoning and

procedures clearly, including appropriate terminology

*Use locally or provincially approved levels, symbols, or numeric ratings.

Master 10.2


Name Date

Performance Assessment Rubric: Indoor Recess! Not Yet

Adequate Adequate Proficient Excellent


• shows understanding of attributes and patterning by explaining the patterns and pattern rules (using concrete objects and drawing)

unable to apply the required concepts of patterning; may be incomplete or indicate misconceptions

applies relevant concepts to partially explain or demonstrate the patterns; may indicate some misconceptions

applies relevant concepts to explain or demonstrate the patterns; may have minor flaws in reasoning

applies relevant concepts of patterning to effectively explain or demonstrate the patterns; shows thorough understanding


• accurately follows patterning rules they have devised to create and record: – a repeating pattern

with 2 variables changing

– a growing pattern and its extension

limited accuracy; omissions or major errors in: – repeating pattern – growing pattern

somewhat accurate; omissions or some minor errors in: – repeating pattern – growing pattern

generally accurate; few minor errors in: – repeating pattern – growing pattern

accurate and precise; no errors in: – repeating pattern – growing pattern

Problem-solving strategies

• uses effective strategies (e.g., concrete objects, sketches, tables, grids) to design an activity that uses a pattern on a grid

uses few effective strategies; does not adequately design an activity that uses a pattern on a grid

uses some appropriate strategies, with partial success, to design an activity that uses a pattern on a grid

uses appropriate and successful strategies to design an activity that uses a pattern on a grid

uses innovative and effective strategies to design an activity that uses a pattern on a grid

Communication

• uses appropriate mathematical terminology correctly (e.g., repeat, pattern rule, core, attribute)

uses few appropriate mathematical terms

uses some appropriate mathematical terms

uses appropriate mathematical terms

uses a range of appropriate mathematical terms with precision

• explains the patterns clearly

unable to explain the patterns

partially explains the patterns; may be vague and somewhat unclear

explains the patterns clearly

explains the patterns clearly, precisely, and confidently

Master 10.3


Name Date

Unit Summary: Patterns in Number and Geometry Review assessment records to determine the most consistent achievement levels for the assessments conducted. Some cells may be blank. Overall achievement levels may be recorded in each row, rather than identifying levels for each achievement category. Most Consistent Level of Achievement*

Strand: Patterns and Relations



Problem solving

Communication Overall

Ongoing Observations

Strategies Toolkit (Lesson 4)

Work samples or portfolios; conferences

Show What You Know

Unit Test

Unit Problem Indoor Recess!

Achievement Level for reporting

*Use locally or provincially approved levels, symbols, or numeric ratings. Self-Assessment:

Comments: (Strengths, Needs, Next Steps)

Master 10.4


Name Date

To Parents and Adults at Home … Your child’s class is starting a mathematics unit on patterns in number and geometry. Patterns occur in the world around us, as they do in mathematics. Recognizing and understanding patterns are key steps in developing a higher level of mathematical thinking. In this unit, your child will:

• Identify, create, and extend number patterns. • Find pattern rules. • Display number patterns in tables. • Identify, create, and extend growing patterns. • Create patterns by changing attributes. • Identify, create, and extend patterns on grids.

Number and geometry patterns can be found outside the classroom. Encourage your child to look for patterns around the home, and talk about them. Here are some suggestions for activities that you can do at home:

• Look for patterns in your family’s activities marked on the calendar at home.

• Look for repeating patterns in the schedule for television shows.

• Use coins to make patterns in which 2 or 3 attributes change.

• Look for patterns in fabric and wallpaper.

• Find examples of patterns on a grid, such as in bathroom tiles and on

game boards.

Master 10.5


Name Date Additional Activity 1: Roll and Go! Work with a partner.

You will need a number cube.

How to play:

Each player chooses a number between 5 and 10. This is the start of a number pattern.

Each player rolls the number cube. This is the number that is added each time.

Write the next 5 numbers in your pattern.

Trade patterns with your partner. Find your partner’s pattern rule. Check to make sure all numbers fit.

Take It Further: Each player chooses a number between 31 and 40. This is the sixth number in a number pattern. Each player rolls the number cube. This is the number that was added each time. Work backward to find the first 5 numbers in your pattern. Trade patterns and find your partner’s pattern rule.

Master 10.6


Name Date

Additional Activity 2: Patterning Mix-Up Work in groups of 4.

You will need 1-cm grid paper and scissors.

Each student folds a piece of grid paper into 4 congruent parts. Cut out the parts.

Write a pattern rule for a growing pattern in one part.

Use squares to draw the first 3 frames of the pattern in another part.

