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Assessment on the Pythagorean Theorem

By Donna Ventura

This assessment is to be used with the three lesson plans on the series to assess your student's knowledge of order of operations and the Pythagorean theorem.

The assessment is aligned to the Common Core State Standards for Mathematics – Grade 5 – Operations and Algebraic Thinking

5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

Materials Required: calculator, graph paper

Independent Work

Items 1 – 5

Find the value of each numerical expression. Remember to use the rules of Order of Operation.

  1. 16 / 4 + 4 x 2
  2. 6 x 6 - 12 / 3 + 9
  3. 8 + (3 x 8) - 8
  4. 28 - (3 x 5)
  5. (12 - 3) / (3 x 3)

Items 6 - 9

Write each numerical expression for the following.

6. Subtract 5 from 30, then multiply 2

7. 2 times larger than the difference between 168 and 144

8. Add 25 and 5, then divide by 2

9. Add the quotient of 16/ 2 to the product of 4 x 4

Items 10 - 13

Write the meaning for each of the following numerical expressions.

10. 2 x (3 + 6 - 1)
11.33 / 3 + 4 x 2
12. (5 + 6) - (2 x 4)
13. 18 / 3 + 4 x 2

Items 14– 18

In the chart below, generate a numerical pattern for each rule shown below.

14. Rule 1: Start at 0. Add 4.

 

15. Rule 2: Start at 0. Add 12.

16.  What relationship is there between each of the corresponding terms of the patterns?

17.  Form ordered pairs using the corresponding terms where x is the value of the terms in the pattern generated from Rule 1 and y is the value of the terms in the pattern generated from Rule 2.

18.  Graph the ordered pairs on a coordinate grid.

Answers

Items 1 – 5

Find the value of each numerical expression. Remember to use the rules of Order of Operation.

  1. 16 / 4 + 4 x 2 = 4 + 8 = 12
  2. 6 x 6 - 12 / 3 + 9 = 36 - 4 + 9 = 41
  3. 8 + (3 x 8) - 8 = 8 + 24 - 8 = 24
  4. 28 - (3 x 5) = 28 - 15 = 13
  5. (12 - 3) / (3 x 3) = 9 / 9 = 1

Items 6 - 9

Write each numerical expression for the following.

6. 2 x (30 - 5)
7. 2 x (168 - 144)
8. (25 + 5) / 2
9. 16 / 2 + 4 x 4

Items 10 - 13

Write the meaning for each of the following numerical expressions.

10. Add 3 and 6, then subtract 1, then multiply by 2
11. Divide 33 by 3, multiply 4 x 2, then add the quotient and the product
12. Add 5 and 6, multiply 2 x 4, then subtract the sum and the product
13. Divide 18 by 3, multiply 4 x 2, then add the quotient and the product

Items 14 - 18

In the chart below, generate the first six terms of the numerical pattern for each rule shown below.

14. 0, 4, 8, 12, 16, 20
15. 0, 12, 24, 36, 48, 60
16. Each term in the pattern generated by Rule 2 is 3 times the corresponding term in the pattern generated by Rule 1.
17. (0, 0) (4, 12) (8, 24) (12, 36) (16, 48) (20, 60)
18. Ordered pairs should be graphed on a coordinate grid.