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Name: ___________________________ Date: ____________________________

Grade 4 – Patterning Review

1. Fill in or draw the next three terms in each pattern and write the rule in words.

a) pink, blue, pink, pink, blue, pink, _______, _______, _______, … Rule:

b) 4, 8, 16, 32 ___ , ___, ___, …

Rule: c) 267, 263, 259, 255, ___, ___, ___, …

Rule: e)

Rule: f)

Rule: Fill in the missing terms and write the pattern rule. g) 3, 6, 9, ____, ____, 18, … Rule: h) 75, ____, 63, 57, ____, 45, 39,… Rule:

i ) 5, 10, ____, 40, 80, 160, … Rule: j ) 1, 1, 3, 2, 1, 1, ____, 2, … Rule:

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2. Create a number pattern and a geometric pattern using the pattern rule given. Write or draw the first 4 terms.

a) Start at 2. Multiply each term by 2 to get the next number.

Number Pattern:

Geometric Pattern: b) Start at 18, subtract 4 each time to get the next number.

Number Pattern:

Geometric Pattern:

c) Repeating pattern with the pattern core ABAC

Number Pattern:

Geometric Pattern:

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3. Start with the shape below and reflect it up, down, left, or right, to create a pattern core. Repeat the pattern core once.

Describe your pattern and how you created it.

4. Olivia made a pattern with marshmallows.

Figure 1 Figure 2 Figure 3 Figure 4

a) How many marshmallows does she need to make the 5th figure? Show your work. b) How many marshmallows does she need to make the 10th figure? Show your work.

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5. Mya started saving money for her school trip. She saved $4 every week. a) Complete the table of values to show how much Mya saved for the first five weeks.

b) How much money would Mya have saved in 12 weeks? Show all your work.

6.

What will the 20th term in this pattern be? Show your work and justify your thinking.

Term

Number

(Number of

Weeks)

Term

(Money

Saved $)

1 4

2

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7. Mr. Bee created this number pattern. * Start at 1 and add 5 each time. Mrs. Ant created this number pattern. * Start at 3 and add 7 each time. !

What number is in both Mr. Bee’s and Mrs. Ant’s pattern? Show your work and justify your answer.

8. A growing pattern starts with 3 and ends with 28. What could the pattern rule be? Show your work and justify your thinking.

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Review Answer Key

1. Fill in or draw the next three terms in each pattern and write the rule in words.

a) pink, blue, pink, pink, blue, pink, pink, blue, pink, …

Rule: Repeating pattern, pattern core “pink, blue, pink” b) 4, 8, 16, 32, 64, 128, 256, …

Rule: Start at 4. Multiply by 2 or double each term to get the next number.

c) 267, 263, 259, 255, 251, 247, 243, …

Rule: Start at 267. Subtract 4 each time. e)

Rule: Repeating pattern, pattern core AB f)

Rule: Start with 13 squares. Subtract 2 squares from the top each time. Fill in the missing terms and write the pattern rule. g) 3, 6, 9, 12, 15, 18, … Rule: Start at 3. Add 3 each

time.

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h) 75, 69, 63, 57, 51, 45, 39,… Rule: Start at 75. Subtract 6 each time.

i ) 5, 10, 20, 40, 80, 160, … Rule: Start at 5. Multiply by

2 or double each term to get the next number.

j ) 1, 1, 3, 2, 1, 1, 3 , 2, … Rule: Repeating pattern core,

“1, 1, 3, 2”

2. Create a number pattern and a geometric pattern using the pattern

rule given. Write or draw the first 4 terms.

a) Start at 2. Multiply each term by 2 to get the next number.

Number Pattern: 2, 4, 8, 16, …

Geometric Pattern:

Possible Answer: b) Start at 18, subtract 4 each time to get the next number.

Number Pattern: 18, 14, 10, 6, …

Geometric Pattern: Possible Answer:

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c) Repeating pattern with the pattern core ABAC

Number Pattern: 20, 30, 20, 40, …

Geometric Pattern: Possible Answer:

3. Start with the shape below and reflect it up, down, left, or right, to create a pattern core. Repeat the pattern core once.

Possible Answer:

Describe your pattern and how you created it.

Possible Answer: Repeating pattern, pattern core: ABA Created by reflecting the shape up.

4. Olivia made a pattern with marshmallows.

Figure 1 Figure 2 Figure 3 Figure 4

1 5 9 13 a) How many marshmallows does she need to make the 5th figure? Show your

work. The pattern rule is start with one and add 4 marshmallows each time. 1, 5, 9, 13 13 + 4 = 17 She needs 17 marshmallows to make the 5th figure.

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b) How many marshmallows does she need to make the 10th figure? Show your work.!!

Continue the pattern. She needs 37 marshmallows for the 10th figure.

5. Mya started saving money for her school trip. She saved $4 every week.

a) Complete the table of values to show how much Mya saved for the first five weeks.

b) How much money would Mya have saved in 12 weeks? Show all your work.

