Presented By Tracy Flinchbaugh and Lisa MarstellerPresented By Tracy Flinchbaugh and Lisa Marsteller

South Eastern School DistrictSouth Eastern School District

Ideas for transitions modified fromhttp://www.swsd.k12.pa.us/baresvle/MathMaterials/alternat_algor.htm

Partial SumsPartial SumsAn Addition AlgorithmAn Addition Algorithm

658+ 4871000Add the hundreds (600 + 400)

Add the tens (50 +80) 130 Add the ones (8 + 7)

Add the partial sums(1000 + 130 + 15)

+ 15

1145

Partial SumsPartial Sums

572+ 8431300Add the hundreds (500 + 800)

Add the tens (70 +40) 110Add the ones (2 + 3)

Add the partial sums(1300 + 110 + 5)

+ 5

1415

You try it!You try it!

A Subtraction Algorithm A Subtraction Algorithm

8 1 2

- 5 5 7 Starting with the ones column, ask yourself, can I do 2 minus 7? No, so the 2 goes next door and borrows a ten. We change the 1 to a 0, and our 2 in the ones column becomes 12.

12

0

Next, go to the tens column, and ask yourself, can I subtract 5 from 0? No, so the 0 goes next door and borrows a hundred. The 8 becomes a 7, and the 0 becomes a 10.

10 7

Now subtract right to left.

2 5 5

You try it!You try it! 9 2 5

- 2 9 9 Starting with the ones column, ask yourself, can I do 5 minus 9? No, so the 5 goes next door and borrows a ten. We change the 2 to a 1, and our 5 in the ones column becomes 15.

15

1

Next, go to the tens column, and ask yourself, can I subtract 9 from 1? No, so the 1 goes next door and borrows a hundred. The 9 becomes an 8, and the 1 becomes an 11.

11 8

Now subtract right to left.

6 6 2

Lattice Multiplication

A Multiplication Algorithm

To solve 56 * 43, write the problem around the grid.

5 6

4

3Multiply each of the numbers around the grid writing one number on each side of the diagonal line.

AddAdd each diagonal column, regrouping regrouping (carrying)(carrying) when necessary.

Rewrite the answer with the problem.

5 * 4 = 20 6 * 4 = 245 * 3 = 156 * 3 = 18

20

24

81

51

8800

44

22

11

56 * 43 = 2,408

Lattice Multiplication

To solve 41 * 38, write the problem around the grid.

4 1

3

8Multiply each of the numbers around the grid writing one number on each side of the diagonal line.

AddAdd each diagonal column, regrouping (carrying) when necessary.

Rewrite the answer with the problem.

4 * 3 = 12 1 * 3 = 34 * 8 = 321 * 8 = 8

12

03

80

23

8855

55

11

41 * 38 = 1,558

You try it!You try it!

A Multiplication Algorithm

Multiply 80 * 50

86* 52

Multiply 80 * 2

4,000 160 300 12

Multiply 6 * 50

Multiply 6 * 2 +Add the partial products 4,472

Break down 86 into 80 + 6 and 52 into 50 + 2.

Multiply each part of the first number by each part of the second number.

Multiply 30 * 20

31* 27

Multiply 30 * 7

600 210

20 7

Multiply 1 * 20

Multiply 1 * 7 +Add the partial products 837

You try it!

Partial Partial QuotientsQuotients

A Division AlgorithmA Division Algorithm

The Partial Quotients Algorithm uses basic facts and extended facts that students know. There are multiple ways of getting to the correct answer.

6 158

Ask yourself about how many 6’s are in 158. Are there at least 10? Yes, because 10 [6’s] are 60.

Are there 20? Yes, because 20 [6’s] are 120.

Record 20 to the right and subtract 120 from 158.

20

- 12038

Subtract

6 - 36

2 26 R2

Subtract

Ask yourself how many 6’s are in 38. Is there at least 1? 2? 3? 4? 5? 6? Yes, because 6 [6’s] are 36.

Record 6 to the right and subtract 36 from 38.

Can I take anymore 6’s out? No, so I’m finished.Add the numbers on the right, and record the answer with the remainder.

+

You try it!

12 6,481300

- 3,6002,881

200

- 2,400

540 R1

48140 - 480

1

+

Ask yourself about how many 12’s are in 6,481. Are there at least 100? 200? 300? Yes, because 300 [12’s] are 3,600. Record 300 to the right and subtract 3,600 from 6,481.

About how many 12’s are in 2,881? Are there at least 100? 200? Yes, because 200 [12’s] are 2,400. Record 200 to the right and subtract 2,400 from 2,881.

Can I take anymore 12’s out? No, so I’m finished.Add the numbers on the right, and record the answer with the remainder.

About how many 12’s are in 481? Is there at least 10? 20? 30? 40? Yes, because 40 [12’s] are 480. Record 40 to the right and subtract 480 from 481.

Math websiteswww.studyisland.com (PSSA math and reading practice)http://everydaymath.uchicago.edu (supports EDM math curriculum)www.mathisfun.com (timed math facts practice, illustrated math dictionary)http://matti.usu.edu/nlvm/nav/vlibrary.html   (great graphics, manipulatives, and enrichment activities)www.aaamath.com  (explanation of math skills, interactive practice, challenge games)www.mathfactcafe.com (basic facts practice using flashcards, printable worksheets for time and money)http://www.mathleague.com/ (challenging mathematics and math contests for 4th grade and up)http://www.coolmath4kids.com/  (an amusement park of math)http://arcytech.org/java/  (tutorial for specific math skills - great graphics) 

Top-It (addition, subtraction, multiplication, and division)

Multiplication Baseball Multiplication Wrestling War Games (addition, subtraction,

multiplication) Subtraction Target Practice

http://everydaymath.uchicago.edu

MATH TIPS FOR

PARENTS

Ideas modified fromhttp://athomewithmath.terc.edu/math_kits.html

Number of the day…

Find one way to make the “Number of the day”.38 + 27 – 24 = 41 1 quarter, 1 dime, 1 nickel and 1 penny is $0.41

Find more ways to make the number100 - (3 x 25) + 16 = 41 82 x 0.5 = 41

Take time to find 11 in your day.The time is 41 minutes after 9:00. How long does it take to drive 41 miles?

If someone is born in 1941, how old would they be?

Food for thought…

How many pizzas do we need for our party?How many guests will we have?How many slices per person?

How many batches of cookies will we need to bake for friends and family?

How many people?How many cookies per person?How many cookies in a batch?Ingredients and amount needed?

How much longer?

Talk through the problem.“Are we there yet?”“How long until we eat?”

Figure out how much longer.Round to a time that’s easier to

work with and then adjust, such as round 5:18 to 5:20.

Explain solutions.

How much do we save? Talk about grocery coupons and store savings.

Cut out coupons with your child.Make grocery list for the week.Predict cost and savings.

Use a calculator as you shop or estimate in your head.

Have your child pay the cashier and count the change.

Find out the savings.Check totals on receipt and compare with

predictions.

Wish list… How much would you get to spend?

$20? $50? $100? $300? $1,000? What would you buy?

Browse catalogs, internet, or go window shopping.

Have your child make a wish list.Estimate the cost, tax, shipping, and

totals. Discuss everyone’s choices.

Comparison shopping…did you make the

best buys?What would you have done

differently?