Page 1 of 17 Math Live © 2009 Alberta Education (www.learnalberta.ca) Math Live – Patterns: Assessment Task Grade: 4 Strand: Patterns and Relations (Patterns) Outcome: 1, 2, 3, 4 SPECIFIC LEARNER OUTCOMES - Patterns and Relations (Patterns) P1 Identify and describe patterns found in tables and charts. P2 Translate among different representations of a pattern, such as a table, a chart or concrete materials. P3 Represent, describe and extend patterns and relationships, using charts and tables, to solve problems. P4 Identify and explain mathematical relationships, using charts and diagrams, to solve problems. PROCESSES Communication (C), Connections (CN), Mental Mathematics and Estimation (ME), Problem Solving (PS), Reasoning (R), Technology (T), Visualization (V) C, CN, PS, R, V EVIDENCE the student has achieved the outcomes Each student will: • model a pattern from a problem-solving context using manipulatives and drawings. • complete a chart to reveal a pattern. • describe in words/symbols the rule used to generate a pattern. • predict and justify the solution to a problem by extending a pattern rule. TEACHER NOTE • In this assessment task, students will be asked to demonstrate their understanding of patterns within a problem-solving context. They will use wooden trapezoid blocks to represent tables placed side by side in a cafeteria. Students will first complete a chart to represent the number of chairs that can be placed around a one, two, or three-table arrangement. Students then draw extensions of the pattern and find the relationship between the number of tables and the number of chairs that can be placed around the table arrangements. Finally, students explain the rule that generates the pattern and predict the number of chairs that can be placed around 10 tables without drawing. • Students should have easy access to wooden isosceles trapezoid blocks or cut-out copies of the master.
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Page 1 of 17Math Live © 2009 Alberta Education (www.learnalberta.ca)
Math Live – Patterns: Assessment Task
Grade: 4 Strand: Patterns and Relations (Patterns) Outcome: 1, 2, 3, 4 SPECIFIC LEARNER OUTCOMES - Patterns and Relations (Patterns)
P1 Identify and describe patterns found in tables and charts.
P2 Translate among different representations of a pattern, such as a table,
a chart or concrete materials.
P3 Represent, describe and extend patterns and relationships, using charts and tables, to solve problems.
P4
Identify and explain mathematical relationships, using charts and diagrams, to solve problems.
PROCESSES Communication (C), Connections (CN), Mental Mathematics and Estimation (ME), Problem Solving (PS), Reasoning (R), Technology (T), Visualization (V)
C, CN, PS, R, V EVIDENCE the student has achieved the outcomes
Each student will: • model a pattern from a problem-solving context using manipulatives and drawings. • complete a chart to reveal a pattern. • describe in words/symbols the rule used to generate a pattern. • predict and justify the solution to a problem by extending a pattern rule.
TEACHER NOTE • In this assessment task, students will be asked to demonstrate their understanding of
patterns within a problem-solving context. They will use wooden trapezoid blocks to represent tables placed side by side in a cafeteria. Students will first complete a chart to represent the number of chairs that can be placed around a one, two, or three-table arrangement. Students then draw extensions of the pattern and find the relationship between the number of tables and the number of chairs that can be placed around the table arrangements. Finally, students explain the rule that generates the pattern and predict the number of chairs that can be placed around 10 tables without drawing.
• Students should have easy access to wooden isosceles trapezoid blocks or cut-out copies of the master.
• There are several rules that students may use to generate this pattern:
Page 2 of 17Math Live © 2009 Alberta Education (www.learnalberta.ca)
Number of Tables 1 2 3 Number of Chairs 5 8 11
Rule #1: Add 3 each time you add a table
5 + 3 + 3 + 3… 5 + [(Number of tables – 1) x 3] = Number of chairs
Rule #2: (Number of tables x 3) + 2 = Number of chairs
Rule #3: (Number of tables x 5) – (2 x Number of sides touching) = Number of chairs
Rule #4: (Number of tables x 5) – [2 x (Number of tables – 1)] = Number of chairs
Math Live – Patterns: Assessment Task The school bought tables in the form of trapezoids for the cafeteria. Two chairs are placed on the long side of the table and one chair is placed on each of the short sides.
As shown below, the cafeteria staff placed the tables end to end to save space.
Page 3 of 17Math Live © 2009 Alberta Education (www.learnalberta.ca)
1 table 2 tables 3 tables
1. Use the trapezoid shapes provided to build models of arrangements made with 4, 5 and 6 tables. Draw a picture of each model below and record the number of chairs surrounding each arrangement.
4 tables
5 tables
6 tables
2. Show how many chairs can be placed around 1 to 6 tables by completing the chart below.
Number of tables
Number of chairs
3. Describe a pattern rule that can be used to describe the relationship between the number of tables and the number of chairs.
4. Use your pattern rule to find out how many chairs will fit around 10
tables. Show all your thinking.
