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Name
Master 1.1
Reasoning;
Applying concepts
 shows
understanding by
demonstrating,
explaining, and
applying:
– relationships in
patterns
– equivalence in
Date
Unit Rubric: Number Patterns
Not Yet
Adequate
Adequate
may be unable to
demonstrate, explain,
or apply:
partially able to
demonstrate, explain,
and use:
– relationships in
– relationships in
patterns
– equivalence in
simple numerical
equations
patterns
Proficient
appropriately
demonstrates,
explains, and uses:
– relationships in
patterns
– equivalence in
simple numerical
equations
– equivalence in
simple numerical
equations
Excellent
in various contexts,
appropriately
demonstrates,
explains, and uses:
– relationships in
patterns
– equivalence in
simple and more
complex numerical
equations
simple numerical
equations
Accuracy of
procedures
 accurately identifies
and applies pattern
rules; extends
number patterns
 finds the missing
terms in an equation
 represents numbers
to 10 000
often makes major
errors in:
makes frequent minor makes few errors in:
errors in:
– identifying pattern
– identifying pattern
rules
rules
– applying pattern
– applying pattern
rules
rules
– extending number
– extending number
patterns
patterns
– finding missing
– finding missing
terms in an
terms in an
equation
equation
– representing
– representing
numbers to
numbers to
10 000
10 000
makes no errors in:
may be unable to use
appropriate strategies
to solve and create
problems that involve
patterns
with limited help, uses
some appropriate
strategies to solve
and create problems
that involve patterns;
partially successful
uses appropriate
strategies to solve and
create problems that
involve patterns
successfully
uses appropriate, often
innovative, strategies
to solve and create
problems that involve
patterns successfully
unable to explain
reasoning and
procedures clearly
partially explains
reasoning and
procedures clearly
explains reasoning
and procedures
clearly
explains reasoning and
procedures clearly,
precisely, and
confidently
uses few
mathematical terms
appropriately
uses some
mathematical terms
appropriately
uses appropriate
mathematical terms
uses a range of
appropriate
mathematical terms
with precision
– identifying pattern
–
–
–
–
Problem-solving
strategies
 uses appropriate
strategies to solve
and create problems
that involve number
patterns; includes
use of calculator
Communication
 explains reasoning
and procedures
clearly
 uses appropriate
language to
describe number
patterns (e.g.,
pattern rule, core,
growing pattern,
repeating pattern)
rules
applying pattern
rules
extending number
patterns
finding missing
terms in an
equation
representing
numbers to
10 000
– identifying pattern
rules
– applying pattern
rules
– extending number
patterns
– finding missing
–
terms in an
equation
representing
numbers to
10 000
Copyright © 2004 Pearson Education Canada Inc. 27
Name
Master 1.2
Date
Ongoing Observations: Number Patterns
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: Number Patterns
Student
Reasoning;
Applying concepts
Accuracy of
procedures
Problem solving
Communication
 Explains and applies
concepts related to:
– identifying and
extending
patterns
– equivalence
 Accurately
identifies and
extends a
number pattern
 Finds missing
terms in an
equation
 Uses appropriate
strategies to solve
and create number
pattern problems
 Uses appropriate
language to
describe number
patterns
 Explains reasoning
and procedures
*Use locally or provincially approved levels, symbols, or numeric ratings.
