If students can’t get started….
Assessing Questions:
- Tell me what information you know.
- What is the problem asking you to do?
- What do you know about fractions? What does the denominator tell you?
- What does the numerator tell you?
Advancing Questions:
- What will you try first to determine who ate more cookies?
- What other model could you use?
If students finish early….
Assessing Questions:
- Tell me about your work.
- Prove to me that Nathan ate more cookies than Josh.
- Explain how you know that there are 5/12 cookies leftover. How many cookies is that?
Advancing Questions:
- Is your answer of 5/12 cookies leftover reasonable? How can you justify it?
- How would your solution change if Josh and Nathan each had their own package of 12 cookies?
- Is there another way to solve this problem?
- How much more was leftover than was eaten by Josh and Nathan combined?
- Change the problem so that there are only 3 cookies leftover.
Whole Group Questions
A fraction can be named in more than one way and the fractions will be equivalent as long as the same portion of the set or area of the figure is represented.
- What does it mean for fractions to be equivalent?
- How can we use equivalent fractions to compare ¼ and 1/3?
- Does anyone agree or disagree?
- Explain how you renamed ¼ to 3/12 and 1/3 to 4/12. How did this affect the amount of cookies that were eaten by each person?
- What does 7/12 represent? What does 5/12 represent?
When comparing two fractions with different numerators and different denominators, recognize that comparisons are only valid when the fractions refer to the same whole.
- Did anyone compare these fractions a different way?
- What diagrams did you use to compare ¼ and 1/3? How did these help you to compare the fractions?
- What inequality can you write to show who ate more cookies?
Adding fractions and subtracting fractions refers to joining or separating parts of the same whole.
- When adding these fractions, what did you need to do first? When you renamed ¼ and 1/3, you found equivalent fractions, how did this affect
- the amount of cookies eaten by each person?
- Why didn’t you add the denominators?
- What does 7/12 represent? What does 5/12 represent?
- Multiplying a fraction by a whole number, results in a product that is part of the original whole number.
Multiplication by a fraction is similar to division of whole numbers.
- How could we use multiplication to solve this problem?
- How did you multiply a fraction by a whole number? Usually when we multiply we get a product that is larger than the number we started with, for example 4 x 6 = 24. When multiplying ¼ x 12 we got a product of 3, which is smaller than what we started with? Is this always true when multiplying a whole number by a fraction?
- How is multiplying a fraction by a whole number similar to division?