Make a table to show the pattern in another part.

Write the number of squares in the 5th frame in the last part.

Put all the parts together. Mix them up.

Trade with another group. Sort the mixed-up patterns. The first group to do this correctly wins.

Take It Further: Use only the parts labelled with the number of squares in the 5th frame. Trade these parts with another group. Find a possible pattern rule for each.

Master 10.7


Name Date

Additional Activity 3: Missing Blocks Work with a partner. Take turns completing the activity. You will need Attribute Blocks and a large piece of cardboard.

Face your partner with a cardboard divider between you.

Take 12 blocks. Make a pattern in which 2 attributes change.

Remove one block from your pattern. Put it inside your desk.

Take down the divider. Guess your partner’s missing block. If you are correct, give yourself 1 point.

Repeat with a different pattern. Continue in this way. The first person to get 5 points wins.

Take It Further: Repeat the activity. Remove 2 blocks each time.

Master 10.8


Name Date

Additional Activity 4: Tower Power Work on your own.

You will need Pattern Blocks to build a hexagon-shaped tower.

Start with a yellow Pattern Block.

Cover the yellow block completely with other blocks.

Continue to add layers. Do not use another yellow block.

Add another yellow block.

Look at each face of the tower. Repeat the colour pattern you see, from the base up, to add other layers.

Add another yellow block and repeat.

When you have finished, you will have a tower that shows repeating colour patterns.

Record the colour pattern for each face of the tower.

Take It Further: Predict the colours in the 10th and 20th layers.

Master 10.9


Name Date

Step-by-Step 1 Lesson 1, Question 6

Step 1 Continue the pattern. Add 2 each time.

2, 4, ___, ___, ___, ___

What is the pattern rule? _______________________________________________________

Step 2 Continue the pattern. The number you add goes up by 1 each time.

2, 4, ___, ___, ___, ___


Step 3 Continue the pattern. Use a calculator. Multiply by 2 each time.

2, 4, ___, ___, ___, ___


Step 4 Continue the pattern. Choose a different way.

2, 4, ___, ___, ___, ___


Master 10.10


Name Date


Step 1 What is the pattern rule for the “In” row? _______________________________________________________

Step 2 What is the pattern rule for the “Out” row?

_______________________________________________________ Step 3 Extend each pattern. Fill in the table.

In 2 3 4 5

Out 6 7 8 9

Step 4 When the “In” number is 6, what is the “Out” number? __________ Step 5 When the “Out” number is 12, what is the “In” number? _________

Master 10.11


Name Date


Use Colour Tiles. Here are the first 3 frames in a growing pattern. Step 1 Make Frame 4. Sketch the frame. Step 2 Make Frame 5. Sketch the frame. Step 3 Write about your pattern. How does it grow?

_______________________________________________________

_______________________________________________________

_______________________________________________________

Master 10.12


Name Date


Use Attribute Blocks or Pattern Blocks. Step 1 Choose 2 different blocks. Get 6 of each block. Step 2 Choose 2 different attributes. ________________________________ Make a pattern where these attributes change. Draw pictures to record your pattern. Write about your pattern. ______________________________________________

________________________________________________________

Step 3 Use the same blocks. Make a different pattern where two attributes change. Draw pictures to record your pattern. Write about your pattern. ______________________________________________

________________________________________________________

Master 10.13


Name Date


Use Attribute Blocks. Step 1 Choose 3 different blocks. Take 4 of each block. Step 2 Make a pattern.

Draw pictures to record your pattern. Write about your pattern.

What is the pattern rule?

Step 3 Use the same blocks. Make a different pattern.



Step 4 Use the same blocks. Make another different pattern.



Master 10.14


Name Date


Use 2-cm grid paper. Step 1 Draw 4 different pictures below. Step 2 Repeat these pictures on a grid.

Keep the order the same. Make a pattern.

Step 3 Look at the rows in your pattern.

In which rows are the patterns the same? ______________________ Step 4 Look at the columns. In which columns are the patterns the same? ___________________ Step 5 Write about your pattern.____________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________

Master 10.15


Name Date

Unit Test: Unit 10 Patterns in Number and Geometry Part A 1. a) Fill in the missing numbers.

A: 23, 26, 29, 32, 35, , ,

B: 42, 38, 34, 30, 26, , ,

C: 2, 4, 8, , , , 128, 256

D: 5, 6, 8, 11, 15, , , b) Match each pattern in part a with its description. Fill in the blanks with A, B, C, or D.

