Lesson 5: Multiplication and the Abacus
Activities
Activity 1: Multiplication on the Abacus
Materials: abacus (kit), colored pencils
Ask your child to use the beads on the first side of the abacus (has an A in the top right corner) to show the following numbers: 18, 30, and 57. He should move beads from the left to the right to show the numbers (for example, to show 18, he should move 10 beads to the right on the top wire and 8 beads to the right on the second wire). Now, ask him to find the following sums using the abacus: 10+40 (50, 5 rows of beads moved to the right), 22+9 (31, 3 rows of beads moved to the right plus 1 more bead on the fourth wire). Be sure that your child can trade beads on the abacus correctly by moving the same number of beads from the right and from the left at the same time.
Now, tell your child to use the abacus to show a 4 by 5 array. He can move 4 rows of 5 beads or 5 rows of 4 beads to the right. Ask, "What's the product of 4 times 5?" and, if needed, "How many beads are in your array?" (20)
Ask your child to show 5 on the abacus. Next, ask him to show two more groups of 5 on the next two wires. He should now have 3 rows of 5 beads each. Say, "Now, you have created an array that shows 3 groups of 5 which we know is the same as 3 times 5. What's the product?" and "What can you count by to find the product?" He should count by 5 to 15.
Now, ask your child to show 10 groups of 4 on the abacus. He should show 10 rows of 4 beads each. Ask, "What multiplication sentence does this show?" (10 times 4, 10×4) "How might you figure out the product of this sentence?" Show him that he can count by 10 by counting the beads in columns rather than rows and that there are 4 columns of 10 beads. Ask, "What's the product?" (40)
Write 7×2 on the whiteboard, and tell your child to show it on the abacus and find the product. He should show 7 rows of 2 beads each for a product of 14. Repeat this process with 10×6 (60) and 5×8 (40).
Your child will complete the "Arrays on the Abacus" sheet by first writing multiplication sentences for the given arrays and then by coloring beads on the abacus to show a given multiplication sentence. He can use one color when he colors the beads.
Ask your child to show 5 on the abacus. Next, ask him to show two more groups of 5 on the next two wires. He should now have 3 rows of 5 beads each. Say, "Now, you have created an array that shows 3 groups of 5 which we know is the same as 3 times 5. What's the product?" and "What can you count by to find the product?" He should count by 5 to 15.
Now, ask your child to show 10 groups of 4 on the abacus. He should show 10 rows of 4 beads each. Ask, "What multiplication sentence does this show?" (10 times 4, 10×4) "How might you figure out the product of this sentence?" Show him that he can count by 10 by counting the beads in columns rather than rows and that there are 4 columns of 10 beads. Ask, "What's the product?" (40)
Write 7×2 on the whiteboard, and tell your child to show it on the abacus and find the product. He should show 7 rows of 2 beads each for a product of 14. Repeat this process with 10×6 (60) and 5×8 (40).
Your child will complete the "Arrays on the Abacus" sheet by first writing multiplication sentences for the given arrays and then by coloring beads on the abacus to show a given multiplication sentence. He can use one color when he colors the beads.
"Arrays on the Abacus" Answer Key
Student Activity Page
Activity 2: Finding Products on the Abacus
Your child will complete the "Finding Products on the Abacus" sheet by using the abacus to figure out the products for the given multiplication sentences. Remind him to look for chances to count by 2, 5, and 10 and for places where he can make 10 by trading beads to figure out the products.
"Finding Products on the Abacus" Answer Key
Student Activity Page