Unpacking the Common Core Standards

1. Unpacking the Common Core Standards Grades 4-6 October 16, 2013

2. Counting Around the class • Fraction work… • Whole numbers… • Simplify to fourths • Simplify to fourths or halves • Simplify to halves • Don’t simplify at all

3. 12/8, 36/8, 60/8

4. Counting Around the class • Ratio work

5. Bracelet Making • You are making bracelets for a school fundraiser. You have purchased: • 3 types of glass beads, 3 types of spacer beads (go between sections of glass beads), and Beading wire • Design a bracelet using at least 2 types of glass beads and one type of spacer bead. • Use between 8 and 12 glass beads • Use at least 6 spacer beads • No more than 25 total beads • Use letters (A, B, C, D, E, F) to represent beads and make a list of your necklace- remember you can only have 25 beads.

6. Bracelet Making- Ratio • Write 5 ratios that can be used to mathematically describe your bracelet… What do we mean? • Options- • Relationship between one type of glass bead used and another type of glass bead • Relationship between one type of glass bead used and total number of beads • Relationship between one type of glass bead and a type of spacer bead • Relationship between one type of spacer bead used and total number of beads • Relationship between all glass beads and all spacer beads

7. Bracelet Making- Ratio Relationship between: • one type of glass bead used and another type of glass bead • one type of glass bead used and total number of beads • one type of glass bead and a type of spacer bead • one type of spacer bead used and total number of beads • all glass beads and all spacer beads

8. Bracelet Making- when will we run out? • Use the information sheet to determine how many bracelets you can make before you run out of beads? You can only have 1 bag of each type of bead that you need. • Draw a picture and write an equation to explain how you found your answer.

9. Bracelet Making- costs • One clasp and beading wire costs 25 cents. Use the information sheet and your bracelet from Part A to determine the cost of 1 bracelet. Write an equation to show your work. • How much will it cost to make all the bracelets that you can?

10. Making our bracelet into a necklace… • Your bracelet was 8 inches. • Your Principal wants matching 24-inch necklaces (using the same pattern of beads). • If the cost of the clasp and wire is $0.30, what is the cost of making 1 necklace? • How much of each type of bead will you need to make a 24-inch necklace?

11. Predicting Profits • Your Principal wants you to make a profit that is 60% of the cost to make each piece of jewelry. How much should each bracelet and necklace cost? • You decide to offer a “special” so that when customers buy 3 bracelets, you only make 40% profit.

12. Debriefing Jewelry Task • Where would students get hung up or stuck? • How do you battle fatigue? • What would you/could you assess or grade? How much would you focus on grading the various parts of the task?

13. Contexts… • 4th grade- • 5th grade- • 6th grade-

14. Contexts… • 4th grade- • Brownies, cakes, square pizzas that focus on the costs of ingredients and the area of shapes • 5th grade- • Making lemonade, juice, punch, etc.

15. Proportions… grade levels? • A) Understand the concept of unit rate • B) Make tables of ratios • C) Convert measurement units within a system • D) convert measurement units by multiplying or dividing quantities • E) distinguish multiplication comparison from additive comparison • F) Generate a number pattern • G) Generate a number pattern with 2 given rules • H) Express larger measurement units in smaller measurement units in the same system • I) use ratio reasoning to convert measurement units

16. Proportions… • Pick a topic that belongs to your grade level… • What would it look like for students to demonstrate proficiency?

17. Proportions.. How to teach it? • There are 24 cookies. 3 cookies in each bag and are given to students. If each student eats one of their cookies, how many cookies were eaten? • There were 24 cookies divided among 3 people. 1 person ate all their cookies. The other 2 people saved all of theirs. How many cookies were eaten?

18. Proportions.. How to teach it? • There are 24 cookies. 3 cookies in each bag and are given to students. If each student eats one of their cookies, how many cookies were eaten? • There were 24 cookies divided among 3 people. 1 person ate all their cookies. The other 2 people saved all of theirs. How many cookies were eaten? • 1/3 of 24… • 24 objects in rows of 3… for every group of 3, shade 1object • 24 objects in 3 groups, shade 1 entire group • How are they different?

19. Proportions… gas mileage • I am able to drive 30 miles per every gallon of gas in my car…. • How many miles can I drive if I have 10 gallons? 20 gallons? 5 gallons? • How many miles can I drive if I have 3.25 gallons? • I have 4/5 of a gallon. How far can I go? • I have enough gas left to drive 130 miles. How many gallons do I have? • I have 12 and 1/2 gallons left when I start my trip. How far can I go if I only use 2 and ½ gallons before my first stop? What if I use 3 and ¾ gallons?

20. Mathematical Tasks • Professional Reading • As you read…. What are the essential characteristics of good mathematical tasks? How can a task dictate or influence how a lesson goes?

21. Mathematical Tasks Reading • Let’s look at the tasks embedded in the article • Which is the “easiest”? Why? • Which is the “most difficult”? Why?

22. Where in your classroom does each task type fit? • What type(s) do you most naturally use?

23. Mathematical Tasks Reading • Examples in the back…. • What levels should we aim for when we plan most of our instructional tasks?

24. Wrapping Up our time together • Questions?