Purpose: To illustrate products involving mixed decimals Materials: Decimal Squares and Decimal Squares Grid (attached) Activity 1 Multiplying with Mixed Decimals Decimal Squares Grid

1. Distribute Decimal Squares Grids to students.

What observations can you make about the Decimal Squares Grid on your sheets? (Some students may notice the bold lines and that they form 10 by 10 squares like the green decimal squares. Point this out, if it is not noticed.) How many of these 10 by 10 squares are there are in this grid? (35)

If each side of these large 10 by 10

squares has a length of 1 unit, what is the length of the side of each small square? (.1)

If each large square represents 1, that

is, has an area of 1 square unit, what does each small square represent? (.01, that is, has an area of .01 square units because each large square contains 100 small squares.)

2. Kendall made a quilt with dimensions of 2.3 yards by 1.7 yards. Use your grid to outline a rectangle having these dimensions and label the lengths of two of its sides:

a. What is the number of whole squares and parts of a square for this diagram? (3 whole squares and 91 parts of a square.)

b. What is the area of the quilt in square yards? (3.91 square yards.)

c. Can this area be found by multiplying 2.3 × 1.7? (Yes)

TEACHER MODELING/STUDENT RESPONSE

MULTIPLICATION 6.NS.3 MULTIPLICATION WITH MIXED DECIMALS

3. On your grid, outline and label the sides of a rectangle having dimensions of 2.8 by 1.6.

How many whole squares and parts of

a square are in this rectangle? (4 whole squares and 48 parts out of 100.)

If each 10 by 10 square on your grid

represents 1 square unit, what is the area of your rectangle? (4.48 square units.)

Determine the area by writing a multiplying

equation for the product of the two dimensions. (2.8 × 1.6 = 4.48)

Activity 2 Summarizing to See Patterns and Relationships

Look at the products from the previous examples and write a rule for the product of a mixed decimal times a mixed decimal. (Multiply the two numbers as if they were whole numbers. The total number of decimal places in the two numbers is the number of decimal places in the product.)

Activity 3 Approximating Products by Rounding

Approximate the following products by rounding each mixed decimal to the nearest whole number and then multiplying the two whole numbers. a. 3.21 × 5.07 ≈ 3 × 5 = 15 b. 4.86 × 1.12 ≈ 5 × 1 = 5 c. 4.6 × 8.21 ≈ 5 × 8 = 40 d. 7.66 × 9.8 ≈ 8 × 10 = 80

Worksheets 6.NS.3 #22, #23, and #24

decimalsquares.com Laser Beams At the Advanced Level, this game requires rounding mixed decimals to whole numbers and computing with all four operations on whole numbers.

INDEPENDENT PRACTICE AND ASSESSMENT

3