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SchoolNova Math3
CW 15
Solving math problems using notebooks.Write one digit or letter per box.
1
2
A pound of bananas costs
a dollars and a pound of
b
pineapples costs dollars more than bananas. How much
would 3 pounds of bananas and 8 pounds of pineapples cost
altogether?
c
We can buy 5 pounds of apples for dollars. How much do
we have to pay for 8 pounds of the apples?
We can buy 5 pounds of apples for
c dollars. How many
d dollars?
A table costs x dollars, and a chair costs y dollars. How
pounds of apples can we buy for
much is the cost of 2 tables and 8 chairs?
a dollars. How much do we have to pay for 2
boxes of pencils if the first box contains m pencils, and the
second box contains n pencils?
After Anna spent b dollars, she had twice as much left as she
A pencil costs
spent. How much money did Anna have before her spending?
Write an expression for each problem.
3
The total number of students in a school is 656. The number of girls is 86 more than the
number of boys.
Renee is 26 years younger than her mother. Her mother is 52 years old.
The sum of two numbers is 85. The greater number is 13 more than the smaller number.
Ram is 10 years more than twice the age of Rahim. Ram’s age is 56 years.
The perimeter of a rectangle is 20 m. Its length is 2 m greater than is width.
4
Use the long division algorithm to calculate the following.
1630÷5
5067÷9
1020÷12
1845÷15
5
a) There were 10 girls on the school yard. 7 of them had scrunches and 6 of them had
ponytails. How is that possible?
b) There are apples and pears on a table. There are 4 less apples than apples and pears
together. There are 7 less pears than apples and pears together. How many fruits are on
the table? How many are apples? How many are pears?
c) 5 students in 5th grade class study Spanish only, 8 kids in class study French only. Every
student in class studies at least one foreign language. How many people study 2 foreign
languages if there 22 kids in that class.
6
Solve the following equations:
6y + 8 = 26
7x + 16 = 72
12z + 2 = 38
25a ÷ 5 + 4 = 49
7
Angle Sum of a Triangle
Can a triangle have two obtuse angles?
Why or why not?
Can a triangle have two right angles? Why
or why not? What happens to the sides of
two right angles if we extend them?
Compare the sides and the angles of a triangle ABC. Which side is the longest? Which angle is
the largest? Which side is the shortest? Which angle is the smallest?
Conclusion: In a triangle, the largest angle lies opposite the longest side. In a triangle the
smallest angle lies opposite a shortest side. Also, the opposite is true: the shortest side is across
from the smallest angle.
Does any isosceles triangle have two equal angles?
Think! If the angles were not equal then one of the angles would be greater than the other. For
example angle ABC would be greater than angle ACB. In a case like this would the sides AB
and AC be equal?
1) Draw a triangle ABC and cut out the three angles.
2) Rearrange the three angles to form a
straight angle on a straight line.
So, the angle sum of a triangle is 180°.
Just like regular numbers, angles can be added to obtain a sum. Sometimes, we can determine a
missing angle because we know that the sum must be a
certain value. Remember -- the sum of the degree measures
of angles in any triangle equals 180 degrees.
Look at the triangle ABC, where angle A = 60 degrees,
angle B = 50 degrees and angle C = 70 degrees.
If we add all three angles in any triangle we get 180
degrees. So, the measure of angle A + angle B + angle C = 180 degrees. This is true for any
triangle in the world of geometry. We can use this idea to find
the measure of angle(s) where the degree measure is missing
or not given.
In triangle ABC, angle A = 40 degrees and angle B = 60
degrees. What is the measure of angle C?
We know that the sum of the measures of any triangle is 180
degrees. Using the fact that angle A + angle B + angle C = 180 degrees, we can find the
measure of angle C.
Angle A = 40
Angle B = 60
Angle C = we don't know
To find angle C, we simply plug into the formula above and solve for C.
A + B + C = 180
C = 180 - A - B
C = 180 - 40 - 60
C = 80
To check if 80 degrees is correct, let's add all three angle measures. If we get 180 degrees, then
our answer for angle C is right.
Here we go: 40 + 60 + 80 = 180
It works!
You don't always have to plug in those values to the equation and solve. Once you're
comfortable with this sort of problem you'll be able to say "okay, 40 + 60 =100, so the other
angle has to be 80!" and it's much quicker.
8
In
ABC, A = 45, B = 90, find C.
In
ABC, A = 70, B = 30, find C.
In
ABC, A = 100, B = 50, find C.
9
The commander of the Cat Island said something and it he told the truth.
The Prime minister of the Cat Island repeated the same sentence but he was lying. How can
this be?