Activity 1
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Sixth Grade
Math
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This!packet!includes!four!sections!that!cover!the!major!content!of!6
th
!grade!math.!!Each!section!
includes!four!pages!of!notes!and!practice!for!each!topic.!!For!additional!support,!visit!KCS!TV!on!
YouTube!for!instructional!videos!that!accompany!each!section.!!
!
The!following!content!is!included!in!this!packet:!
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!
Topic!
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I. Area!of!!
Polygons!
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II. Ratio!!!!!
Reasoning!!
III.!Rational!
Numbers!
IV.!Equations!and!
Expressions!
Activity!
1!
Area!of!
Quadrilaterals!!
Rates!
Dividing!Mixed!
Numbers!!
Order!of!
Operations!
Activity!
2!
Area!of!!
Triangles!
Ratios,!Rates,!
Tables,!and!Graphs!
Adding!and!
Subtracting!
Decimals!
Addition!and!
Subtraction!
Equations!
Activity!
3!
Solving!Area!
Problems!
Solving!Problems!
with!Proportions!
Multiply!Decimals!
Evaluating!
Expressions!
!
Activity!
4!
!
Area!of!Polygons!
Understanding!
Percent!
Dividing!Decimals!
Generating!
Equivalent!
Expressions!
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!
!
!
!
!
!
!
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!
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Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
262
Area of Quadrilaterals
Reteach
You can use formulas to find the areas of quadrilaterals.
The area A of a parallelogram is the product
of its base b and its height h.
A = bh
A = bh
= 3 • 7
= 21 cm
2
The area of a trapezoid is half its height
multiplied by the sum of the lengths of its
two bases.
A =
1
2
h(b
1
+ b
2
)
A =
1
2
h(b
1
+ b
2
)
=
1
2
• 6(5
+ 9)
=
1
2
• 6(14)
= 3 • 14
=
42 m
2
The area of a rhombus is half of the product
of its two diagonals.
A =
1
2
d
1
d
2
A
=
1
2
d
1
d
2
=
1
2
(5)(8)
= 20 in
2
Find the area of each figure.
1. 2.
________________________________________ ________________________________________
3. 4.
________________________________________ ________________________________________
LESSON
13-1
Section I
Activity 1
Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
268
Area of Triangles
Reteach
To find the area of a triangle, first turn your triangle into a rectangle.
Next, find the area of the rectangle. 6 • 3 = 18 square units
The triangle is half the area of the formed rectangle or A =
1
2
bh, so
divide the product by 2.
18
2 = 9 So, the area of the triangle is 9 square units.
Find the area of each triangle.
1. 2.
________________________________________ ________________________________________
3. 4.
________________________________________ ________________________________________
5. 6.
________________________________________ ________________________________________
LESSON
13-2
Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
274
Solving Area Equations
Reteach
You can use area formulas to find missing dimensions in figures.
The formula for area of a parallelogram is A = bh.
The formula for area of a trapezoid is A =
1
2
h(b
1
+ b
2
).
The formula for area of a rhombus is A =
1
2
d
1
d
2
.
The formula for area of a triangle is A =
1
2
bh.
Suppose you know the area of a triangle is 28 square feet. You also
know the length of the base of the triangle is 7 feet. What is the height of
the triangle?
Use the formula for area of a triangle. A =
1
2
bh
Substitute known values. 28 =
1
2
(7)h
Multiply both sides by 2. 56 = 7h
Divide both sides by 7. 8 = h
The height of the triangle is 8 feet.
Solve.
1. The area of a parallelogram is 150 square meters. The height of the
parallelogram is 15 meters. What is the length of the parallelogram?
_________________________________________________________________________________________
2. The length of one diagonal of a rhombus is 8 cm. The area of the
rhombus is 72 square centimeters. What is the length of the other
diagonal of the rhombus?
_________________________________________________________________________________________
3. The area of a triangle is 32 square inches. The height of the triangle is
8 inches. What is the length of the base of the triangle?
_________________________________________________________________________________________
4. The area of a rectangle is 34 square yards. The length of the rectangle
is 17 yards. What is the width of the rectangle?
_________________________________________________________________________________________
5. The area of a trapezoid is 39 square millimeters. The height of the
trapezoid is 6 millimeters. One of the base lengths of the trapezoid is
5 millimeters. What is the length of the other base of the trapezoid?
_________________________________________________________________________________________
LESSON
13-3
Section I
Activity 3
Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
280
Area of Polygons
Reteach
Sometimes you can use area formulas you know to help you find the area of more complex
figures.
You can break a polygon into shapes that
you know. Then use those shapes to find
the area.
The figure at right is made up of a
triangle, a parallelogram, and a rectangle.
Triangle
A =
1
2
bh
=
1
2
(3 × 4)
= 6squareunits
Parallelogram
A
=
bh
= 3 × 4
= 12 square units
Rectangle
A
=
lw
= 4 × 5
= 20 square units
Finally, find the sum of all three areas.
6 + 12 + 20 = 38
The area of the whole figure is 38 square units.
Find the area of each figure.
1. 2.
________________________________________ ________________________________________
3. 4.
________________________________________ ________________________________________
LESSON
13-4
Section I
Activity 4
Answer'Key'
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IV. Area'of'Polygons''
Activity'1:'Area'of'Quadrilaterals''
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Activity'2:'Area'of'Triangles''
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Activity'3:'Solving'Area'Problems''
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Activity'4:'Area'of'Polygons''
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