Download Unit 8

Grade 4 – Unit 8
Lesson Focus
Anytime Problems
Lesson 1
Draw and
describe points,
rays, angles, and
other geometric
figures.
Hannah has been asked to baby-sit
her sisters from 9:30 in the morning
until 2:15 in the afternoon. How
many hours is that?
Lesson 2
Draw and
measure angles.
The perimeter of a rectangle is 15
inches. Two of the sides are each 2 ½
inches long. What is the length of
each of the other two sides.
Lesson 3
Identify,
measure, and
draw angles in a
circle.
Lesson 4
Draw and
classify triangles
by their angles
and sides.
Marita wrote a 3-digit number. The
digit in the tenths place is 5 less than
the digit in the ones place. The digit
in the hundredths place is the sum of
the digits in the tenths and the ones
places. What are the possible
numbers?
Mitch has saved $13.00 so that he
can buy a T-shirt. When he goes to
the store, he finds a second T-shirt
that he wants to get for his brother’s
birthday. If each T-shirt costs $8.50,
how much more money does Mitch
need to buy both T-shirts?
Lesson 5
Find unknown
angle measures.
Karen and her sister Jean are packing
for a trip. They can each bring only
one suitcase that weighs no more
than 40 pounds. Jean finds that her
suitcase weighs 52 pounds, but Karen
still has room in her suitcase and it
only weighs 25 pounds. What can
they do? Explain how they might
work together to solve this problem.
Writing PromptIntervention
Explain all the ways you
can tell the difference
between a right angle, an
acute angle, and on obtuse
angle.
Writing Prompt-On level
Writing Prompt-Challenge
Explain how you remember
what the terms right angle,
acute angle, and obtuse
angle mean. Draw
examples of each kind of
angle.
Explain how to use a
protractor to draw an angle
with a measure of 87⁰.
Chin said that on his walk he
followed a path that made
two acute angles, an obtuse
angle, and he ended where
he started. Can he be
correct? Explain.
How is measuring an obtuse
angle different from
measuring an acute angle?
Explain how to find an
3
angle that traces a 4 turn in
a circle.
Why does a 90⁰ turn
counterclockwise have the
same effect as a 270⁰ turn
clockwise? Name another
pair of turns that have the
same effect.
Draw and label a scalene
triangle, and isosceles
triangle, and an equilateral
triangle. Explain why the
triangles are scalene,
isosceles, or equilateral.
Use letters, angles, and
sides to describe all the
ways to name a triangle.
With words and pictures,
explain why it is impossible to
have a right triangle with an
obtuse angle.
Explain what operation you
would use to solve the
equation x + 50⁰ = 125⁰.
When an obtuse angle is
separated into two smaller
angles, what kinds of
angles might be formed?
Describe the steps in an angle
measure problem as if you
were telling a friend how to
draw the diagram and how to
write and solve an equation
to find an unknown angle
measure.
Describe how you measure
an angle. Do you turn the
angle to be horizontal, or
do you turn the protractor
to fit the angle?
If one angle drawn from
the center of a circle
measures 130⁰, what is the
measure of the other angle
that is formed? Explain.
Lesson 6
Add and
subtract angle
measures.
Teams in a hockey league receive two
points for a win, no points for a loss
during the regular game time, and
one point if they lose in overtime. If a
team has played 6 games this season
and has 10 points, how many games
have they won?
What are the two types of
angles that are easiest to
use as “whole angles”
when writing an equation
about angle measures?
Explain why.
Explain why angles in real
world situations are
sometimes difficult to
measure directly. How
does it help to use an
equation to find the
measure?
Write a real world problem
about angle measures.
Include a diagram, with angle
measures noted. You might
use the Internet to find
angles or do your own
measuring in your classroom
or at home.
Lesson 7
Demonstrate
understanding
of parallel and
perpendicular
figures.
Use triangles, squares, and circles to
make a pattern that matches the
pattern A, A, B, B, C, C, A, A, B, B, C, C.
If the pattern continues, what shape
will the fifteenth figure be?
Explain how you can use
lined paper or grid paper to
check whether two lines
are parallel or
perpendicular.
How many different lines
can you draw through one
point? How many different
lines can you draw through
two points? Explain your
thinking.
The lines drawn on your
MathBoard all lie on the
same surface. Look around
your home or classroom. Do
you see any pairs of lines that
are not parallel but are not
intersecting either? Describe
how you could model a pair
of these lines using your
arms.
Lesson 8
Name and
classify
quadrilaterals
based on sides
and angles.
Decompose
quadrilaterals
and triangles
into other
figures.
One triangle has 3 angles, each with
measure 60⁰. What is the sum of
those angle measures? What other
kind of figure has that result as its
angle measure?
Sixteen dogs are at the dog park
today. Six of them have blue leashes.
Twelve of the dogs have brown
collars. Four of the dogs have a blue
leash but don’t have a brown collar?
Explain why every square is
a rhombus, but not every
rhombus is a square.
Explain why a trapezoid can If a trapezoid has three equal
never be a rectangle, a
sides, explain why it must be
rhombus, a square, or a
an isosceles trapezoid.
parallelogram.
What is the diagonal of a
quadrilateral? Use pictures
and words to explain. How
many diagonals can you
draw in a quadrilateral?
Sort triangles
and
quadrilaterals
by a number of
different rules.
Suppose that you cut a string in half.
Then cut each half in half. Then you
cut each new half in half again. If you
cut all the pieces in half two more
times, how many pieces of string will
you have? What is the pattern?
Give an example of a
sorting that would have no
figures in it.
In your own words, explain
how a perpendicular drawn
in a triangle makes right
triangles and explain when
those triangles are the
same size and shape.
Explain why a sorting of
figures by right angles is
the same as a sorting of the
figures by perpendicular
sides.
Lesson 9
Lesson
10
Suppose you want to make a
rhombus from two triangles
that are the same size and
shape. Thinking of sides and
angles, list all the triangles
you can use.
Draw a picture to help you
explain why a sorting of
figures by parallel sides never
has a triangle figure in it.
Lesson
11
Recognize and
draw lines of
symmetry and
determine when
figures have line
symmetry.
Lesson
12
Use the CCSS
and Practices in
a variety of real
world problem
solving
situations.
Chen, Wendy, Lourdes, and Rick have
bikes. Each bike is a different color:
red, green, black, or white. Wendy’s
bike is white. Chen’s bike is not red.
Rick’s bike is not green. Lourdes’s
bike is not black or red. What color is
each person’s bike?
Barney made $785 last week at his
job. He spent $135 at the grocery
store and wants the rest of the
money to last for 2 weeks. How much
can Barney spend each of the 2
weeks if he spends the same amount
each week?
What is special about the
polygons on the Activity
Card? Draw a 5-sided
polygon that is special in
the same way. How many
lines of symmetry does it
have?
Explain how you determine
if a figure has a line of
symmetry.
Draw half of a figure.
Explain how to draw the
other half so that the
whole figure has line
symmetry.
Which of the capital letters
do not have line symmetry,
but can be cut into two
matching halves? Explain
your thinking.
Explain the relationship
between a quadrilateral
and a polygon.
Explain how finding a line of
symmetry in a rectangle is
different than finding a line of
symmetry in a triangle. How
is it the same?