Investigations

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

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

3. 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?

4. One thing to bring • Train of chairs – two directions • Musical Chairs – Three Musketeers • #1Talks, #2 and #3 quiet • #1 Describe why you chose this writing utensil and not another one?

5. One thing to bring • #2 Is it enough to just have this writing tool to do math today? Why or why not?

6. One thing to bring • #3 Do we have what we need to learn math today? Explain.

8. Solve this math problem. • Line up. Count in thirds. Match yourself with a similar third. Partner Quiz: you keep your A if you work well together  • Allowed to use whatever tools in the room you need. • There are 40 girls and 32 boys who want to participate in 6th grade intramurals. If each team must have the same number of girls and the same number of boys, what is the greatest number of teams that can participate in intramurals?

9. 6th grade Continue with 2.1 Explore Find someone who has the same birthday month or as close to your birthday month as you for Partner A – Partner B . Mix A yet • After part C and D are done, consider Mix A: • B ask, “How many servings can one recipe make?”

10. 6th grade Continue with 2.1 Explore Partner A – Partner B . Mix A yet • A ask, “What if each serving is an 8 oz. glass the same as 1 cup?”

11. 6th grade Continue with 2.1 Explore Partner A – Partner B Mix A . • B ask, “What if each serving is ½ cup?”

12. 6th grade Continue with 2.1 Explore Partner A – Partner B Mix A . • A ask, “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?”

13. 6th grade Continue with 2.1 Explore Partner A – Partner B Mix A – last question . • B ask, “If you were going to serve juice to 240 people, how many batches would you have to make if each person gets ½ cup of juice?”

14. 6th grade Continue with 2.1 Explore Mix B, C, D New Partner A and Partner B – go through the same questions again, but now pairs in thirds sections and are assigned mix B, C, or D • Line up back to back, two lines, take a step to the right twice…

15. 6th grade Continue with 2.1 Explore . If not, how are your strategies the same? Different? • After discussion in partners, form groups of four. Compare your notes on how you found your answers. Did you use the same strategy?

16. 6th grade Continue with 2.1 Explore . • Whole group time! • Let’s create a record of our strategies for finding equivalent proportions! • Next slide…

17. 6th grade Continue with 2.1 Explore Partner A – Partner B * * How many batches for 240 campers? • Mix A: • Mix B: • Mix C: • Mix D:

18. 6th grade Continue with 2.1 Explore Pointer finger out of holster in our groups of three or four Show your strategy in a book. • Start our library of strategies! • Title? • How shall we arrange the pages? • What is criteria we need to have in our book?

19. Three Musketeers • High five and greet each other! • (Summarizing 2.1)

20. Three Musketeers • #1 What does it mean to be the most orangey tasting? • (Summarizing 2.1)

21. Three Musketeers • #2 To be the least orangey? • (Summarizing 2.1)

22. Three Musketeers • #3 Canvass your group and see who likes more orangey or less orangey; be ready to report. • (Summarizing 2.1)

23. 6th grade * Go to edmodo.com poll soon. Check for understanding for 2.1

24. 6th grade Launch 2.2 “Sharing Pizza” – discuss with a partner Which table would you sit at? Huh, huh?

25. 27 Pieces with Partner • What does this model represent? • Keep track of your ideas; be prepared to share out. • Stack, pack, I’ll be back!: Go find a new partner. Take three steps, make a right angle by taking two more steps. Closest person. Cannot have same partner in the same day.

26. 13 Pieces with Partner • What does this model represent? • Keep track of your ideas; be prepared to share out.

27. Cookie Problem • Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her teacher friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookie. If she wants each container to have the greatest number of cookies possible, how many plastic containers does she need?

28. Cookie Problem • What math concept did you use to solve this problem?

29. ??? Speaking of Christmas trees  Two neon lights are turned on at the same time. One blinks every 4 seconds and the other blinks every 6 seconds. In 60 seconds, how many times will they blink at the same time? • Why do we try to find common multiples?

30. ??? What are the simplest numbers I can use to describe a really big number?

31. Vocabulary • Vocabulary • Factors • Prime factors • Multiples • Least common multiple • Greatest common factor • exponents

32. 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?

33. 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.

34. 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?

35. 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?

36. 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?

37. 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?

38. 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?

39. 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)?

40. 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.

41. 6th grade • Student presentations for this investigation shared after two class session spent on final preparations to share. Spruce up your presentations with color, drawings, neatness, etc. • Presentation Days: compare work in your Math Tab to the presentations presented by student groups. Be prepared to critique their argument for solving the problems. Teacher assesses with rubric and checks for reliable valid strategies and solutions. (see next slide)

42. 6th grade • Summative Assessment Piece • Reflections shared in Reflection Journal • Check our vocabulary and fill in definitions. • Check word wall progress.