Investigations

1. Investigations For 6th, 7th, and 8th grades

2. Project commitment • D level: part one of investigation and do two “Connections” problems completed with all criteria (strategy shown how to solve the problem and picture models/manipulative models representing the problem and answer) Up to 11 points

3. Project commitment • C level: D level plus part two of investigation and do four “Connections” problems completed with all criteria Up to 13 points

4. Project commitment • B level: C level plus part three of investigation, two problems from “Applications” and four “Connections” problems completed with all criteria Up to 15 points • A level: B level plus part four of investigation (if available), two problems from “Applications” , four problems from “Connections”, and two problems from “Extensions” completed with all criteria Up to 17 points

5. Project commitment • Sign up for what level you plan to go for as we begin investigation. • You are also expected to complete a word wall project for each investigation unit. Comparing and Scaling is 6th grade. Stretching and Shrinking is 7th grade. Thinking with Mathematical Models is 8th grade. Label your word wall on the back with the appropriate unit that your word belongs to with your S.A.N.D.

6. 6th grade Investigation 2 Opener Did you know…?

7. 6th grade Launch 2.1: “Mixing Juice” Explore Show the “juice” Students work with Mix A and B, then stop Can I keep adding cans of water without making the juice less orangey? How much juice is made from one recipe? Continue with investigation. • Goal: Become comfortable with ratio and related forms of comparisons to solve. • How many students have made orange juice? • What involved in making it?

8. 6th grade Continue with 2.1 Explore Show your strategy poster. What are different strategies you might use to answer this question? Here is where you should have your strategy poster to show how you would find the answer for any type of ratio to mix. • After part C and D are done, consider Mix A: • What are your ideas about how many people one batch of this juice might serve? • What if each serving is an 8 oz. glass the same as 1 cup? • What if each serving is ½ cup? • If you were going to serve juice to 50 people, how many batches would you have to make if each person gets ½ cup of juice?

9. 6th grade 2.1 Summarize Go to edmodo.com poll soon. Check for understanding for 2.1 • What does it mean to be the most orangey tasting? To be the least orangey?

10. 6th grade Launch 2.2 “Sharing Pizza” Which table would you sit at? Do others have a different choice?

11. 2.2 Explore 6th grade Goal: Continue to work with ratio comparisons Can you find another way to think about Question A? Are your two ways related? If so, how?

12. 6th grade 2.2 Summarize Go to edmodo.com to share your argument too. What if one table had 10 people and 5 pizzas and another had 3 people and 1 pizza? Would you decide to sit by just choosing the one with the fewest people? Why or why not? Does it make sense to add people and pizzas to make a whole (population)? • What if one table had 30 people and 5 pizzas and another table had 5 people and four pizzas? Model with a drawing. Would you decide where to sit by choosing the table with the most pizza? Why or why not? Create a viable argument to share. Critique another’s argument.

13. 6th grade 2.2 Summarize Summarize some more Did anyone think of more than one strategy? If you want to go to the table with the most pizza per person, what two strategies can you share? What happens to a fraction when you add one to both the numerator and the denominator? Is the new fraction greater or lesser? Go to edmodo.com and share a fraction and then do this activity of adding one to both the numerator and denominator. Answer these questions. • What is the ratio of pizza to people at the two tables in the previous slide? • What do these ratios mean? • Can you scale these ratios so that they have a number in common? • So, now which table gives you the most pizza? • Can you scale the ratios so that the number of pizzas is equal to make the comparison easy?

14. 6th grade Launch 2.3 “Finding Equivalent Ratios” Reader’s Digest vs. National Geographic 3:2 • 100 to 80 • How do you scale down this ratio to make it easier to understand? • What are some other ratios equivalent to this ratio in which the numbers are greater? Finding greater numbers is scaling up the ratio. • How is scaling ratios like finding equivalent fractions for 100/80? How is it different?

15. 6th grade 2.3 Explore What a chimp! Suppose you are feeding two baby chimps. How much of each part of the mix will you need? What did you do to find the amounts of each part of mix? • Goals: Find equivalent ratios. Further develop strategies for comparing ratios. • What differences do you notice in how the mix changes as a chimp moves from being a baby to a young adult to an older chimp?

16. 6th grade 2.3 Explore * ** • After a few entries in your table, how can you use the patterns you see? • How much will the total amount of feed differ for two baby chimps compared to just one?

17. 6th grade 2.3 Summarize Go to edmodo.com for a poll soon. Check for understanding Question C I do not see the quantities 3 and 2 in the recipe for the mix for young adults. What did Darla do to get these numbers? Student presentations here. • Question A • What would you do to find the table entry for feeding 60 baby chimps? • Question B • What is an efficient method of finding a ratio equivalent to a given ratio? • How do you choose what to multiply or divide by?

18. 6th grade • 2.3 Summarize Final Page • Is Darla or Lamar correct? • Who can talk to us about their answer and strategy for part (2)? • What about part (3)? • What about part (4)?

19. 6th grade Part 4: Extension #22 “Gestation Time…” What is a scatter plot? • Work with this extension problem, while others finish up other lab sections.

20. 6thgrade • Summative Assessment Piece • Reflections shared in Reflection Journal • Check our vocabulary and fill in definitions. • Check word wall progress.