Academic standards
- 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
- about appropriateness of answers.]
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?
