Math 3

Review

1. Divide and indicate the remainders.

2. We paid a dollars for 4 loaves of bread.

How much money do we have to pay

for 6 loaves?

We paid a dollars for 4 loaves of

bread. How many loaves of bread can

we buy with c dollars?

Maria has b dollars. She bought 5

cookies for d dollars. How much

money does she have left?

Dan has a dollars. His mom gave him

b dollars. How many more dollars

does Dan have now?

2.

3. Cut out a circle from the last page.

Fold the circle in half. Then unfold it and fold it in half again. Your circle would have

two crease lines. Trace them with a pencil. The point of intersection of the lines is

called the center of a circle.

4. Mark the center of the circle on the picture below:

Point O is the center of a circle. The border of a circle is called circumference.

5. Draw 3 points on the circumference of the circle. Call them A, B, and C. Construct

segments OA, OB, and OC. Compare their lengths. Complete the sentence: OA,

OB, OC are _________________.

A circumference is a flat closed curve each point of which is on the same distance of the point we chose as a center.

A circle is a part of the plane, bounded by the circumference.

6. We can construct a circle by using a compass. One of the legs of the compass marks

the center of a circle; another leg marks the circumference of the circle.

Draw a circle (using a compass) with a center O and a point A on the side of the

circle. OA is called a radius of the circle.

7. Construct another circle with a radius equal to OA.

All the points of the circumference are equidistant from the center.

Radius connects the center of a circle and a point on its border.

8. Find equal circle on the picture below. Color equal circles with the same color.

Compare the radii of these circles.

If you put equal circles on top of each other they will coincide.

The radii of equal circles are equal.

9. Draw a circle, which intersects ray AB at two points

10. Draw a circle, which intersects the line below at 4 points;

11. Draw a circle, which intersects segment AB at 1 point;

12. Draw a circle, which intersects ray AB at 1 point.

Tangent Lines and tangent circles

A tangent line is a line that intersects a circle at one point. The point of intersection is

called the point of tangency.

Tangent circles are circles that intersect in a single point.

* * *

* *

13. In the circle, draw:

a radius a diameter two radii, which are not on the same line

Draw: a tangent line a line which intersects the circle, but is NOT a tangent line

14. Draw: a tangent circle inside tangent circle outside a circle that intersects (color in the intersection)

15. On the picture below, construct a circle with a center outside of the given circle so

that the new circle would have:

a) 1 point of intersection with a circle on the picture;

b) 2 points of intersection with a circle on the picture;

c) no points of intersection with a circle on the picture.

16. Meanwhile our mice discovered new facts about Cat Island inhabitants.

Read the descriptions and draw the graph’s edges.

Each of five cats is a friend of all others

Cats that visit each other

In the winter In the summer

Connect all cats that

Visit each other in winter and in the summer

Visit each other in winter or summer

Don’t visit each other in the summer

Connect all cats that

Don’t visit each other in winter

Don’t visit each other in winter and don’t visit each other in the summer (don’t visit each other at all)

Don’t visit each other in the summer or don’t visit each other in winter

17. Which door would you choose?

• Remember, we assume that there is a cat and there is a shovel and they are in the different

rooms.

Here the sign on one door is true and the sign on the other door is false. Which door would you choose?

Here labels are both true.

There are two cat tribes living on the island. Cats from the south tribe always lie

and cats from northern tribe always tell truth.

18. Jake The Mouse once met two cats – Miayu and Mrrrr. They belong to the different tribes. After

he asked them if they we married. Here is what the answers were:

Miayu: We are both married.

Mrrrrr: I am married.

To which tribe does Miayu belong and to which tribe does Mrrrr belong?

19. This is simple, right?

20. And this is simple as well

How many tens and how many ones? Write each of the following numbers in the expanded

form.

56; 34; 18; 9; 28; 74; 34; 80; 66; 19; 21; 77; 13; 23; 89

21. But what will we do with this?

16=10+6

(10 + 6) × 3= 10 × 3 + 6 × 3 =30 + 18 = 48

22. Using a picture below explain how we can multiply numbers 24 and 8. Examine

the different ways to multiply the numbers. Which way is the most convenient?

23 × 4

23 is 2 tens and 3 ones.

3 ones multiplied by 4 gives 12 ones and

2 tens multiplied by 4 gives 8 tens (that is 80).

80 and 12 are added to give the final product 92.

The 3 ones are first multiplied by 4 giving the product 12, which is 1 ten and 2

ones. 2 is written in the ones column and the 1 is recorded in the tens column.

Now the 2 tens are multiplied by 4 to give 8 tens. The 1 ten recorded before is

added on, so the product has 9 tens.

23. Multiply