Teaching Algebra with Manipulatives

Using Overhead Manipulatives
• Repeat for 7 (4). Write 7 (4) 3 on the blank transparency. Ask
students to make a general statement about the two sentences involving
integers with opposite signs. Sample answer: find the difference of the
absolute values of the addends; the sign of the sum is the same as the
integer with the greater absolute value.
Demonstration 2
Subtracting Integers
• Show students the integer
models transparency. Tell
them that these are some
guidelines we use when
modeling integers. Discuss
the properties that allow
these guidelines. additive
inverse; additive identity Replace the transparency with the integer mat
transparency.
• Place 7 positive counters on the mat and then remove 4 of them.
Ask students what operation is suggested by removing counters.
subtraction Ask them to state an equation for this model. 7 4 3
Write the equation in the lower right corner of the blank transparency,
aligned with 7 (4) 3.
• Repeat with negative counters for 7 (4) 3. Write the equation
on the blank transparency, aligned with 7 4 3.
• Clear the mat. Tell students
you want to model 7 (4).
Place 7 positive counters on
the mat. Tell students that
since there are no negative
counters on the mat, you
cannot remove 4 negatives.
Remind them that zero
pairs do not affect the
value. Place 4 zero pairs on the mat. Ask students what the value of the
mat is. Remove 4 negative counters. Ask students to state an equation for
this model. 7 (4) 11 Write the equation on the blank transparency,
aligned with 7 4 11.
• Repeat for 7 4. Place 7 negative counters on the mat. Since there are
no positive counters to remove, add 4 zero pairs. Remove 4 positive
counters. Have students state an equation for the model. 7 4 11
Write the equation on the blank transparency, aligned with
7 (4) 11.
• Ask them to compare the subtraction equations in the right column with
the addition equations in the left column. Then ask them to make a
general statement comparing subtraction of integers with addition.
Sample answer: subtracting a number gives the same result as adding
the opposite number.
© Glencoe/McGraw-Hill 41 Teaching Algebra with Manipulatives
Algebra 1—Chapter 2