2. Learning Outcomes
I can develop ideas to build conceptual understanding of math process for my students.
I can understand and apply the C-R-A approach.

3. Calculate

4. Are these equal?
1 = 13

5. Which expression has the larger value?
10 + x x
What are some possible answers that your students might give?
What do the different responses speak about what students know and are able to do?

6. ? ? Why is math so hard? Different/changing rules Vocabulary
Math Anxiety

7. You have just got a summer job mowing lawns
You have just got a summer job mowing lawns. You did a test run in your own yard and you mowed your yard in two hours. You plan on working 8 hours a day, how many lawns can you mow in one day?
(Lawn sizes are the same)

8. Fractions 1 ¾ divided by ½
Write a Story Problem to show what is happening with this expression.
How would we teach this to our students?

9. So what’s another approach?
Division of Fractions
American Approach
Flip and multiply
Answers don’t match
Confused dividing by 2 and ½
So what’s another approach?

10. Bean Party
6 divided by ½

11. For each Cup of Beans---
I get two portions if I divide by 1/2

12. What if I divide by ⅓? How would my diagram look?
How many portions would I have?
Why are my number of portions getting larger?

13. Division of Fractions 1 ¾ divided by ½
Draw a model to represent and write a Story Problem to show what is happening with this expression.
What was different writing a story this time compared to the beginning?

14. Other Ways to Solve? Do we always have to invert and multiply?
Discuss the order of working with fractions - first whole number by fraction

15. So where does invert and multiply come from?

16. Algorithms Algorithms without understanding…
Errors practiced and hard to break
Extensive practice time
Limited retention
Think negative numbers - number line and understanding is key
Kids in Canada do not struggle as much because they are use to the temp

17. Algorithms Algorithms with understanding… Conceptual development
Reduction in practice time
Extended retention and application

18. Misconceptions
You will always divide the larger number by the smaller number
Every time you divide, your result will be smaller
Others?

19. C-R-A Approach Concrete Representational Abstract
Manipulatives, real life, touch and see the math
Representational
Pictures, number lines, graphs, models, etc.
Abstract
Numbers and symbols

21. Jigsaw
Pick a topic from the list below, brainstorm ideas for how to teach this topic using the C-R-A approach. Will get in groups to plan and will then return to Home Group to share ideas.
Negative Numbers
Adding & Subtracting Decimals
Linear Functions
Graphing Coordinates
Area/Perimeter/Volume
Probability
Mean/Median/Mode
Your Choice

22. Math Tasks
There is so decision that teachers make that has a greater impact on students’ opportunities to learn and on their perception about what mathematics is than the selection or creation of the tasks with which the teacher engages students in shaping mathematics.

24. Fraction Puzzle Determine the fraction of each puzzle piece
Reflection:
Prior Knowledge?
Access?

25. Let’s Do Some Math

27. CCR on ACT is 22 - 88.5% of the standards to receive between a 20-23 are from MS

28. Building procedural fluency from conceptual understanding
A rush to fluency undermines students’ confidence and interest in mathematics and is considered the cause of mathematics anxiety

29. Resources sudds.co achievethecore.org
Scaling Up Digital Designs Study through NC State
Learning Map
achievethecore.org
Coherence Map

30. Don’t Forget... All the resources you have....
The more you do it, the better you will be
The more your students do it, the better they will be
What to do when you don’t know what to do?
Read, write, think, and talk in every class, every day
Know your stuff and know who you are stuffing

31. Enjoy the beautiful day!!
Resources found on my website
Staff Math Resources - County PD - March 16th PD
Fill out Evaluation
Enjoy the beautiful day!!

32. Resources NCSIP Math Foundations Deborah Ball’s Math Summit
NCDPI Math Wiki
Sharon Griffin