Teacher:
Cathy Spencer
Grade
7
This
is a variety of problems written by the Algebra 1 class of our middle school.
#1 (by: Allie, Chelsea, Vanessa, Kirsti)
For
grades 6-8, Ratios
Standard: Algebra
*Understand
patterns and relations.
Standard: Problem Solving
*Build
new mathematical knowledge through problem solving
*Solve
problems that arise in mathematics and other contexts
*Apply
and adapt a variety of appropriate strategies to solve problems.
The
problem:
Allie’s
shadow-
The
shadow of the pole is 11 yards 16 inches.
How
to work the problem:
1. Find the length of
4. Find the length of the pole’s shadow in inches. 5. Multiply
the answer to
Answer»8 yards 32 inches (Or 8 yards, 2 feet, 8
inches)
#2 Vanessa’s triangle-
For
grades 5-7, Geometry
Standard: Geometry
*Analyze
characteristics and properties of two and three dimensional geometric shapes.
Standard: Problem Solving
*Build
new mathematical knowledge through problem solving
*Solve
problems that arise in mathematics and other contexts
*Apply
and adapt a variety of appropriate strategies to solve problems.
The
Problem: Triangle
How
to work the problem: a2+b2=c2 62+82=C2 36+64=100
Answer: c=10 meters
#3. Kirsti’s locker-
For
grade 7-8, Volume of Rectangle prism and sphere
Standard: Geometry
*Analyze
characteristics and properties of two and three dimensional geometric shapes.
Standard: Problem Solving
*Build
new mathematical knowledge through problem solving
*Solve
problems that arise in mathematics and other contexts
*Apply
and adapt a variety of appropriate strategies to solve problems.
The
Problem: The top section of the locker is 10 inches
wide, 11 inches tall, and 11 inches deep. The lower section is 1 meter 19
inches tall. If you put a small ball in it with a radius of 2 inches, how much
space will be left in the locker?
Hint: The equation for the volume of a sphere is
V=4/3pr3
How to work the problem: Find the volume of the locker, then find the volume of the sphere. Subtract the volume of the sphere from the volume of the locker.
Answer»7579inches3
#4. Chelsea Tires-
For grades 5-7, Area of a Circle
Standard: Geometry
*Analyze
characteristics and properties of two and three dimensional geometric shapes.
Standard: Problem Solving
*Build
new mathematical knowledge through problem solving
*Solve
problems that arise in mathematics and other contexts
*Apply
and adapt a variety of appropriate strategies to solve problems.
The
Problem: The diameter of one tire is 25 inches. There
are 10 tires. Find the total area of all 10 tires.
How
to work the problem: Find the area of one tire by dividing 25 by 2 to find the radius,
then do the equation pr2. Multiply that
number by ten to find the area of all ten.
Answer»491 inches2
#5 Micheal’s Jungle
Gym
For grades 5-7, Area of a Circle
Standard: Geometry
*Analyze
characteristics and properties of two and three dimensional geometric shapes.
Standard: Problem Solving
*Build
new mathematical knowledge through problem solving
*Solve
problems that arise in mathematics and other contexts
*Apply
and adapt a variety of appropriate strategies to solve problems.
The Problem: This
is the jungle gym at our middle school. Many kids play on this. But we wanted
to know; what would be the circumference of the two half circles, if you put
them together to make a circle. We took the measurement of the height of the
jungle gym; which is 6 ft 1 in. What is the circumference in inches? What is
the area in inches?
A way to solve the
problem:
6 ft 1 in = 73 in. Convert to common units
R = 73 Identify the information you
will need
D = 146
3.14 x 146 =458.44 in. Use the formula Circumference=Diam.X
Pi
73 x 73 =5329 Use the formula Area=
PiXradiusXradius
3.14 x 5329 = 160633.06
Solution:
A = 160633.06 in2
C = 458.44 in.
#6 Michael’s Rim Problem
For grades 5-7, Area of a Circle
Standard: Geometry
*Analyze
characteristics and properties of two and three dimensional geometric shapes.
