1. Pima Elementary School 5th Grade Math Ms. Haas
Welcome to Math Night!
Pima Elementary School
5th Grade Math
Ms. Haas

2. The Essential Question? “Do you feel like it is YOUR MATH Homework?”

3. Math Night Summary
Help is here! Tonight we will learn the essential multiplication and division algorithms. I know this is not how we all did math when we were going to school.

4. Math Night Presentation: CFQ’s
Why do I feel like it is my homework?
What are all these “new” ways to multiply and divide?
Why doesn't my child know how to multiply and divide YET?

5. Multiplication and Division Facts!
Why is my student STILL struggling with division, fractions, and number sentences?
Multiplication and Division Facts!

6. Lattice Method
The lattice method is an alternative to long multiplication for numbers. In this approach, a lattice is first constructed, sized to fit the numbers being multiplied.
28 x 13 2 8 1 3

7. Lattice Method
The multiplicand is placed along the top of the lattice so that each digit is the header for one column of cells The multiplier is placed along the right side of the lattice so that each digit is a header for one row of cells.
Before the actual multiplication can begin, lines must be drawn for every diagonal path in the lattice from upper right to lower left to bisect each cell. 2 8 1 3

8. Lattice Method
Now we calculate a product for each cell by multiplying the digit at the top of the column and the digit at the right of the row. The tens digit of the product is placed above the diagonal that passes through the cell, and the units digit is put below that diagonal. If the product is less than 10, we enter a zero above the diagonal. 2 8 1 2 8 2 3 4 6

9. Lattice Method
Now we are ready to calculate the digits of the product. We sum the numbers between every pair of diagonals and also between the first (and last) diagonal and the corresponding corner of the lattice. We start at the bottom half of the lower right corner cell (4). Since this is the only number below this diagonal, the first sum is 4. We place the sum along the bottom of the lattice below the rightmost column. We continue summing the groups of numbers between adjacent diagonals, and also between the top diagonal and the upper left corner. 2 8 1 1 2 8 2 3 3 4 6 6 4

10. Lattice Method
The final product is composed of the digits outside the lattice which were just calculated. We read the digits down the left side and then towards the right on the bottom to generate the final answer:
364 2 8 1 1 2 8 2 3 3 6 4 6 4

11. Partial Quotients 352 8 Partial-quotients division involves:
-Breaking the dividend into parts
Finding multiples of the divisor
Finding partial quotients, and
Finding the sum of the partial quotients
352 8
Dividend
Divisor

12. Partial Quotients 352 8 Partial-quotients division involves:
-Breaking the dividend into parts
How many 8s in 352?
- Finding the multiples of the divisor
What times 8 will equal 352?
Begin by thinking of easy multiples of eight: 8x10=80; 8x20=160; 8x50=400
352 8
Dividend
Divisor

13. Partial Quotients 8 352 20 x 8 = 160 20 160 192 20 20 x 8 = 160 160 32
-Finding the partial quotients
Think how many 8s in 352? 8x10=80; 8x20=160; 8x50=400
There are at least 20 [8s] in 352.
Partial quotients 8
352
20 x 8 = 160 20
160
192 20
20 x 8 = 160
160 32

14. Think how many 8s in 352? 8x10=80; 8x20=160; 8x50=400
Partial Quotients
Think how many 8s in 352?
8x10=80; 8x20=160; 8x50=400
Partial quotients 8
352 20
20 x 8 = 160
160
192 20
20 x 8 = 160
160 4
32 x 4 = 32 32 32
Remainder

15. Partial Quotients
- Finding the sum of the partial quotients
Now add the partial quotients to solve for the quotient.
Partial quotients 8
352 20
160
192 20
160 4 + 32 44
Quotient 32
Remainder

16. Partial Quotients 8 352 40 x 8 = 320 40 320 32 4 4 x 8 = 32 32
Note the process would be more efficient if I was proficient in my multiplication facts.
8 x 40 = 320; and 8 x 4 = 32
Partial quotients 8
352
40 x 8 = 320 40
320 32 4
4 x 8 = 32 32
Remainder

17. Now add the partial quotients to solve for the quotient.8
352 40
320 32 4 + 32 44
Quotient
Remainder

18. Math in Cartoons Using Videos to Help Understand Math Multiplication and Division Strategies
Learning Strategies
(Click on for video link)

19. Algorithm Unit Study Essential Question:
Which multiplication and division algorithm works best?
Lattice
Partial Products
Egyptian

20. Curriculum Framing Questions
Unit Questions
Content Questions
What are the three multiplication algorithms?
What are two division algorithms?
What are the steps to each algorithms?
What is the best approach to solving multiplication and division problems?