Write, Interpret, and Evaluate Numerical Expressions
Write, Interpret, and Evaluate Numerical Expressions
Objectives
Objectives haven't been entered into the unit plan.
Essential Questions
How can data be organized and represented to provide insight into the relationship between quantities?
How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations?
How can mathematics support effective communication?
How can patterns be used to describe relationships in mathematical situations?
How can probability and data analysis be used to make predictions?
How can recognizing repetition or regularity assist in solving problems more efficiently?
How does the type of data influence the choice of display?
How is mathematics used to quantify, compare, represent, and model numbers?
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.
- Calculator Chaos: http://www.mathplayground.com/calculator_chaos.html
- Interpreting Numerical Expressions
- National Governors Association Center for Best Practices & Council of Chief State School Officers (2010). Common Core State Standards in Mathematics. Washington D.C: Authors.
One to Ten Game: http://www.theproblemsite.com/games/onetoten2.asp
- Order of Operations: http://cemc2.math.uwaterloo.ca/mathfrog/english/kidz/order.shtml
- Order of Operations Bingo:
http://illuminations.nctm.org/LessonDetail.aspx?id=L730
- Order of Operations Review and Practice:
http://www.learnalberta.ca/content/mec/flash/index.html?url=Data/1/A/A1A2.swf
- Writing and Interpreting Numerical Expressions
http://www.mathgoodies.com/lessons/vol7/expressions.html
- Writing Equations
http://www.mathgoodies.com/lessons/vol7/equations.html
Formative Assessment
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View
Multiple-Choice Items:
- What is the value of the expression 4 + 7 × 3?
A
14
B
25
C
33
D
40
2. What is the value of the expression 12 – 8 ÷ 2?
A
2
B
3
C
6
D
8
3. What is the value of the expression (3 + 4) ÷ (10 – 8 + 5)?
A
0
B
1
C
7
D
14
4. What is the value of the expression 18 – (7 + 2) ÷ 3² × 4?
A
4
B
5
C
14
D
18
5. Both Jack and Henry found the value of the expression 20 + 3 × 4 – 5. Jack says the answer is 87 and Henry says the answer is 27. What did Jack do wrong?
A
He subtracted before he multiplied.
B
He didn’t do exponents first.
C
He added and subtracted before he divided.
D
He added before he multiplied.
6. Both Tina and Rochelle found the value of the expression (36 – 6) × 2 ÷ 2 + 1. Tina found the correct value. Which answer must be Tina’s?
A
8
B
13
C
20
D
31
7. Ella, Jack, and Sophia received money for doing chores. Ella and Jack got $12 to share equally. Sophia got $3 more than Ella. Which expression represents how much money Sophia received for doing chores?
A
3 ÷ 12 + 2
B
3 + 2 ÷ 12
C
12 ÷ 2 + 3
D
12 ÷ 3 + 2
8. Sean baked 150 cookies. He gave 6 containers of 12 cookies each away. Which expression represents the number of cookies Sean has left?
A
6 × 12 – 150
B
6 + 12 – 150
C
150 + (6 × 12)
D
150 – (6 × 12)
9. Chris made 4 times as many paper flowers as his little sister. Chris’s mom made 12 paper flowers. Chris’s little sister made 4 paper flowers. Which expression represents the number of paper flowers Chris’s family made in all?
A
4 × (4 + 12)
B
4 × 4 + (4 ×12)
C
4 × (4 + 12) + 4
D
4 × 4 + 12 + 4
Multiple-Choice Answer Key:
1. B
2. D
3. B
4. C
5. D
6. D
7. C
8. D
9. D
Short-Answer Items:
10. Evaluate the expression 8 × 6 ÷ [5² – (7 × 3)]. Show all your work.
11. Ayden and Eric evaluated the expression 17 – 3 × 4 + 5². Both got different values. Which of them has the correct value? Explain your thinking.
12. Hiro described the expression 5 + 8 – 9. He said the expression represents “9 less than the sum of 5 and 8”. Hiro is correct. Hiro described the expression (12 – 3) ÷ 6 as “12 minus 3 divided by 6”. What makes Hiro’s second description incorrect?
