### Lesson 9 - Math Techniques for Adult Basic Education (ABE) Learners Illinois State Library

#### More Math Activities

Page 4 of 6

Many adult learners want to learn certain math skills like multiplication or fractions. They may need these math skills for specific purposes like securing better employment, helping their children with math assignments, or calculating their home budget.

The following are suggested strategies to build specific math skills.

#### Fractions (1/2, 1/3, 1/4)

One half

Fill a 1/2 cup measuring cup and empty into a 1-cup measuring cup. Talk with the student about how much is filled. Repeat and talk about how many 1/2-cup measuring cups it takes to fill the 1-cup.

Fold paper in 1/2 lengthwise and have the student find another way to fold it in 1/2.

One third

Use rectangular shapes for this activity, such as graham crackers. Discuss how many parts make up a whole cracker. Use the measuring cup activity and paper activity from the one half activity to demonstrate one third.

One fourth (or one quarter)

Repeat the activities in One half and One third using measuring cups, paper, or graham crackers to illustrate quarters.

#### Tools

Kit-Kat and Hershey's candy bars also divide well into fractions. Egg cartons are already divided into twelve sections and can be cut easily to further demonstrate fractions.

#### Adding and Subtracting 2-Digit Numbers without Borrowing

Place 2 dimes together, 3 pennies together, and 5 pennies together into three separate sets. Ask the learner to write the number in each set, tens and ones, and find out how many there are altogether. Stress that ones are added to ones and tens are added to tens.

Using dimes and pennies, show 47 cents. Ask the learner to write the number and to show the value that will be left if 6 pennies are taken away. Remind them that pennies are taken from pennies. Have them take the 6 pennies away.

Arrange 47 paper clips in 4 strings of 10 with 7 in the final column. Ask the learner how many will be left if 23 are taken away. Remove 2 groups of 10 and 3 loose paper clips.

Give the student a dime and 3 pennies and say: "Write the example that will tell how many are left if I take away 5 pennies. Help me find a way to take away 5 pennies." (The dime must be exchanged for 10 pennies.)

13 − 5 = 8

#### Multiplication Tables

Multiplication facts often present a problem for learners. One strategy the tutor can use to ease the fears of learners is to explain that there are really only 15 facts to learn (memorize). Start by showing your learner that any number multiplied by 1 is just the number itself.

Next, have the learner count by 2s showing the answers to 2x1, 2x2, 2x3, etc. Then have the learner do the same counting by 5s for 5x1, 5x2, 5x3, etc. The tutor should write out the problems and fill in the answers as the learner counts.

Finally, show the learner that multiplying by the greatly feared "9" is not what it appears. Start by showing your learner that if you put the problems in a row first. Then, start at 2x9 and count from 1 to 8. Last, start at 2x9 and count backwards from 8 to 1. You have your answers for the 9s. Also point out to learners that all the answers for each problem add up to 9.

First, Then, on left Last, on right Answer
1 x 9 = 0 9 9
2 X 9 = 1 8 18
3 x 9 = 2 7 27
4 x 9 = 3 6 36
5 x 9 = 4 5 45
6 x 9 = 5 4 54
7 x 9 = 6 3 63
8 x 9 = 7 2 72
9 x 9 = 8 1 81

Still another way to teach the 9s, particularly to learners who have tactile/kinesthetic learning strengths, is to use the hands. Try it and see!

1. Place both hands flat on the table.
2. Starting with the left little finger, number your fingers from 1-10.
3. For 9 x 1, go to finger #1 (left pinkie) and tuck it under.
4. Count all the fingers on the other side of that finger. Total is 9!
5. Try another! 9 x 7 = (tuck finger #7, right pointer finger)
6. How many fingers on the left of #7? 6-Right!
7. How many fingers on the right of #7? 3-Right! The answer is 63
8. GOOD! Now try a few! 9 x 4 =, 9 x 8 =

#### Probability

If a person tosses a coin, only 1 out of 2 sides can show when it lands, so the probability for either side is 1 out of 2 or 1/2. If a die with numbers 1-6 is rolled, the probability of any number showing is 1 out of 6 or 1/6. If there are 3 socks in a drawer - 2 red and 1 blue - the probability of blindly pulling out a red sock is twice as great as that for a blue sock. Red sock - 2 out of 3 or 2/3 and blue sock - 1 out of 3 or 1/3.

• You need two boxes, each containing 5 marbles (buttons, cards, socks) that are alike in color. Write A on one box and B on the other. In Box A, place 4 items of one color (say, red checkers) and 1 item of the other color (say, black) and in Box B, place 2 items of one color (say, red checkers) and 3 items of the other color (say, black).
• Using Box A, draw 1 checker. Use a graph to record each draw by coloring in a square in the proper column. Return the checker to the box after each draw.
• After about 15 draws, discuss which color was drawn more times (red) and why? Do the same with Box B. Compare the two graphs and discuss from which box did they draw more blacks and why? More red and why? Do the same thing again, only now don't replace the checker after the draw. Discuss how this changes the probability.

Show a die and ask which number will be on top when you roll it. Have the student roll the die 20-30 times and record the results on a graph.

Show the student the following graph and two dice. Have the student roll the dice several times, and after each roll, color in a square above the sum of the 2 numbers. After about 50 rolls, ask which sum was rolled the most times? (Probably 7) Which sums were rolled least? (Probably 2 and 12) Discuss why?

#### Place Value

To Reinforce Value of Hundreds Place:

Show the learner nine bundles of ten sticks and nine individual ones (Popsicle sticks, toothpicks, etc.). Make certain to have rubber bands on the table for this activity. Ask the learner to count the number of 10s and ones and record the number. Place one more stick with the 9 ones and ask how many sticks there are. Observe to see if the student bundles the 10 ones to make 1 ten. If not, ask: "What do we do when we have 10 ones?" (make a ten) Then ask how many 10s do we have now? (ten) We have 10 tens. What do we do when we have 10? (We bundle them) So we will bundle the 10 tens and we have? (100) One bundle of tens is 100. Continue this activity showing other sets of hundreds, tens, and ones from 100 to 999. Have the student record each number.

Hundreds Tens Ones
1 0 0
1 10
(Bundled)
0
1 10 100