Objective
Multiply and divide with rational numbers using properties of operations.
Common Core Standards
Core Standards
The core standards covered in this lesson
7.NS.A.2— Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
The Number System
7.NS.A.2— Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
7.NS.A.2.C— Apply properties of operations as strategies to multiply and divide rational numbers.
The Number System
7.NS.A.2.C— Apply properties of operations as strategies to multiply and divide rational numbers.
Foundational Standards
The foundational standards covered in this lesson
4.NBT.B.5
Number and Operations in Base Ten
4.NBT.B.5— Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
3.OA.B.5
Operations and Algebraic Thinking
3.OA.B.5— Apply properties of operations as strategies to multiply and divide.Students need not use formal terms for these properties.Example: Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)Example: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.)
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Apply the commutative property of multiplication to rearrange factors in more efficient ways.
- Apply the associative property of multiplication to group factors in more efficient ways.
- Apply the distributive property of multiplication to create equivalent expressions, which lend to different ways to solve.
- Rewrite expressions with division as problems using multiplication as a strategy to solve.
Tips for Teachers
Suggestions for teachers to help them teach this lesson
- There are many different approaches students can take to multiply and divide with rational numbers, and some of these approaches may be more efficient or easier than others, especially when looking carefully at the structure of the expression and thinking quantitatively about the values (MP.7 and MP.2).Using the examples, have students brainstorm various approaches to tackling each one; in addition to the strategies mentioned in the notes and guiding questions, students are bound to come up with other great approaches.
- Continue building fluency with mental math and other activities.
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Anchor Problems
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Problem 1
Evaluate each expression below. Compare your approaches with others in the class to determine the most efficient approach.
a.$${-6 \times 2 \times (-2) \times (-5) \times (-3)}$$
b.$${4 \times {1\over 3} \times (-8) \times 9 \times \left( -{1\over2} \right)}$$
Guiding Questions
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References
EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic B > Lesson 16—Example 1 and Exercise 2
Grade 7 Mathematics > Module 2 > Topic B > Lesson 16 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..
Problem 2
Evaluate the expression below. Compare your approachwith others in the class to determine the most efficient approach.
$${1 \div {2\over3} \times (-8) \times 3 \div \left ( -{1\over2} \right )}$$
Guiding Questions
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References
EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic B > Lesson 16—Example 4
Grade 7 Mathematics > Module 2 > Topic B > Lesson 16 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..
Problem 3
Evaluate the expression below. Can you determine an approach to solving this problem using the distributive property?
$${-6 \times \left(5{1\over3} \right)}$$
Guiding Questions
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References
EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic B > Lesson 16—Example 2
Grade 7 Mathematics > Module 2 > Topic B > Lesson 16 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..
Problem Set
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Fishtank Plus Content
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Use the properties of operations to evaluate the expression below.
$$-\frac{5}{6}\times24\times(-9)\div(-\frac{3}{2})\div\frac{25}{12}$$
Student Response
An example response to the Target Task at the level of detail expected of the students.
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Additional Practice
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
- Challenge: Evaluate:$$\frac{2(-8)+(-4)^2+2(-2)(-4)}{32\div2}$$
- Illustrative Mathematics Drill Rig
- Open Middle Equivalent Equations
- EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic B > Lesson 15—Problem Set
- EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic B > Lesson 16—Remaining Examples and Exercises, and Problem Set
Lesson 16
Lesson 18