Short-Answer Key and Scoring Rubrics:
10. Evaluate the expression 8 × 6 ÷ [5² – (7 × 3)]. Show all your work.
8 × 6 ÷ [5² – (7 × 3)] =
8 × 6 ÷ [5² – 21] =
8 × 6 ÷ [25 – 21] =
8 × 6 ÷ 4 =
48 ÷ 4 =
12
Points
Description
2
- All work is shown and answer is correct.
- Student demonstrates thorough understanding of order of operations.
1
- Some work is shown and answer is correct.
- Student demonstrates some understanding of order of operations.
0
- No correct response is given.
- Student does not demonstrate understanding of order of operations.
11. Ayden and Eric evaluated the expression 17 – 3 × 4 + 5². Both got different values. Which of them has the correct value? Explain your thinking.
Eric has the correct value. Ayden did not follow the order of operations. He subtracted and added before multiplying. Multiplication is before addition and subtraction in the order of operations.
Points
Description
2
- Correct answer is indicated.
- Explanation is thorough, clear, and correct.
- Student demonstrates thorough understanding of order of operations.
1
- Correct answer is indicated.
- Explanation may be lacking or unclear.
- Student demonstrates some understanding of order of operations.
0
- Incorrect answer is indicated or no answer is chosen.
- Student does not demonstrate understanding of order of operations.
12. Hiro described the expression 5 + 8 – 9. He said the expression represents “9 less than the sum of 5 and 8”. Hiro is correct. Hiro described the expression (12 – 3) ÷ 6 as “12 minus 3 divided by 6”. What makes Hiro’s second description incorrect?
If it were just 12 – 3 ÷ 6, then the order of operations would require that 3 be divided by 6 first (division before subtraction), which would leave 12 – ½ or 11.5 as the answer. Since parentheses are used, they must be mentioned in the description. This ensures that the subtraction happens before the division, leaving 9 ÷ 6 or 3/2 or 1.5 as the correct answer. A better description would be “Divide the difference of 12 and 3 by 6.”
Points
Description
2
- Explanation is clear, complete, and correct.
- Student demonstrates thorough understanding of order of operations and modeling real-world problems as numeric expressions.
1
- Explanation may be unclear or incomplete.
- Student demonstrates some understanding of order of operations and modeling real-world problems as numeric expressions.
0
- Explanation is incorrect or missing.
- Student does not demonstrate understanding of order of operations and modeling real-world problems as numeric expressions.
Performance Assessment:
MATCHING. Write the letter of the corresponding expression in the blank.
1. _____ 3 × (7 – 5) a. The sum of 3 and 7 divided by 5.
2. _____ 3 + 7 ÷ 5 b. Five less than the product of 7 and 3.
3. _____ 3 × 7 – 5 c. Three more than the quotient of 7 and 5.
4. _____ (3 + 7) ÷ 5 d. Five less than the quotient of 7 and 3.
5. _____ 7 ÷ 3 – 5 e. Three times the difference between 7 and 5.
6. Danielle must find the value of the following expression: 15 – 3 × 4. Write out the steps necessary to simplify this expression. Explain each step.
7. Tad simplified the following expression but got the wrong answer.
Step 1: (2 + 14) – 3 × 5
Step 2: 16 – 3 × 5
Step 3: 13 × 5
Step 4: 65
Each step is shown. On which step did Tad make his first mistake? Find the correct value for the expression. Show each step.
8. Chadwick made 72 cookie dough balls for a school fundraiser. Shay made 6 less than twice as many. Write an expression that can be used to find how many cookie dough balls Chadwick and Shay made altogether. Find the value of the expression. Show all steps.
9. Jeneisha sold 50 packages of wrapping paper for a band fundraiser. Whitley sold 15 less than 4 times as many packages. Write an expression that can be used to find how many more packages of wrapping paper Whitley sold than Jeneisha. Find the value of the expression. Show all steps.
