Ray's New Primary Arithmetic by Joseph Ray Ray's New Primary Arithmetic by Joseph Ray    

Lesson 60: Multiply by 1

Directions

Have children complete the steps below.

Have children practice until they perfectly master each task.

Steps

STEP 1

Demonstrate multiplication with various physical objects, marks on the board, and/or an abacus with counters (beads).

To teach 2x1 and 1x2, demonstrate with 2 objects of various types and ask:

• How many are 1 coin and 1 coin?
• How many are 2 groups of 1 coin? (Separate the coins and treat each as its own group.)
• How many are 1 group of 2 coins? (Combine the two coins into a single group.)
• When children readily call out the correct answers, give them each 2 coins and direct them do the divisions themselves.

Represent the operations using dots or other symbols on the board. Draw the dots and ask:

• How many are 1 dot and 1 dot?
• How many are 2 groups of 1 dot? (Make two dots and circle each one.)
• How many are 1 group of 2 dots? (Make two dots and circle them both.)
• When children readily call out the correct answers, direct them to make the marks on the board and circle the groups themselves.

If using an abacus, demonstrate by sliding the counters to illustrate:

• How many are 1 counter and 1 counter?
• How many are 2 groups of 1 counter? (Slide over 1 counter each on 2 rows.)
• How many are 1 group of 2 counters? (Slide over 2 counters on 1 row.)
• When children readily call out the correct answers, direct them to slide the counters to make the groups themselves.

STEP 2

Children multiply objects they can't see, but can imagine (bears, mountains, trees).

Ask the following:

• How many are 1 skyscraper and 1 skyscraper?
• How many are 1 airplane and 1 airplane?
• How many are 2 groups of 1 airplane?
• How many are 1 group of 2 skyscrapers?

STEP 3

In this phase, do not mention objects. Children multiply numbers directly.

Ask the following:

• How many are 1 and 1?
• How many are two 1s?
• How many are 2 times 1?
• How many are one group of 2?
• How many are 1 times 2?

STEP 4

Write the problems listed in the table below on the board. Show the children the symbol for times (x).

Direct children to write and then recite each of these equations as follows:

• 1 time 2 is 2
• 1 x 2 = 2
• 2 times 1 are 2
• 2 x 1 = 2

STEP 5

Repeat steps 1-4 for each combination in the table below until the children master the tasks.

STEP 6

Assess mastery by reading aloud the listed word problems and having the children mentally compute and recite the solutions.

If children have difficulties, repeat the prior phases as needed and then reassess.