1. Multiplication as area demonstrates the proportional change that is critical to understanding place value, decimals, fractions
3 sets of fours or 4 sets of threes.
Both fill an area of 12 squares.

2. Array or area models make the commutative property visible
Array or area models make the commutative property visible. 3 x 4 = 4 x 3.
Area models allow us to visibly demonstrate the distributive property.

3. BASIC FACTS
1.) Multiplication IS NOT REPEATED ADDITION. It is related to addition.
2.) EQUAL GROUPS arranged into ARRAYS is a powerful visual model for allowing students to generate personal understandings as they engage in multiplication.
3.) Multiplication is dimensional.. The unit does not change direction.
4.) Multiplication is COMMUTATIVE.
5.) THE DISTRIBUTIVE PROPERTY is a critical BASIC FACT.
6.) Zero and one represent special cases.
7. Cartesian Products, Proportions, Rates and Ratios, Division and Fractions (which include decimal fractions) are interrelated.

4. Grade 3:
Demonstrate an understanding of multiplication to 5 × 5 by:
representing and explaining multiplication using equal grouping and arrays
creating and solving problems in context that involve multiplication
modeling multiplication using concrete and visual representations, and recording the process symbolically

5. Grade 4 (p 23)
Applying the distributive property.
Grade 5 : (p 29)
Apply mental strategies & number properties,
to determine with fluency, answers for basic multiplication facts to 81 and related division facts

6. What would you cut out of grid paper? 6

7. 6
Is this what you cut out and folded?

8. 6
Diagram and label what you created.
Do you know what multiplication fact this is?

9. 6
5 + 3 = 8 therefore this is another way to think of 8 x 6.
Cutting and folding allows us to discuss the distributive property.

10. 6
Here is how you represent what we built with an equation.
(5 + 3 ) x 6 = 8 x 6 This is the distributive property.

11.
(5 + 3) x 6 = 8 x 6 6
Record the distribution equation under or inside your diagram of the “fact” we cut out.

12. 6
I went back to the original cut out and changed where I folded.
Can you diagram my new distribution?

13. 6
How would you record the changed distribution equation?

14. 6
(6 + 2 ) x 6 = 8 x 6

15. 6
And now diagram this distribution.

16. 6
Record the changed distribution equation?

17. 6
End of first session.
(1 + 7 ) x 6 = 8 x 6

18. Cut out and fold the model for this puzzle. 5
Day 2: Repeat the task with a different puzzle. Then invite students to build a different distribution on their own.

19. 5
Is this what you cut out and folded?
Diagram and label.

20. 5
Do you know what multiplication fact this is?
Can you record the distribution equation?

21. 5
(4 + 3 ) x 5 = 7 x 5

22. Go back to the cut out and fold somewhere else
Go back to the cut out and fold somewhere else. Diagram, label and record the distribution equation.

23. Share and compare as a class.
End of Day two practice session.
Share and compare as a class.

24. Next step.
Day three: Add the next step to the distribution equations.

25. Cut out and fold the model for this puzzle. 7
Day 2: Repeat the task with a different puzzle.

26. 5 + 3 7

27. Now we will add the next step 7
The second step in distributing:
(5 + 3) x 7 = 8 x 7

28. We can record the multiplications in each part of the diagram
We can record the multiplications in each part of the diagram. Can you explain?
5 x 7
3 x 7 7
(5 + 3) x 7 = 8 x 7

29. + Join them with an addition sign 5 + 3 5 x 7 3 x 7 7
5 x 7 +
3 x 7 7
(5 + 3) x 7 = 8 x 7

30. + We can record a second distribution equation.
Watch and repeat along with me…..
5 x 7 +
3 x 7 7
(5 + 3) x 7 = 8 x 7

31. + (5 + 3) x 7 We can record a second distribution equation.
Watch and repeat along with me…..
5 x 7 +
3 x 7 7
(5 + 3) x 7 = 8 x 7
(5 + 3) x 7

32. + (5 + 3) x 7 = (5 x 7) We can record a second distribution equation.
Watch and repeat along with me…..
5 x 7 +
3 x 7 7
(5 + 3) x 7 = 8 x 7
(5 + 3) x 7 = (5 x 7)

33. We can record a second distribution equation.
Watch and repeat along with me…..
5 x 7 +
3 x 7 7
(5 + 3) x 7 = 8 x 7
(5 + 3) x 7 = (5 x 7) + (3 x 7)

34. Let’s try another one 6 4 + .

35. Step one 6x (4 + 4) = 6 x 8
See it? 6 4 + .

36. Step 2: 6 x (4 + 4) = (6x4) + (6x4) x 4 See it?
Step one 6x (4 + 4) = 6 x 8 6
(6x4) + 4 + .
Step 2: 6 x (4 + 4) = (6x4) + (6x4) x 4 See it?

37. Use the attached sheets to have students practice just the distributive property as their warm up for several days.
Build fold, diagram and record the 2 distribution equations.
Fight the urge to focus on finding products.
This task is about distribution.

38. 2.)Record both equations.
1.)If you really understand the distributive property then you can work from a diagram to equations or from equations to diagrams.
2.)Record both equations.
3.) Show several other ways to distribute the same equation.
4.) The final step will be to record the products. At this point use mental addition PLEASE.
I do not recommend moving to the final step of solving to find products until you are convinced that all students can record distribution equations.

39. Practice with BERCS.
Build, Explain, Represent, Compare
Practice every day by doing one or two “facts”. Once you are confident, practice once or twice a week to stay “fresh”.
Practice should make you have to actively think. The best practice is when you risk by teaching someone else. If you try to teach your mom or dad and it does not go over well then you need more practice.
Practice should push you to try to work mentally and simply record the equations.
Practice should be regular and short so that it is enjoyable, not torture.
Practice should include rotating or reflecting the images to prove that position does not matter. Explain the commutative property as it relates to the distributive property.