Using Patterns in Algebraic Thinking
Using Patterns in Algebraic Thinking
Objectives
Students will work with number and shape patterns, as well as number patterns represented in input/output tables. Students will:
- generate number patterns, given a rule and starting number, while identifying features of the sequence.
- generate shape patterns, given a rule and description/drawing of the first element in the pattern, while also identifying features of the pattern.
- determine the rule used to create an input/output table and apply the rule to find the missing elements in the table.
Essential Questions
- How is mathematics used to quantify, compare, represent, and model numbers?
- How are relationships represented mathematically?
- How can patterns be used to describe relationships in mathematical situations?
- How can recognizing repetition or regularity assist in solving problems more efficiently?
- How can data be organized and represented to provide insight into the relationship between quantities?
Related Unit and Lesson Plans
Related Materials & Resources
The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.
- NLVM applet that provides students an opportunity to fill in missing terms, in a sequence.
http://nlvm.usu.edu/en/nav/frames_asid_185_g_2_t_1.html?from=category_g_2_t_1.html
- NLVM applet that provides students an opportunity to see different number patterns, on a hundreds chart.
http://nlvm.usu.edu/en/nav/frames_asid_337_g_2_t_1.html?open=instructions&from=category_g_2_t_1.html
- NLVM applet that provides students an opportunity to explore functions.
http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_1.html?open=instructions&from=grade_g_3.html
- Illuminations applet that allows students to create their own shape patterns.
http://illuminations.nctm.org/ActivityDetail.aspx?ID=70
- NLVM applet that allows students to create AB, ABBA, and other shape patterns.
http://nlvm.usu.edu/en/nav/frames_asid_169_g_1_t_2.html?open=activities
- IXL activity that asks students to determine the rules used in input/output tables and type missing values into the tables.
- IXL activity that provides brief contexts and rules written with variables and asks students to type missing values into tables.
http://ca.ixl.com/math/grade-4/function-tables
Formative Assessment
-
View
Multiple-Choice Items:
- Which of the following number patterns shows the rule “Add 9”?
- 6, 9, 12, 15, 18, . . .
- 2, 11, 15, 24, 30, . . .
- 8, 17, 25, 34, 41, . . .
- 4, 13, 22, 31, 40, …
- What is the rule used to create this sequence: 7, 14, 28, 56, 112, . . . ?
- Add 7.
- Add 14.
- Multiply by 2.
- Multiply by 3.
- Which of the following creates a number pattern with alternating odd and even numbers?
- Add 8, starting with 4.
- Subtract 2, starting with 15.
- Add 5, starting with 3.
- Multiply by 3, starting with 2.
- What is the rule used to create the shape pattern below?
- Add 2 squares to the column.
- Add 1 square to the row.
- Add 4 squares to the column.
- Add 2 squares to the row.
- What is the rule used to create the shape pattern below?
- Increase the number of vertices by 1.
- Increase the number of vertices by 2.
- Increase the number of sides by 2.
- Increase the number of angles by 2.
- Given the shape pattern below, which of the following statements is true?
A. The area of the shaded part increases by 12 units.
B. The perimeter of the shaded part doubles in units.
C. The perimeter of the shaded part increases by 8 units.
D. The area of the shaded part increases by 4 units.- What is the rule used to create the input/output table below?
In
Out
4
15
9
20
14
25
17
28
21
32
- Add 3.
- Add 5.
- Add 9.
- Add 11.
- What is the rule used to create the input/output table below?
In
Out
2
8
5
20
9
36
14
56
20
80
- Add 6.
- Multiply by 4.
- Add 12.
- Add 16.
- Which of the following tables represents the rule “Multiply by 2?”
Multiple-Choice Answer Key:
1. D
2. C
3. C
4. A
5. A
6. B
7. D
8. B
9. C
Short-Answer Items:
- Kelsey’s savings doubles each month. At the end of the first month, Kelsey had $9 in her savings account. How much money will she have in her account at the end of 6 months? Write the sequence and solve.
- Describe a rule that may be used to create the shape pattern below. Identify the number of circles that will be found in the sixth shape.
- Find the rule for the table below and fill in the missing value.
Short-Answer Key and Scoring Rubrics:
- Kelsey’s savings doubles each month. At the end of the first month, Kelsey had $9 in her savings account. How much money will she have in her account at the end of 6 months? Write the sequence and solve.
The correct sequence is 9, 18, 36, 72, 144, 288, . . .
The solution is $288.
Points
Description
2
The student provides an accurate sequence and a solution.
1
The student provides an accurate sequence or a solution.
0
The student does not provide an accurate sequence or a solution.
- Describe a rule that may be used to create the shape pattern below. Identify the number of circles that will be found in the sixth shape.
Answers will vary.
A possible rule is “Add a new column on the right that has 1 more circle than the tallest column in the shape.” The 6th shape will have 28 circles.
Points
Description
2
The student provides an accurate rule and a solution.
1
The student provides an accurate rule or a solution.
0
The student does not provide an accurate rule or a solution.
- Find the rule for the table below and fill in the missing value.
The correct rule is “Multiply by 7.”
The missing value is 8.
Points
Description
2
The student provides an accurate rule and a missing value.
1
The student provides an accurate rule or a missing value.
0
The student does not provide an accurate rule or a missing value.
Performance Assessment:
- Arlan collects stamps. He starts his collection with 6 stamps and adds 4 stamps during each of the following months. How many stamps will he have after 1 year? Show how you found your answer.
- Arlan’s friend, George, also collects stamps. He starts his collection with 2 stamps, but doubles the number of stamps during each of the following months. After which month will George have more stamps than Arlan? Explain.
- Describe how the number of stamps George has at the end of 1 year compares to the number of stamps Arlan has.
- Provide a model of the number of stamps Arlan has during the first half of the year. Explain how a model of the number of stamps George has after 6 months would compare.
Performance Assessment Key:
- Arlan collects stamps. He starts his collection with 6 stamps and adds 4 stamps during each of the following months. How many stamps will he have after 1 year? Show how you found your answer.
50 stamps
- Arlan’s friend, George, also collects stamps. He starts his collection with 2 stamps, but doubles the number of stamps during each of the following months. After which month will George have more stamps than Arlan? Explain.
Month 5
- Describe how the number of stamps George has at the end of 1 year compares to the number of stamps Arlan has.
George will have 4,096 stamps. Arlan will have 50 stamps. George will have 4,046 more stamps than Arlan.
- Provide a model of the number of stamps Arlan has during the first half of the year. Explain how a model of the number of stamps George has after 6 months would compare.
Performance Assessment Scoring Rubric:
Points
Description
4
- All answers are complete and correct.
- Work is shown and goes beyond problem requirements.
- Student demonstrates advanced understanding of using patterns to solve problems, explain ideas, make comparisons, and model mathematical or real-world situations.
3
- Most answers are complete and correct.
- Work is shown for most problems and all problem requirements are met.
- Student demonstrates a strong understanding of using patterns to solve problems, explaining ideas, making comparisons, and modeling.
2
- Many answers are complete and correct.
- Little work is shown and it fails to meet all problem requirements.
- Student demonstrates a limited understanding of using patterns to solve problems, explaining ideas, making comparisons, and modeling.
1
- Some answers are complete and correct.
- Very little correct work is shown.
- Student demonstrates a very limited understanding of using patterns to solve problems, explain ideas, make comparisons, or model mathematical and real-world situations.
0
- No answers are correct.
- No work is attempted.
- Student demonstrates no understanding of using patterns to solve problems, explain ideas, make comparisons, or model mathematical and real-world situations.
Final 06/28/2013
