1. Grade 4-6 MGSD, Summer 2014

2. Coat Sale A few coats on sale in the store now each cost $176. What were the original prices of each coat? Blue coat: sale price is 8/9 of the original price. Yellow coat: sale price is between 5/9 and 11/18 of the original price. Green coat: original price is 1 and 3/4 times as much as the sales price. Red coat: original price is between 1 and 1/11 times as much and 1 and 1/10 times as much as the sales price. Solve with a representation/picture as well as an equation.

3. Where is the alignment between equation and picture? How are these similar/different?

4. Standards 4 th - word problems, fraction by whole number – Breaking numbers into parts – Decomposing… 8/9 = 1/9 + 1/9 + 1/9 + …. 5 th - numerator/denominator, visual models, product as partition, fraction by fraction multiplication 6 th - divide fractions and mixed numbers, algebra and finding unknown, ratio and unit rate

5. Coat Sale What representations and pictures did you use?

6. Coat Sale- Equations ?

7. Coat Sale In your groups which grade levels does each task align to? How could you modify each task to align to your specific grade level?

8. Article As you read… Teacher actions? Student actions?

9. Article As you read… What are the big “take aways” as it relates to your classroom? What strategies have you used to help your students with the concepts mentioned in this article?

10. Multiplication and Division Independently— Write a one sentence definition of each. Where do your students struggle? What does addition and subtraction skills have to do with multiplication and division?

11. Problem Types Debrief Consider 22 x __ = 132 using… – A picture. – An array. – A number line. – An equation. – Then write a story problem to go with it. Which representations are more difficult for you? Why? How can you help support students with these types of tasks?

12. Multiplication and Division Are all problems “equal” in difficulty? Why or why not? What makes some problems more difficult than others for students? Think about… How can we help students who struggle with these operations?

13. Multiplication and Division Problem Types Let’s check out what the Common Core authors have to say about types of problems…

14. Problem Types Think about last year… – Out of all the time your students worked with multiplication and division ideas, including fractions, decimals, ratios, etc., which types of problems did: You focus a lot on? You not focus a lot on? Your students do well with? Your students struggle more with?

15. Guess the problem type There are 186 peanut butter sandwiches. How many bags can be filled if we put 6 sandwiches in a bag? There are 36 girls on the playground. The number of boys is 1 and 2/9 larger than the number of girls. How many boys are on the playground? There are 4 and 2/3 cups of flour in the bowl. If the flour is scooped into 7 equal portions how large would each portion be? The total distance around the track is 1 and 1/4 miles. Samuel ran 3/4 of that distance. How far did Samuel run? There are 12 pencils on the desk. There are 1/3 as many pencils in the bag than there are on the desk. How many pencils are on the desk?

16. Problem Types…carrying it forward Where do they fit in your pacing guide for the year? How can you be more diligent on posing these types of tasks? How do we help students with these types of tasks?

17. Number Talks

18. Number Talks- 72 I want you to think about the number 72. What do you know about the number 72? Can you think of a few ways to put 72 objects into equal groups? Draw pictures and write equations for the different ways that you have.

19. Number Talks What math concepts did you work with? Describe the questions… what were they like? How would you carry this out in your classroom? How long would it take your students to complete?

20. Number Talks- Powers of 10 I want to now think about the number 360. What if we multiplied it by powers of 10? What are some equations we could write and products that we could get? What if we divided 360 by powers of 10? What are some equations we could write and quoteints that we could get?

21. Number Talks What math concepts did you work with? Describe the questions… what were they like? How would you carry this out in your classroom? How long would it take your students to complete?

22. Rigor What does rigor mean in terms of your students’ math work? Does rigor matter in your grade? How can you increase the rigor in your classroom?

23. Efficiency What does efficiency mean in terms of your students’ math work? How does efficiency relate to “speed” in math? Does efficiency matter in your grade? How can you guide students to becoming more efficient?

25. Questions?

26. An egg salesman was asked how many eggs he had sold that day. He replied, “My first customer said, “I’ll buy half your eggs and half an egg more”. My second and third said the same thing. When I had filled all three orders I was sold out and I had not had to break a single egg all day”

27. Egg Task Approaches? Representations? Equations?

28. Egg Task Embedded math concepts… How is this different from basic, low-level tasks and/or problems?