ALEX Resources

   View Standards     Standard(s): [MA2019] REG-7 (7) 8 :

8. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

[MA2019] ACC-7 (7) 9 :

9. Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable. [Grade 7, 5]

[MA2019] ACC-7 (7) 17 :

17. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions, and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies. [Grade 7, 8]

In this learning activity, students will learn to solve multistep problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. The students will apply properties of operations to calculate numbers in any form; convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies.

This learning activity can be used as a stand-alone activity but is best used as a Before Activity, the During and After Activities can be found in the Tools or Recommendations section.

   View Standards     Standard(s): [MA2019] REG-7 (7) 8 :

8. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

[MA2019] ACC-7 (7) 9 :

9. Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable. [Grade 7, 5]

[MA2019] ACC-7 (7) 17 :

17. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions, and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies. [Grade 7, 8]

In this learning activity, students will learn to solve multistep problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. The students will apply properties of operations to calculate numbers in any form; convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. This learning activity can be used as a stand-alone activity but is best used as a During Activity, the Before and After Activities can be found in the Notes or Recommendations section.

   View Standards     Standard(s): [MA2019] REG-7 (7) 8 :

8. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

[MA2019] ACC-7 (7) 9 :

9. Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable. [Grade 7, 5]

[MA2019] ACC-7 (7) 17 :

17. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions, and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies. [Grade 7, 8]

Students will use the Quizizz response system to review solving multi-step problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals) and to use tools strategically. This Multi-Step Real-Life and Mathematical Practice Problems Quizizz game has fifteen questions to test the understanding of solving multi-step real-life problems and is intended to be used as an after-activity. Quizizz allows the teacher to conduct student-paced formative assessments through quizzing, collaboration, peer-led discussions, and presentation of content in a fun and engaging way for students of all ages.

(This learning activity can be used as a stand-alone activity but is best used as an After Activity, the During and After Activities can be found in the Notes or Recommendations section.)

   View Standards     Standard(s): [MA2019] REG-7 (7) 4 :

4. Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals.

a. Identify and explain situations where the sum of opposite quantities is 0 and opposite quantities are defined as additive inverses.

b. Interpret the sum of two or more rational numbers, by using a number line and in real-world contexts.

c. Explain subtraction of rational numbers as addition of additive inverses.

d. Use a number line to demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

e. Extend strategies of multiplication to rational numbers to develop rules for multiplying signed numbers, showing that the properties of the operations are preserved.

f. Divide integers and explain that division by zero is undefined. Interpret the quotient of integers (with a non-zero divisor) as a rational number.

g. Convert a rational number to a decimal using long division, explaining that the decimal form of a rational number terminates or eventually repeats.

[MA2019] REG-7 (7) 5 :

5. Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable.

[MA2019] ACC-7 (7) 8 :

8. Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals.

a. Identify and explain situations where the sum of opposite quantities is 0 and opposite quantities are defined as additive inverses. 

b. Interpret the sum of two or more rational numbers, by using a number line and in real-world contexts.

c. Explain subtraction of rational numbers as addition of additive inverses.

d. Use a number line to demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

e. Extend strategies of multiplication to rational numbers to develop rules for multiplying signed numbers, showing that the properties of the operations are preserved.

f. Divide integers and explain that division by zero is undefined. Interpret the quotient of integers (with a non-zero divisor) as a rational number.

g. Convert a rational number to a decimal using long division, explaining that the decimal form of a rational number terminates or eventually repeats. [Grade 7, 4]

[MA2019] ACC-7 (7) 9 :

9. Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable. [Grade 7, 5]

In Topic C, students problem-solve with rational numbers and draw upon their work from Grade 6 with expressions and equations. They perform operations with rational numbers, incorporating them into algebraic expressions and equations.  They represent and evaluate expressions in multiple forms, demonstrating how quantities are related. The Integer Game is revisited as students discover “if-then” statements, relating changes in players’ hands (who have the same card-value totals) to changes in both sides of a number sentence. Students translate word problems into algebraic equations and become proficient at solving equations of the form px + q = r and p(x + q) = r, where p, q, and r, are specific rational numbers. As they become fluent in generating algebraic solutions, students identify the operations, inverse operations, and order of steps, comparing these to an arithmetic solution. The use of algebra to represent contextual problems continues in Module 3.