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

Lesson 86: Divide Where 2 is an Operand or a Result

Directions

Have children complete the steps below.

Have children practice until they perfectly master each task.

Using a 10x10 abacus to demonstrate multiplication and division operations may be helpful, although it is not required. Look for one with two colors of beads (5 and 5) on each row. Inexpensive ones can be found online on sites such Amazon for around $10.00.

Steps

STEP 1

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

To teach 6 ÷ 2 and 6 ÷ 3, demonstrate with 6 objects of various types.

• Write 2 + 2 + 2 = 6 on the board.
• Ask children how times does 2 go into 6? (Divide the 6 objects into 3 groups of 2.)
• Write 3 + 3 = 6 on the board.
• Ask children how times does 3 go into 6? (Divide the 6 objects into 2 groups of 3.)
• When children readily call out the correct answers, give them each 6 objects 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 groups of 2 can we form? (Make 3 groups of 2 dots. Circle each group of dots.)
• How many groups of 3 can we form? (Make 2 groups of 3 dots. Circle each group of dots.)
• 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 groups of 2 can we form out of 6 counters? (Slide over 2 counters on 3 rows.)
• How many groups of 3 can we form out of 6 counters? (Slide over 3 counters on 2 rows.)
• When children readily call out the correct answers, direct them to slide the counters to make the groups themselves.

STEP 2

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

Ask the following:

• How many times 2 in 6 princesses?
• How many times 3 in 6 ninjas?

STEP 3

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

Ask the following:

• How many times 2 in 6?
• How many times 3 in 6?
• How many are 6 divided by 3?
• How many are 6 divided by 2?

STEP 4

Write the problems listed in the table below on the board. Show the children the symbol for division ('/' or '÷').

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

• 6 divided 3 is 2
• 6 ÷ 3 = 2
• 6 divided 2 is 3
• 6 ÷ 2 = 3

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.