1. 5 th Grade Math Expressions October 6, 2010 Dr. Monica Hartman Laura Chambless

2. Introductions Write on a sticky note  One thing you noticed about teaching Math Expressions so far this year.  Share with someone that is not in your building.  Stand back to back when you are done sharing.  Partner with shortest hair reports out to group.

3. Agenda Common Core Standards Looking at Data from End of Year Assessment Problem Solving Closing and Evaluations

4. Common Core See Power Point

5. Looking at Data  2009-2010 End of Year Assessment  Frequency Table  Find the top 5 items. CELEBRATE!  Find the bottom 5 items. REFLECT!  Look in your textbooks for where the lowest scoring items are taught.

6. Representing Word Problems 1. Situation Equation – shows the situation in the problem 2. Solution Equation – shows how you are going to solve the problem0

7. Situation and Solution Equations There were 6 horses in the barn. More horses came into the barn. Now there are 10 horses. How many horses came into the barn? Situation equation: 6 + h = 10 Solution equation: h = 10 - 6

8. Situation and Solution Equations There were 9 horses in the barn. Then some of them went out into the pasture. Now there are 4 horses left in the barn. How many are out in the pasture? Situation equation: 9 - h = 4 Solution equation: h = 9 - 4

9. Situation and Solution Equations There were some horses in the barn. Then 3 more horses came into the barn. Now there are 8 horses in the barn. How many horses were in the barn to start with? Situation equation: h + 3 = 8 Solution equation: h = 8 - 3

10. Situation and Solution Equations There were some horses in the barn. Then 7 of them went out. Now there are 3 horses left in the barn. How many horses were in the barn at the beginning? Situation equation: h – 7 = 3 Solution equation: h = 3 + 7

11. From Situation to Solution In a solution equation, the unknown quantity is by itself on one side of the equals sign. Write a word problem that relates to this equation. a + 5 = 20

12. 6 6 6 6 24 4 × Equal Groups Equal Groups Problems – Involve objects that are separated into groups with the same number in each group

13. Arrays 4 × 6 = 24 6 × 4 = 24 Note: The number in the circle represents the number of objects in a row. Fast Arrays 24 4 6 Array problems involve objects organized in equal rows and columns that are not connected

14. Area Model 6 4 4 × 6 = 24 Note: The number in the circle represents the number in each row. Area problems do not involve objects. They involve the number of square units that cover a shape

15. Combination Model Katy had 2 pairs of pants and 5 shirts. whiteblackredgreenyellow BlueBwBbBrBgBy TanTwTbTrTgTy Combination problems involve objects that can be organized in a table that has rows and columns of equal groups pants shirts

16. Comparison Model Katie picked 5 times as many flowers as Bernardo. Comparison problems involve one quantity that is a number of times as many as or as much as another Bernardo picked 1/5 as many flowers as Katie.

17. Comparison Model 22222 Katie picked 5 times as many flowers as Bernardo. 2 Bernardo Katie Comparison problems involve one quantity that is a number of times as many as or as much as another Bernardo picked 1/5 as many flowers as Katie.

18. Problem Solving I First, think about and solve the problem by yourself using the comparison method. Draw a model. Write a situation equation and a solution equation. Prepare to explain your solution. Share your solution with your partner. Share your solution with your team. Remember…Everybody Understands! The length of a fence is 1/3 the length of another longer fence. The longer fence is 21 feet. How long is the shorter fence?

19. Problem Solving II First, think about and solve the problem by yourself using the comparison method. Share your solution with your partner. Share your solution with your team. Can you rewrite and solve the problem so it involves finding inches? Remember…Everybody Understands! The length of the swimming pool is 9 yards. How long is the pool in feet? There are 3 feet in one yard.

20. Problem Solving III First, think about and solve the problem by yourself using the comparison method. Share your solution with your partner. Share your solution with your team. Can you rewrite the problem so it is an example of the other type of comparison problem? Remember…Everybody Understands! The length of one rope is 3 times the length of another piece of rope. If the longer rope is 21 feet 9 inches, what is the length of the shorter rope?

21. Closing and Evaluation On a sticky note, write one thing that you are going to do in your classroom. Put your sticky note on your evaluation sheet. In the comment section, please indicate any topic that you would like to learn more about in the future.

22. Thank you! Monica and Laura