4 + 4 + 4 + 4 + 4 + 4 +4 + 4 + 4 + 4 + 4 + 4 or 12 x 4 = 48 She would have $48 saved in 12 weeks.

Figure Number of

Marshmallows

6 21

7 25

8 29

9 33

10 37

Term

Number

(Number of

Weeks)

Term

(Money

Saved $)

1 4

2 8 3 12

4 16

5 20

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6.

What will the 20th term in this pattern be? Show your work and justify your thinking.

Pattern Core: Terms : 1 2 3 4

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 The 20th term will be because all terms that are multiples of 4 are the white circle. 20 is a multiple of 4 so it will be the white circle. 7. Mr. Bee created this number pattern. * Start at 1 and add 5 each time. Mrs. Ant created this number pattern. * Start at 3 and add 7 each time. !

What number is in both Mr. Bee’s and Mrs. Ant’s pattern? Show your work and justify your answer.

Mr. Bee’s pattern: 1, 6, 11, 16, 21, 26, 31, 36, 41 Mrs. Ant’s pattern: 3, 10, 17, 24, 31 A number that is in both Mr. Bee’s and Mrs. Ant’s pattern is 31.

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8. A growing pattern starts with 3 and ends with 28. What could the pattern rule be? Show your work and justify your thinking. Guess and test: Add 2: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29 Add 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 Add 4: 3, 7, 11, 15, 19, 23, 27 Add 5: 3, 8, 13, 18, 23, 28 The pattern could be 3, 8, 13, 18, 23, 28 The pattern rule is start at 3 and add 5 each time.

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Name: __________________________ Date: ____________________________

Grade 4 – Patterning Unit Test Part A: Knowledge and Understanding

1. Fill in the next three terms in each pattern.

a) ____, ___, ___, … b) 92, 81, 70, 59, ____, ____, ____, … c) 3, 6, 12, 24, ___, ___, ___, … d)

40 41 42 43 44 45 46 47 e) ____, ____, ____, … 2. What is the 5th term in each pattern?

a) 5th term: _______ b) 18, 15, 12, 9, 6, 3, … 5th term: _______

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3. Write the pattern rule in words for each pattern. a) Rule:

b) Rule:

c) 1, 3, 9, 27, … Rule: Part B: Problem Solving and Thinking

4. Create a pattern using the pattern rules given. Write or draw the first 5 terms.

a) Numeric pattern; start at 20, subtract 3 each time

b) Geometric pattern; start at 1, multiply by 2 each time c) Repeating pattern, pattern core A B C B

d) Numeric pattern; start at 350, subtract 5 each time

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5. Asha created a pattern with toothpicks. How many toothpicks does she need for figure 10? Show your work.

Figure 1 Figure 2 Figure 3 Figure 4

Part C: Application and Communication

6. Mr. Corda alternates taking the subway to work, riding his bike, and driving his car. On day 1 he takes the subway, on day 2 he rides his bike, and on day 3 he drives his car, and then he repeats this pattern for the rest of the month. How will Mr. Corda get to work on the 31st day of the month? Explain how you know and justify your thinking.

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7. Raji created a pattern where the 3rd term is 15. a) What could the 1st, 2nd and 4th terms be if the pattern is a growing pattern? Show all your work and prove your answer.

b) What could the 1st, 2nd and 4th terms be if the pattern is a shrinking pattern? Show all your work and prove your answer.

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Test Answer Key Part A: Knowledge and Understanding

2. Fill in the next three terms in each pattern.

a) ___, ____, ___, … b) 92, 81, 70, 59, 48, 37, 26, … c) 3, 6, 12, 24, 48, 96, 192, …

d) 40 41 42 43 44 45 46 47 48 50 e) ____, ____, ____, … 2. What is the 5th term in each pattern?

a) 5th term: 10 b) 18, 15, 12, 9, 6, 3, … 5th term: 6

52

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3. Write the pattern rule in words for each pattern. a) Rule: Start at 45. Add 11 each time

to get the next term.

b) Rule: Start with three squares. Add one square to the top and one square to the bottom each time.

c) 1, 3, 9, 27, … Rule: Start at 1. Mulitply by 3 or triple each number to get the next term. Part B: Problem Solving and Thinking

4. Create a pattern using the pattern rules given. Write or draw the first 5 terms.

a) Numeric pattern; start at 20, subtract 3 each time 20, 17, 14, 11, 8, …

b) Geometric pattern; start at 1, multiply by 2 each time

c) Repeating pattern, pattern core A B C B

d) Numeric pattern; start at 350, subtract 5 each time

350, 345, 340, 335, 330, …

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5. Asha created a pattern with toothpicks. How many toothpicks does she need for figure 10? Show your work.

Figure 1 Figure 2 Figure 3 Figure 4 Possible solution: Asha would need 21 toothpicks for the 10th figure.