Page 4 of 17Math Live © 2009 Alberta Education (www.learnalberta.ca)
Blackline Master – Trapezoid Shapes
Page 5 of 17Math Live © 2009 Alberta Education (www.learnalberta.ca)
Math Live – Patterns: Scoring Guide
Level
Criteria
Models a pattern from a problem- solving context using drawings
Question #1
Completes a chart to reveal a pattern
Question #2
Describes a rule used to generate a pattern
Question #3
Solves a problem by extending a pattern rule
Question #4 Wow! Provides a logical
and insightful description strongly supported by evidence
Applies an insightful and efficient pattern rule (i.e. beyond just adding by 3) supported by evidence of how the pattern was used to arrive at a solution
Yes
Correctly represents the pattern formed by the tables and chairs in an accurate drawing
Accurately completes the chart including labeling the number of tables as well as the resulting number of chairs
Provides a description
Applies a pattern rule supported by
supported by evidence
evidence of how pattern was used to arrive at a solution
Yes, but… Represents the pattern formed by the tables and chairs with minor errors in the drawing
Completes the chart with the pattern formed by the chairs without labeling the number of tables
Provides a description which is partially supported by evidence
Applies a pattern rule but shows only partial evidence of how the pattern was used to arrive at a solution
No, but… Draws a representation which fails to represent the pattern formed by the tables and chairs
Inaccurately completes the chart or only partially records the pattern formed by the chairs
Provides a description which is inaccurate and/or unsupported
Applies an inappropriate pattern rule and/or shows little evidence of how a solution was generated
Insufficient / Blank
No score awarded due to insufficient evidence of student learning based on the requirements of the assessment task
No score awarded due to insufficient evidence of student learning based on the requirements of the assessment task
No score awarded due to insufficient evidence of student learning based on the requirements of the assessment task
No score awarded due to insufficient evidence of student learning based on the requirements of the assessment task
Page 6 of 17Math Live © 2009 Alberta Education (www.learnalberta.ca)
Page 7 of 17Math Live © 2009 Alberta Education (www.learnalberta.ca)
Math Live – Patterns: Assessment Task Wow!
The school has bought tables in the form of trapezoids for the cafeteria. Two chairs are placed on the long side of the table and one chair is placed on each of the short sides.
The cafeteria staff placed the tables end to end to save space as shown below.
1 table 2 tables 3 tables
5. Use the trapezoid shapes provided to build models of arrangements made with 4, 5 and 6 tables. Draw a picture of each model below and record the number of chairs surrounding each arrangement.
6. Show how many chairs can be placed around 1 to 6 tables by completing the chart below.
Wow! 7. Describe a pattern rule that can be used to describe the relationship
between the number of tables and the number of chairs. 8. Use your pattern rule to find out how many chairs will fit around 10
tables. Show all your thinking.
Math Live © 2009 Alberta Education (www.learnalberta.ca)
Page 8 of 17
Math Live – Patterns: Assessment Task Yes
The school has bought tables in the form of trapezoids for the cafeteria. Two chairs are placed on the long side of the table and one chair is placed on each of the short sides.
The cafeteria staff placed the tables end to end to save space as shown below.
1 table 2 tables 3 tables
1. Use the trapezoid shapes provided to build models of arrangements made with 4, 5 and 6 tables. Draw a picture of each model below and record the number of chairs surrounding each arrangement.
2. Show how many chairs can be placed around 1 to 6 tables by completing the chart below.
Math Live © 2009 Alberta Education (www.learnalberta.ca)
Page 9 of 17
Yes
3. Describe a pattern rule that can be used to describe the relationship between the number of tables and the number of chairs.
4. Use your pattern rule to find out how many chairs will fit around 10 tables. Show all your thinking.
Math Live © 2009 Alberta Education (www.learnalberta.ca)
Page 10 of 17
Yes
5. Describe a pattern rule that can be used to describe the relationship between the number of tables and the number of chairs.
6. Use your pattern rule to find out how many chairs will fit around 10 tables. Show all your thinking.
Math Live © 2009 Alberta Education (www.learnalberta.ca)
Page 11 of 17
Yes
7. Describe a pattern rule that can be used to describe the relationship between the number of tables and the number of chairs.
8. Use your pattern rule to find out how many chairs will fit around 10 tables. Show all your thinking.
Math Live © 2009 Alberta Education (www.learnalberta.ca)
Page 12 of 17
Yes
9. Describe a pattern rule that can be used to describe the relationship between the number of tables and the number of chairs.
10. Use your pattern rule to find out how many chairs will fit around 10 tables. Show all your thinking.
Math Live © 2009 Alberta Education (www.learnalberta.ca)
Page 13 of 17
Math Live – Patterns: Assessment Task
Yes, but
The school has bought tables in the form of trapezoids for the cafeteria. Two chairs are placed on the long side of the table and one chair is placed on each of the short sides.
The cafeteria staff placed the tables end to end to save space as shown below.
1 table 2 tables 3 tables
1. Use the trapezoid shapes provided to build models of arrangements made with 4, 5 and 6 tables. Draw a picture of each model below and record the number of chairs surrounding each arrangement.
2. Show how many chairs can be placed around 1 to 6 tables by completing the chart below.
Math Live © 2009 Alberta Education (www.learnalberta.ca)
Page 14 of 17
Yes, but 3. Describe a pattern rule that can be used to describe the relationship
between the number of tables and the number of chairs.
4. Use your pattern rule to find out how many chairs will fit around 10
tables. Show all your thinking.
Math Live © 2009 Alberta Education (www.learnalberta.ca)
Page 15 of 17
Math Live – Patterns: Assessment Task No, but
The school has bought tables in the form of trapezoids for the cafeteria. Two chairs are placed on the long side of the table and one chair is placed on each of the short sides.
The cafeteria staff placed the tables end to end to save space as shown below.
1 table 2 tables 3 tables
1. Use the trapezoid shapes provided to build models of arrangements made with 4, 5 and 6 tables. Draw a picture of each model below and record the number of chairs surrounding each arrangement.
2. Show how many chairs can be placed around 1 to 6 tables by completing the chart below.
Math Live © 2009 Alberta Education (www.learnalberta.ca)
Page 16 of 17
No, but 3. Describe a pattern rule that can be used to describe the relationship
between the number of tables and the number of chairs. 4. Use your pattern rule to find out how many chairs will fit around 10
tables. Show all your thinking. Math Live © 2009 Alberta Education (www.learnalberta.ca)
Page 17 of 17
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