28 Copyright © 2004 Pearson Education Canada Inc.
Name
Master 1.3
Performance Assessment Rubric:
Calendar Patterns
Not Yet
Adequate
Reasoning;
Applying concepts
 shows
understanding and
ability to apply
concepts by
describing and
explaining
pattern rules
Accuracy of
procedures
 identifies and
describes patterns
accurately
Problem-solving
strategies
 uses appropriate
strategies to
identify and
investigate
number patterns
on a calendar
Communication
 uses appropriate
mathematical
terminology (e.g.,
pattern rule, core,
growing pattern,
repeating pattern)
 shows thinking
clearly
Date
Adequate
Proficient
shows little
understanding; may be
unable to describe or
explain pattern rules
gives a partially
appropriate
description and
explanation of pattern
rules; may be vague
or incomplete
makes major errors in
identifying and
describing patterns
makes frequent minor makes few errors in
errors in identifying
identifying and
describing patterns
and describing
patterns
makes no errors in
identifying and
describing patterns
uses very limited
strategies for
investigating number
patterns on a calendar;
may rely only on those
described in
Steps 1 and 2
uses some
appropriate strategies
for investigating
number patterns on a
calendar including
one that is not
described (Step 3)
uses appropriate and
effective strategies for
investigating number
patterns on a
calendar, including at
least two that are not
described (Step 3)
uses innovative and
effective strategies for
investigating number
patterns on a
calendar, including at
least two that are not
described (Step 3)
uses few appropriate
mathematical terms
uses some
appropriate
mathematical terms
uses appropriate
mathematical terms
uses a range of
appropriate
mathematical terms
clearly and precisely
shows thinking clearly
shows thinking clearly,
precisely, and
confidently
unable to show thinking shows thinking with
clearly
some clarity
gives an appropriate
and complete
description and
explanation of
pattern rules
Excellent
gives clear,
appropriate, and
detailed descriptions
and explanations of
pattern rules
Copyright © 2004 Pearson Education Canada Inc. 29
Name
Master 1.4
Date
Unit Summary: Number Patterns
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
Reasoning;
Applying
concepts
Accuracy of
procedures
Problem
solving
Communication
Ongoing Observations
Strategies Toolkit
(Lesson 6)
Work samples or portfolios;
conferences
Show What You Know
Unit Test
Unit Problem:
Calendar Patterns
Achievement Level for reporting
*Use locally or provincially approved levels, symbols, or numeric ratings.
Self-Assessment:
Comments: (Strengths, Needs, Next Steps)
30 Copyright © 2004 Pearson Education Canada Inc.
OVERALL
Name
Master 1.5
Date
To Parents and Adults at Home …
Your child’s class is starting a mathematics unit on number patterns. From
traffic to petals on a flower—patterns are how we make sense of the world
around us. Patterns occur regularly in mathematics. As children learn to
analyse patterns, they develop powerful reasoning skills that will help them
make sense of mathematics and science.
In this unit, your child will:
 Use charts to display patterns.
 Identify the rule for a number pattern.
 Extend number patterns.
 Create number patterns.
 Use patterns to solve problems.
 Investigate equations.
Patterns occur in many different forms. Encourage your child to look for
patterns around the home, and talk about them. You may find regular repeating
patterns—maybe you mark the calendar to remind you of soccer practice every
week. Other patterns may be growing or shrinking—the number of cookies
remaining in the jar, if it’s “take one at a time.”
Here’s a game you can play with your child that creates a growing pattern
of words.
Growing List Word Game
Think of words to describe a cat or other animal. Each player repeats the words
said by previous players in the correct order, and adds a new word at the end
of the list.
The first player starts by saying, for example, “My cat is an adorable cat.”
The next player must repeat this but add a new descriptive word. For example,
“My cat is an adorable, black cat.”
A player is out of the game when he or she cannot repeat the list or fails to
provide a new word.
Copyright © 2004 Pearson Education Canada Inc. 31
Name
Calendar Page
SUNDAY
MONDAY
TUESDAY
WEDNESDAY
THURSDAY
FRIDAY
SATURDAY
Master 1.6
32 Copyright © 2004 Pearson Education Canada Inc.
Date
Name
Master 1.7
Date
Additional Activity 1:
Number Search
Work on your own.
Use a hundred chart.
 Choose a number less than 50.
Circle the number on your hundred chart.
Add 10 to your number.
Where did you land on the chart?
 Start at the same number.
Add 20. Where did you land on the chart?
 Start at the same number.
Add 30. Predict where you will land on the chart.
Describe how you can use patterns in a hundred chart
to add 10, 20, or 30 to a number.
How could you add 40 or 50 to a number?
Take It Further: Describe how you can use patterns
in the hundred chart to add 9, 18, or 27 to a number.
Copyright © 2004 Pearson Education Canada Inc. 33
Name
Master 1.8
Date
Additional Activity 2:
Patterns to the Nines
Work on your own.
You will need a calculator.
 Look at the 3 products in List A.
What patterns do you see?
 Use the patterns to predict the next 3 products.
Check your predictions with a calculator.
How can you extend the pattern?
Use a calculator to check.
 Repeat the activity for List B.
List A
List B
3 x 9 = 27
99 x 12 = 1188
3 x 99 = 297
99 x 23 = 2277
3 x 999 = 2997
99 x 34 = 3366
3 x 9999 = _____
99 x 45 = ____
3 x 99 999 = _____
99 x 56 = ____
3 x 999 999 = _____
99 x 67 = ____
Take It Further: Use a calculator to find other patterns with nines.
34 Copyright © 2004 Pearson Education Canada Inc.
Name
Master 1.9
Date
Additional Activity 3:
Twenty-One
Work with a partner.
Use 21 Snap Cubes.
The goal is to make the other player remove the last cube.
How to play:
 Join 21 Snap Cubes to form a chain.
 Take turns to remove 1, 2, or 3 Snap Cubes from the chain.
 The player who removes the last cube loses the game.
Play the game several times.
Discuss any patterning strategies you used to win.
Take It Further: Play Twenty-One by removing 2, 3, or 4 cubes each time.
Copyright © 2004 Pearson Education Canada Inc. 35
Name
Master 1.10
Date
Additional Activity 4:
Make It Work
Work with a partner.
Use Pattern Blocks.
Find the value for each block that makes each statement an equation.
The same blocks represent the same number.
Each different block represents a different number.
+
= 20
+
= 15
Take It Further: Create your own number puzzle with Pattern Blocks.
Trade puzzles with your partner.
Solve your partner’s puzzle.
36 Copyright © 2004 Pearson Education Canada Inc.
Name
Master 1.11
Date
Step-by-Step 1
Lesson 1, Question 4
Step 1 Fill in the missing numbers
on this 5-wide hundred chart.
1
2
3
6
7
8
11
9
14
17
24
26
27
30
33
36
38
35
39
42
45
48
Step 3 Count on by 5s.
Shade these numbers with a second colour.
51
55
56
57
59
62
Step 4 Start at 8 and count on by 10s.
Shade these numbers with a third colour.
63
67
69
71
74
76
________________________________
________________________________
Step 7 How are the patterns different?
________________________________
________________________________
75
78
82
Step 5 Use this 10-wide hundred chart.
Repeat the number patterns from
Steps 2, 3, and 4.
Step 6 How are the patterns in the two
charts the same?
________________________________
15
19
21
Step 2 Count on by 2s.
Shade these numbers with one colour.
5
86
90
96
98
100
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
________________________________
Copyright © 2004 Pearson Education Canada Inc. 37
Name
Master 1.12
Date
Step-by-Step 2
Lesson 2, Question 4
Step 1 Here is a number pattern: 5, 8, 11, 14, 17
Is this a growing pattern?
________________________________________________________________
How do you know?
________________________________________________________________
What is the pattern rule?
________________________________________________________________
Step 2 Continue this pattern:
5, 15, 25, 35, ___, ___, ___
Is this a growing pattern?
________________________________________________________________
What is the pattern rule?
________________________________________________________________
Step 3 Use 5 as a start number. Write your own growing pattern.
5, ___, ___, ___, ___, ___
What is the pattern rule?
________________________________________________________________
38 Copyright © 2004 Pearson Education Canada Inc.
Name
Master 1.13
Date
Step-by-Step 3
Lesson 3, Question 5
Step 1 12 + 21
How are 12 and 21 different?
How are they the same?
___________________________________
12
13
14
___
___
___
___
+
+
+
+
+
+
+
21
31
41
___
___
___
___
=
=
=
=
=
=
=
___
___
___
___
___
___
___
Step 2 Continue the pattern. Fill in the blanks.
Find each sum.
Step 3 Write a rule for the pattern in the sums.
_______________________________________________________
_______________________________________________________
Step 4 The next statement is 19 + 91. Find the sum. ___________________
Step 5 What would the next statement be? Find the sum. _______________
Step 6 Does the pattern rule in Step 3 always work? ___________________
Explain your answer.
_______________________________________________________
_______________________________________________________
Copyright © 2004 Pearson Education Canada Inc. 39
Name
Master 1.14
Date
Step-by-Step 4
Lesson 4, Question 5
Step 1 Find the sum: 5 + 4 = ___
Step 2 Write two different numbers that have the same sum as in Step 1.
___ + ___ = ___
Step 3 What other pairs of numbers have the same sum as in Step 1?
5 + 4 = ___ + ___
5 + 4 = ___ + ___
5 + 4 = ___ + ___
5 + 4 = ___ + ___
Step 4 How do you know when you have found all the pairs of numbers with
the same sum?
_______________________________________________________
_______________________________________________________
_______________________________________________________
Step 5 Repeat Steps 1 to 4 with each pair of numbers.
b) 8 + 7 = ___
c) 10 + 3 = ___
40 Copyright © 2004 Pearson Education Canada Inc.
d) 16 + 2 = ___
Name
Master 1.15
Date
Step-by-Step 5
Lesson 5, Question 5
Step 1 Find the difference: 18 – 6 = ___
Step 2 Write two different numbers that have the same answer as in Step 1.