Part C: Application and Communication

6. Mr. Corda alternates taking the subway to work, riding his bike, and driving his car. On day 1 he takes the subway, on day 2 he rides his bike, and on day 3 he drives his car, and then he repeats this pattern for the rest of the month. How will Mr. Corda get to work on the 31st day of the month? Explain how you know and justify your thinking. Possible Solution:

Subway = S Bike= B Car = C

S, B, C, S, B, C, S, B, C, S, B, C, …

On the 6th day he would take his car. He would also drive his car on the 12th, 18th, 24th and 30th day. Since he always takes the subway one day after he drives his car, he will take the subway on the 31st day.

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7. Raji created a pattern where the 3rd term is 15. a) What could the 1st, 2nd and 4th terms be if the pattern is a growing pattern? Show all your work and prove your answer.

Possible solution: ____, _____, 15, _____,

I think I can create an addition pattern. I will work backwards. 15 – 5 = 10 10 – 5 = 5 15 + 5 = 20 Pattern: 5, 10, 15, 20, … OR 15 - 2 = 13 13 - 2 = 11 15 + 2 = 17 Pattern: 11, 13, 15, 17, … b) What could the 1st, 2nd and 4th terms be if the pattern is a shrinking pattern? Show all your work and prove your answer.

Possible solution:

____, _____, 15, _____,

I will create a shrinking pattern with subtraction. I will work backwards and add 3 to each term. 15 + 3 = 18

18 + 3 = 21 15 – 3 = 12 Pattern: 21, 18, 15, 12, …

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Patterning LEVEL “R” LEVEL 1 LEVEL 2 LEVEL 3 LEVEL 4 Below Grade Level Below Grade Level Approaching Grade Level Grade Level Grade Level

PART A: 1, 2, 3

Knowledge and Understanding - knowledge of content; facts, terms, skills, tools) - understanding of concepts - total marks / 10

With help, student demonstrates minimal evidence of understanding basic mathematical concepts. (e.g., 1/10 or 2/10)

With help, demonstrates a partial understanding of most mathematical concepts. There are many errors/omissions. (e.g., 3 or 4/10)

Independently demonstrates some knowledge of mathematical concepts. There are some errors/omissions. (e.g., 5/10 or 6/10)

Demonstrates considerable knowledge of mathematical concepts. There are no major errors or omissions. (e.g., 7/10 or 8/10)

Demonstrates thorough knowledge of content. There are minimal errors or omissions. (e.g, 9/10, or 10/10)

PART B: 4. 5

Problem Solving/Thinking -use of planning skills (understand the problem, make a plan, carry out the plan and look back at solution for reasonableness) - organization of ideas and thinking (clarity, logical organization, using pictures, graphics, numeric or algebraic forms)

Attempts a solution that is unrelated to the problem, or no solution is evident.

Limited evidence of a plan. Solution is incomplete, but attempted. Difficult to understand solution process. (e.g., in question 4, accurately creates one of the patterns when given the rule, and in question 5 student extends the next few figures accurately but does not extend to the 10th figure)

Some evidence of a plan. Needs to look back at solution for reasonableness. Student may not have shown all their thinking. (e.g., in question 4, accurately creates two of the patterns when given the rule, and in question 5 student extends many figures accurately, but information is missing or inaccurate with regard to solving for the 10th figure)

Evidence of a plan. Ideas are mostly organized and expressed using pictures, graphics, tables or numeric/algebraic forms. Most steps in solution are evident. (e.g., in question 4, accurately creates three of the patterns or all four patterns with a few minor errors, and in question 5, student extends required figures accurately using a drawing, numbers, or table of values, but minor errors make solution for the 10th figure incorrect)

Clear evidence of a plan. Ideas and solution are easy to follow. Problem is solved with efficiency and accuracy. All steps in solution are evident.

PART C: 6, 7

Application and Communication - application of knowledge and skills in familiar and new contexts - making conjectures, drawing conclusions, make convincing arguments, justifying, proving and reflecting

Attempts a solution that is unrelated to the problem, or no solution is evident.

Experiences difficulty transferring knowledge to new situations. Explains some simple ideas, but does not provide accurate evidence. (e.g., in question 6 student may identify the pattern core accurately and assign symbols for each method of transportation)

Transfers knowledge to some new situations, but experiences difficulty making connections and convincing arguments. (e.g., in question 6, student identifies pattern core and attempts to extend the pattern to the 31st term; errors in repeating the pattern lead to an incorrect solution; some ideas missing or unclear)

Transfers knowledge to most new situations. Makes convincing arguments and provides some evidence to justify and explain thinking. (e.g., in question 6, student identifies pattern core, and extends it to solve the problem; minor errors may lead to an incorrect solution, but solution is generally logical and clear)

Transfers knowledge to new situations. Makes in-depth inferences, arguments and evidence to justify and explain thinking. (e.g., in questions 6, student shows complete mathematical proof and an accurate answer)

Parent/Student comments: OVERALL SCORE: