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Welcome to Math Night!
Pima Elementary School5th Grade Math
Ms. Haas
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.
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?
Why is my student STILL struggling with division, fractions, and number
sentences?
Multiplication and Division Facts!
Lattice MethodThe 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
Lattice MethodThe 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
Lattice MethodNow 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
3
02
08
06
24
Lattice MethodNow 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
3
02
08
06
24
463
01
Lattice MethodThe 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:
2 8
1
3
02
08
06
24
46
3
01
364
Partial QuotientsPartial-quotients division involves:-Breaking the dividend into parts-Finding multiples of the divisor- Finding partial quotients, and- Finding the sum of the partial quotients
3528Divisor Dividend
Partial QuotientsPartial-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
3528Divisor Dividend
Partial Quotients-Finding the partial quotients
Think how many 8s in 352? 8x10=80; 8x20=160; 8x50=400There are at least 20 [8s] in 352.
352
8Partial quotients
20 20 x 8 = 160
192 20 x 8 = 16020
160
160
32
Partial QuotientsThink how many 8s in 352?
8x10=80; 8x20=160; 8x50=400
352
8
Partial quotients
20 20 x 8 = 160
192 20 x 8 = 16020
160
160
32 4 32 x 4 = 32
32Remainder 0
Partial Quotients- Finding the sum of the partial quotientsNow add the partial quotients to solve for the quotient.
352
0
8
Quotient
Partial quotients20
192 20
160
160
32 4
32
+ 44
Remainder
Partial QuotientsNote the process would be more efficient if I was proficient in my multiplication facts. 8 x 40 = 320; and 8 x 4 = 32
352
8
Partial quotients
40 40 x 8 = 320
32 4 x 8 = 32 4
320
32
0Remainder
Partial QuotientsNow add the partial quotients to solve for the quotient.
352
8
Partial quotients
40
32 4
320
32
0Remainder
44 Quotient
+
Math in CartoonsUsing Videos to Help Understand Math Multiplication and Division Strategies
–Learning Strategies (Click on for video link)
Algorithm Unit Study
• Essential Question: Which multiplication and division
algorithm works best?
Lattice Partial Products Egyptian
Curriculum Framing Questions
Unit Questions • What are the three
multiplication algorithms?
• What are two division algorithms?
Content Questions• What are the steps to
each algorithms?
• What is the best approach to solving multiplication and division problems?
