 7th Grade Task: The Leader of the Pack

### Standards & Objectives

CCSS.Math.Content.7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
CCSS.Math.Content.7.EE.B.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and...
CCSS.Math.Content.7.G.A.1
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a...
CCSS.Math.Content.7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a...
CCSS.Math.Content.7.NS.A.2
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
CCSS.Math.Content.7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers.1
GLE 0706.1.2
Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0706.1.5
Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0706.1.8
Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and...
GLE 0706.2.1
Extend understandings of addition, subtraction, multiplication and division to integers.
GLE 0706.2.2
Understand and work with the properties of and operations on the system of rational numbers.
GLE 0706.2.5
Understand and work with squares, cubes, square roots and cube roots.
SPI 0706.2.1
Simplify numerical expressions involving rational numbers.
SPI 0706.2.3
Use rational numbers and roots of perfect squares/cubes to solve contextual problems.
SPI 0706.2.5
Solve contextual problems that involve operations with integers.
TSS.Math.7.EE.B.3
Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers presented in any form (whole numbers, fractions, and...
TSS.Math.7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a...
TSS.Math.7.NS.A.2
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
TSS.Math.7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for...

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Essential and guiding questions:

Solving the Equation

• In part a), did anyone use an equation to complete the table?
• If you did not use an equation, how did you find the times for each speed?
• Can someone show me how you got one of the times using the equation?
• Can someone else tell me how you got the same time without using the equation?
• How are these approaches the same?
• What operation was used? Why?
• Why do you think that we use formulas and equations to solve problems, when they can be done without them?

Rounding Choices

• As you found the times for the table, were they “nice” decimal numbers? What was not nice about them?
• Can a few people tell me how they handled these unruly decimals?
• Why did you choose to do it that way?
• Did anyone do it differently?
• What seems to be the best approach when solving a real-world problem?
• Do these numbers represent exact answers?
• Why is it okay in this context that they do not?

Dividing by Large Numbers

• As you filled out the table in part b), how did you choose the speeds?
• How do the speeds change as you move down the table?
• How do the times change?
• How is the distance changing?
• What operation is occurring between the distance and the speed in order to give you the time?
• Can you make a general observation about what happens when we divide a constant by larger and larger numbers?
• Will this value ever reach zero? [This provides a good place to discuss the limitations of calculators and why users must always reason

Dividing by Zero

• What is an equation that would represent what happens when t=0 ?
• Are there any other distances that could be covered in 0 seconds?
• Are there any other rates that would satisfy the formula?
• What observations can you make about D and r when t=0?

Blooms taxonomy level:
Understanding
Differentiation suggestions:

If students can't get started...

• If I told you someone was traveling 70 mph for 2 hours, how would you calculate the distance covered?
• How are distances, speeds, and the time it takes to travel them related?
• How would you use this relationship to complete the table?
Extension suggestions:

If students fnish early:

• What concept that we have learned about integers was illustrated in this activity?
• Can you write a paragraph explaining how this activity illustrates division concepts?
• Under what conditions is D=rt a proportional relationship?