Grade 4, Module 9
Core Focus
•
•
•
•
Developing rules for finding the area and the perimeter of rectangles
Investigating multiplication of fractions using the area model and the number line model
Multiplying mixed numbers
Converting length measurements within the customary system (feet to inches, yards
to feet, miles to yards)
Measurement
Ideas for Home
• Extending the learning about area and perimeter from Grade 3, students now
investigate and then develop rules for finding the area and perimeter of rectangles.
• Using the dimensions of a rectangle (length and width), students find its area by
multiplying as they do with arrays. If students know how many squares are in each
row, and how many rows there are, they can multiply to find how many squares in
total. This is where the familiar formula A = L × W for area of a rectangle comes from.
6 yd
8 yd
• Finding the area of rectangles reinforces the use of the partial products to multiply.
The example below involves finding the area of the carpeted floor by decomposing
the rectangles.
6m
7 × 10 = 70
5m
7 × 4 = 28
Tiles
7m
Carpet
so
7 × 14 = 98 m2
and
6 × 5 = 30 m2
98 − 30 = 68 m2
14 m
14 − 6 = 8 m
7−5=2m
2 × 6 = 12 m2
56 + 12 = 68 m2
In this lesson, students explore strategies to find the area of the carpeted
floor, composed of rectangles.
• Students also find the perimeter of two-dimensional geometric figures by adding
the distances around the rectangle. Students discover that since the two lengths
are the same and the two widths are the same, the formula P = (2 × L) + (2 × W)
or P = 2 × (L + W) can be used.
7 in
© ORIGO Education.
15 in
180815
• When in a store, notice boxes
and labels that have length
X width dimensions listed.
Determine the area and
perimeter together using the
dimensions listed. (E.g. “A 5 ft
× 7 ft rug is 35 square feet and
has a perimeter of 24 ft.”)
Glossary
8 × 7 = 56 m2
2×7 =
2 × 15 =
Perimeter
• Use a measuring tape and
work together to find the area
and perimeter of smaller
rectangular shapes and
spaces in your home, e.g. a
cupboard, a tabletop, a book,
picture frames or rugs. Use
the L × W formula to find the
area. Use the (2 × L) + (2 × W)
formula to find perimeter.
Area is a measure of the
space inside a closed
geometric figure and
determined by the number
of units needed to cover
the space.
Perimeter is the distance
measured around a shape.
The word “rim” is contained in
the word “perimeter.”
Dimensions are the side
measurements of a rectangle
that can be used to calculate
area and perimeter.
in
In this lesson, students measure perimeter and develop rules to be used
for finding the perimeter of any rectangle.
1
Grade 4, Module 9
Fractions
• In this module, multiplication is extended to problems that involve a common
fraction multiplied by a whole number. Students use area models and number lines
to visualize and calculate multiplication of a fraction by a whole number.
Exploring the Multiplicative Nature of Common Fractions
(Number Line Model)
9.6
Eva needs 7 pieces of string that are each 43 of a foot long.
What is the total length of string she needs?
How does this number line show the problem?
Write the missing numerators in the fractions below the line.
+
3
4
+
0
3
4
1
3
4
3
4
+
+
2
3
4
4
7×
+
4
3
4
+
3
4
3
4
+
4
4
3
4
5
4
4
6
4
3 What multiplication sentence could you write
3
1
1
can be seen as repeated addition or 7 “jumps of” , which lands on 2 or 5 .
4 to show the total length of string?
4
4
4
• Students also multiply mixed numbers by a whole number ( e.g. 5 × 3 61 ). They can
The jumps help me see
decompose the mixed number using an array to makethethe
thinking
fractions
that arevisible and then
multiples of 34.
What do the jumps on the number line help you identify?
use the distributive
property
to
3 find the area.
Look at the multiples of shown below the number line.
4
What do you notice about the numerators?
A groundskeeper is laying new turf in
1
6
3
1. The distance between each
1 whole number is one whole.
Step
Up measures
The
section
5 yards
bythe
3 equation.
Draw jumps
to show
6 yards.Then write the product.
How many square yards of turf will be needed?
a.
5
4× 8 =
0
1
5×3 6 = 1
2
3
5
b.
1
(5 × 3)0 + (5 ×1 6 ) =2
3
4
5
210
6
© ORIGO Education.
4
5× 3 =
7
Ideas for Home
• Work with your child to
understand how multiplying
whole numbers and
fractions can be shown in an
array. Measure out a garden
plot or floor plan and find the
area using multiplication.
• When measuring for
cooking, woodwork,
sewing or knitting, notice
when mixed fractions are
multiplied and have your
child help you figure out the
multiplication showing their
thinking with a number line.
• Estimate distances in
various units: “How long
is the sidewalk?” “How
long is a car?” “How many
miles to school?” Check the
estimates using a variety of
measurement tools (rulers,
yard stick, tape measure,
and odometer) to help make
measurement more concrete
and easier to understand.
ORIGO Stepping Stones 4 • 9.6
In this lesson, students use an area model to multiply whole numbers by mixed
numbers in parts. The total area is 15 5 square yards.
6
Measurement
• Work with customary measures of length (inches, feet, yards, and miles) involves
reviewing how big each unit is, as well as knowing the official relationships
between them.
× 12
1 inch
×3
×3
1 foot
× 36
1 yard
1 foot
× 1,760
1 yard
1 mile
Glossary
The partial products strategy
uses the distributive property,
multiplying each place value
separately to get a partial
product, and then adding the
products together resulting in
one product.
× 5,280
© ORIGO Education.
These are the important relationships between customary measures. From these,
other relationships can be figured out.
• Students convert measurements and tell which unit of measure would be most
appropriate for different situations. E.g. which unit is best for measuring a piece
of paper, a length of cloth, the length and width of a room, or the distance from
home to school.
2
180815