___ – ___ = ___
Step 3 What other pairs of numbers have the same answer as in Step 1?
18 – 6 = ___ – ___
18 – 6 = ___ – ___
18 – 6 = ___ – ___
How did you find the numbers?
__________________________________________________
__________________________________________________
__________________________________________________
Step 4 Repeat Steps 1 to 3 for 20 – 3 = ___ – ___ .
Copyright © 2004 Pearson Education Canada Inc. 41
Name
Master 1.16
Date
Unit Test: Unit 1 Number Patterns
Part A
1. Use 1-cm grid paper. Make a 6-wide number chart from 1 to 48.
This chart will have 8 rows.
a) What patterns do you see in the rows? Columns? Diagonals?
b) Start at 4. Shade every 5th number.
Describe the position pattern.
c) Write a rule for the number pattern you shaded.
Use the rule to find the next 6 numbers in the pattern.
42 Copyright © 2004 Pearson Education Canada Inc.
Name
Master 1.16b
Date
Unit Test continued
2. a) Find the pattern rule for this pattern.
Write the next 3 terms.
67, 61, 55, 49, ___, ___, ___
b) Look at the pattern in part a.
Add 1 to each number.
Write the first 5 terms in this pattern.
Write the new pattern rule.
c) Look at the pattern in part a.
Use the same start number.
Subtract 1 from the number you take away.
Write the first 5 terms in this pattern.
Write the new pattern rule.
Part B
3. Find all the pairs of numbers that make this statement an equation.
11 + 3 = ___ + ___
Use a pattern rule so you know when you have found all possible ways.
Copyright © 2004 Pearson Education Canada Inc. 43
Name
Master 1.16c
Date
Unit Test continued
4. Each figure represents a different number.
Find the number that each figure represents.
+
+
= 11
8 =
+
Explain how you solved the problem.
Part C
5. Write as many different patterns as you can that begin with 1, 2, 3.
Tell about each pattern you write.
44 Copyright © 2004 Pearson Education Canada Inc.
Name
Master 1.17
Date
Sample Answers
Unit Test – Master 1.16
Part B
Part A
1. a)
b)
c)
2. a)
b)
c)
As you go across a row, each number
increases by 1.
As you go down a column, each number
increases by 6.
In a diagonal going down and to the right,
each number increases by 7.
In a diagonal going down and to the left,
each number increases by 5.
Start at 4. Go down 1 square, then
1 square left. Then start at 24 and go down
1 square, then 1 square left.
Start at 4. Count on by 5.
49, 54, 59, 64, 69, 74
43, 37, 31
Rule: Start at 67. Subtract 6 each time.
68, 62, 56, 50, 44
Rule: Start at 68. Subtract 6 each time.
67, 62, 57, 52, 47
Rule: Start at 67. Subtract 5 each time.
3. I can do this 7 ways.
11 + 3 = 14, so I begin with 0 + 14.
I added 1 to the first number and subtracted 1
from the second number until I reached 6 + 8.
0 + 14; 1 + 13; 2 + 12; 3 + 11; 4 + 10; 5 + 9;
6+8
If I continue, I would get the same pairs of
numbers, but in reverse order.
4. Square = 3, triangle = 5
The 1st equation is 2 squares and 1 triangle
make 11.
The second equation is 1 square and 1 triangle
make 8.
So, the extra square in the 1st equation is
11 – 8 = 3.
So, in the 2nd equation, if the square is 3,
then the triangle is 5.
I tried 3 and 5 in the first equation and
they worked.
Part C
5. 1, 2, 3, 4, 5, 6, … This is a growing pattern that
increases by 1 each time.
1, 2, 3, 1, 2, 3, 1, 2, 3, … This is a repeating
pattern with a core: 1, 2, 3.
1, 2, 3, 3, 2, 1, 1, 2, 3, 3 ,2, 1, … This is a
repeating pattern with a core: 1, 2, 3, 3, 2, 1.
1, 2, 3, 5, 7, 10, 13, 17, 21, … This is a growing
pattern where you start at 1, add 1 two times,
then add 2 two times, then add 3 two times, and
so on.
Copyright © 2004 Pearson Education Canada Inc. 45
Extra Practice Masters 1.18–1.21
Go to the CD-ROM to access editable versions of these Extra Practice Masters.
46 Copyright © 2004 Pearson Education Canada Inc.
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