1. Subtract 4 each time. 2. The number added goes up by 1 each time. 3. Add 3 each time. 4. Multiply by 2 each time.

2. Draw the next 4 objects in each pattern. a) b)

Master 10.16a


Name Date

Unit Test continued 3. This table shows the number of each Pattern Block in a pattern frame.

a) Complete the table.

Frame Number of Triangles

Number of Squares

Number of Trapezoids

1 3 2

2 5

3 8 8

4 16 10

5 17 32 12

6 23 14 b) Write the pattern rule for each column. __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ Part B 4. Use Pattern Blocks to make a growing pattern. Draw the first four frames of your pattern. Write about your pattern.

Master 10.16b


Name Date

Unit Test continued 5. Use 2-cm grid paper. Make a grid with 6 rows and 6 columns.

Use these objects to make a pattern on a grid. Write about your pattern.

Part C 6. A tower is built using marshmallows and toothpicks.

The tower looks like a hexagonal prism. Here is 1 level.

a) Complete this table. Find how many marshmallows and toothpicks are needed to build a tower with 5 levels.

Level Number of

Marshmallows Number of Toothpicks

1 12 18

2 18 30

3

4

5

b) How many marshmallows are needed to build a hexagonal tower 8 levels high? __________

Master 10.16c


Name Date

Unit Test continued c) Another tower looks like a pentagonal prism.

It was also built using marshmallows and toothpicks. Which tower used more toothpicks: a pentagonal prism 10 levels high, or a hexagonal prism 8 levels high? Show your work. Use words, pictures, or numbers to explain.

Master 10.16d


Name Date

Sample Answers Unit Test – Master 10.16 Part A 1. a) A: 38, 41, 44; b) 1. B

B: 22, 18, 14; 2. D C: 16, 32, 64; 3. A D: 20, 26, 33; 4. C

2. a) b) 3. a)

Frame Number of

Triangles

Number of

Squares

Number of

Trapezoids 1 3 2 4 2 5 4 6 3 8 8 8 4 12 16 10 5 17 32 12 6 23 64 14

b) Frame: Start at 1. Add 1 each time. Triangles: Start at 3. Add 2. The number you add goes up by 1 each time. Squares: Start at 2. Multiply by 2 each time. Trapezoids: Start at 4. Add 2 each time.

Part B 4. Sample Answer: I chose the green triangle. There is 1 triangle in

Frame 1, 3 triangles in Frame 2, 5 triangles in Frame 3, and 7 triangles in Frame 4. The pattern rule is: Start at 1. Add 2 each time.

5. Sample Answer: I repeated: leaf, star, flower, leaf, star. This pattern runs across the rows and down the columns. Each diagonal going from top right to bottom left has all objects the same. There are pairs of diagonals that are the same from top left to bottom right.

One diagonal is: leaf, flower, star, star, leaf,

leaf. Two diagonals are: star, leaf, leaf, flower, star. Two diagonals are: flower, star, star, leaf. Two diagonals are: leaf, leaf, flower. Two diagonals are: star, star.

Part C 6. a) A tower with 5 levels needs

36 marshmallows and 66 toothpicks. Level Number of

Marshmallows Number of Toothpicks

1 12 18 2 18 30 3 24 42 4 30 54 5 36 66 6 42 78 7 48 90 8 54 102

b) By extending the table, I see that 54 marshmallows and 102 toothpicks are needed to build a tower 8 levels high.

c) I used a table to show the number of marshmallows and toothpicks used to make a pentagonal prism tower.

Level Number of Marshmallows

Number of Toothpicks

1 10 15 2 15 25 3 20 35 4 25 45 5 30 55 6 35 65 7 40 75 8 45 85 9 50 95

10 55 105 From the table, I see that 105 toothpicks are

needed to build a pentagonal prism tower 10 levels high. From part b, I know that 102 toothpicks are needed to build a hexagonal prism tower 8 levels high. So, the pentagonal prism tower needs the most toothpicks.

Master 10.17


Extra Practice Masters 10.18–10.21 Go to the CD-ROM to access editable versions of these Extra Practice Masters

Program Authors

Peggy Morrow

Ralph Connelly

Steve Thomas

Jeananne Thomas

Maggie Martin Connell

Don Jones

Michael Davis

Angie Harding

Ken Harper

Linden Gray

Sharon Jeroski

Trevor Brown

Linda Edwards

Susan Gordon

Manuel Salvati

Copyright © 2005 Pearson Education Canada Inc.

All Rights Reserved. This publication is protected by copyright,and permission should be obtained from the publisher prior toany prohibited reproduction, storage in a retrieval system, ortransmission in any form or by any means, electronic, mechanical,photocopying, recording, or likewise. For information regardingpermission, write to the Permissions Department.

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