Standard: Problem Solving
*Build
new mathematical knowledge through problem solving
*Solve
problems that arise in mathematics and other contexts
*Apply
and adapt a variety of appropriate strategies to solve problems.
The Problem: These rims are
“Bling Bling.” With a
diameter of 19 inches, what would be the circumference of the rims. What would
be the area of the rims? What would be
the radius of the rims?
A way to solve it:
3.14 x 19 = 58.66 in Use the formula circumference=Pi X
Diameter
R = 19/2 Use the formula Radius=
˝ Diameter
9 ˝ x 9 ˝ =58.25
58.25 x 3.14 Use the formula Area = Pi X
Radius X Radius
Solutions:
Circumference = 58.66 in
Area =
Area Rounded to nearest
hundredths:182. 91 in2
Radius: 9 ˝ Inches
#7 Cassie’s Swings
For grades 4th – 7th
grades, Number and Operations
Standard: Number and operations
*Understand numbers
*Understand meanings of
operations and how they relate to one another
*Compute fluently and make
reasonable estimate
Standard: Algebra
*Use mathematical models to
represent and understand quantitative relationships
The Problem: Swingset: this is a
swing set that needs new swings!!! It is from
It costs $3.75 for 3 feet of
wood, finished. Iit costs $5.00 for 10 feet of chain. So if each swing needs 10 feet
of chain on each side and 1 foot of wood. 8 swings cost $90.
#1How much does 5 swings
cost?
#2 How many full swings can
you get with $16.50?
A way to solve it: One foot of
wood: $3.75 divided by 3;
Chain: $5.00 X 2;
Compute the cost of 1 swing by adding the two answers. Multiply by 5. Divide the cost of one swing
into $16.50, disregarding the “remainder” since we don’t need partial swings.
Answer: #1. $56.25 for
5 swings
#2. One swing can be purchased for $16.50.
#8 John’s tree
For grades 7 or 8, Area of a Cone
Standard: Geometry
*Analyze
characteristics and properties of two and three dimensional geometric shapes.
Standard: Problem Solving
*Build
new mathematical knowledge through problem solving
*Solve
problems that arise in mathematics and other contexts
*Apply
and adapt a variety of appropriate strategies to solve problems.
The Problem: A
logger is wondering how much wood there will be from a trunk tree that has a
diameter of 3ft and a height of 54ft. The trunk is roughly a circle that gets gradually
smaller until it ends in a tip at the top.
A way to solve the problem: To solve this problem you need the formula
you use to find the volume of a cone.
First find the area of the circle formed at the base of the tree: Area= Pi X Radius X Radius. Multiply by the height of the tree. Divide that number by three.
Solution: The Volume of
wood in the trunk is 127.17 cubic feet
#9. Thirsty Kailee
For
grades 7-8, Rate
Standard: Algebra
*Understand
patterns and relations.
Standard: Problem Solving
*Build
new mathematical knowledge through problem solving
*Solve
problems that arise in mathematics and other contexts
*Apply
and adapt a variety of appropriate strategies to solve problems.
The Problem: n
milliliters of water comes out of a drinking fountain per second. If
5n+63=168, then how many milliliters of
water is dispersed per second?
A way to solve the
problem:
To solve this problem you
must get the n alone. Do this by subtracting 63 from both sides, then divide to
get rid of the 5.
5n+63=168
-63
-63
___________
5n=105
___
___
n =
21
The Solution: 21 milliliters
of water comes out of the drinking fountain per second.
#10. Morgan Wants In
For
grades 4-6, Area of a Rectangle
Standard: Algebra
*Understand
patterns and relations.
Standard: Problem Solving
*Build
new mathematical knowledge through problem solving
*Solve
problems that arise in mathematics and other contexts
*Apply
and adapt a variety of appropriate strategies to solve problems.
The
Problem: We hate the color of this door! How much paper will it take to cover it up
with a great door sign? The door is 3
feet wide and 6 feet high.
A
Way to solve this problem: Find the area of the door using
the equation a=bh. . What you do is you put in 3 for
b (base) and 6 for h (height). It looks
like this a=3(6).
The
solution: 18 sq feet.