10. Taro described the expression 10 + (5 − 2) × 7 in words as “ten more than 7 times the difference of 5 and 2”. Describe the following expression in words: 14 + (6 ÷ 2).
11. In the unit, you learned about the order of operations. What is the order of operations and why is it necessary?
Performance Assessment Key and Scoring Rubric:
MATCHING. Write the letter of the corresponding expression in the blank.
1. __e__ 3 × (7 – 5) a. The sum of 3 and 7 divided by 5.
2. __c__ 3 + 7 ÷ 5 b. Five less than the product of 7 and 3.
3. __b__ 3 × 7 – 5 c. Three more than the quotient of 7 and 5.
4. __a__ (3 + 7) ÷ 5 d. Five less than the quotient of 7 and 3.
5. __d__ 7 ÷ 3 – 5 e. Three times the difference between 7 and 5.
6. Danielle must find the value of the following expression: 15 – 3 × 4. Write out the steps necessary to simplify this expression. Explain each step.
15 – 3 × 4
15 – 12 Multiplication before subtraction. I multiplied 3 and 4 to get 12.
3 I subtracted 12 from 15 to get 3.
7. Tad simplified the following expression but got the wrong answer.
Step 1: (2 + 14) – 3 × 5
Step 2: 16 – 3 × 5
Step 3: 13 × 5
Step 4: 65
Each step is shown. On which step did Tad make his first mistake? What did he do wrong? Find the correct value for the expression. Show each step.
Tad made his first mistake at step 3. He subtracted 3 from 16 before multiplying 3 by 5.
Step 1: (2 + 14) – 3 × 5
Step 2: 16 – 3 × 5
Step 3: 16 – 15
Step 4: 1
8. Chadwick made 72 cookie dough balls for a school fundraiser. Shay made 6 less than twice as many as Chadwick. Write an expression that can be used to find how many cookie dough balls Chadwick and Shay made altogether. Find the value of the expression. Show all steps.
72 + 2 × 72 – 6
72 + 144 – 6
216 – 6
210
9. Jeneisha sold 50 packages of wrapping paper for a band fundraiser. Whitley sold 15 less than 4 times as many packages. Write an expression that can be used to find how many more packages of wrapping paper Whitley sold than Jeneisha. Find the value of the expression. Show all steps.
4 × 50 – 15 – 50
200 – 15 – 50
185 – 50
135
10. Taro described the expression 10 + (5 – 2) × 7 in words as “ten more than 7 times the difference of 5 and 2”. Describe the following expression in words: 14 + (6 ÷ 2).
14 more than the quotient of 6 and 2
11. In the unit, you learned about the order of operations. What is the order of operations and why is it necessary?
The order of operations is Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. If the correct order of operations isn’t followed, then you may get the wrong answer. For instance, you may get a different answer by simplifying the expression from left to right instead of following the order of operations. This method ensures that everyone following the rules will get the same answer.
Points
Description
4
- Mathematical calculations are correct with complete work shown.
- Written explanations are thorough, clear, and use specific math language.
- Work displays advanced understanding of the questions, mathematical concepts, and processes related to the order of operations and modeling word problems as numerical expressions.
3
- Mathematical calculations are correct with some evidence of work shown.
- Written explanations are clear and use some specific math language.
- Work displays good understanding of the questions, mathematical concepts, and processes related to the order of operations and modeling word problems as numerical expressions.
2
- Mathematical calculations are mostly correct with minimal work shown.
- Written explanations are present but lack some detail. Specific math language may be present.
- Work displays partial understanding of the questions, mathematical concepts, and processes related to the order of operations and modeling word problems as numerical expressions.
1
- Mathematical calculations are incorrect with minimal work shown.
- Written descriptions are incomplete and lack detail.
- Work displays little understanding of the questions, mathematical concepts, and processes related to the order of operations and modeling word problems as numerical expressions.
0
- Mathematical calculations are incorrect or incomplete. No work shown.
- Written descriptions are illogical or not present.
- Work displays no real understanding of the questions, mathematical concepts, or processes related to the order of operations and modeling word problems as numerical expressions.
Final 05/10/2013
