Problem Sums

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Each problem sum can be answered using different methods. Explore the methods and find one which makes the most sense to your child. You can also combine methods.

Susan has 3 blueberry muffins and 4 chocolate chip cookies. How many muffins and cookies does Susan have altogether?

Answer: 7

3 + 4 = 7

Draw out the number of muffins and cookies. Count them.

- Start at the number for the muffins.
- Count the steps corresponding to the number of cookies.
- The number you end up at (7) is the answer.

- Draw 2 rectangles to represent the numbers.
- The smaller number should be in the smaller rectangle.
- Draw the rectangles side by side.
- Draw a curly brace '{' (bracket) over both rectangles to indicate the sum or total.

I have some pencils. I gave my little brother 2 of my pencils. I have 4 pencils left. How many pencils did I have at first?

Answer: 6

To find the number of pencils at first, imagine that we take the 2 pencils back from the little brother and add it to the number of pencils left:

4 + 2 = 6

- Draw the number of pencils left.
- Add in the number of pencils given away.
- Count all the pencils.

We start at the 4 pencils left.

- Draw a number line with the numbers 1, 2, 3, 4.
- Put a dot on the number 4. Remember that we reached this number after going backwards 2 steps.
- Add in 2 more numbers after 4. This is the number where we started.

4 + 2 = 6

- Draw a rectangle to represent the number of pencils left.
- Add another rectangle at the side to represent the 2 pencils given away.
- Draw a '{' over both rectangles to represent the number of pencils at first.

4 + 2 = 6

Sally has 8 books. John has 3 more books than Sally. How many books do both children have altogether?

Answer: 19

This question has a few steps. It is advisable to write statements to keep track of our working.

Sally's books: **8**

John's books: 8 + 3 = **11**

Altogether: 8 + 11 = **19**

(Both)

We draw 8 books for Sally.

John has 3 more books than Sally. Draw the same number of books as Sally, then draw 3 more books.

Now count all the books.

- Draw a rectangle for Sally. Write the number 8 in it.
- Draw a same sized rectangle for John, then add another rectangle for 3 more.
- Draw the '}' at the positions shown below.

From the model:

Sally's books: **8**

John's books: 8 + 3 = **11**

Total = 8 + 11

= **19**

A book costs $12. A toy car is $7 cheaper than the book. How much money do I need to buy the book and toy car?

Answer: $17

This question has a few steps. It is advisable to write statements to keep track of our working. We don't need to write the $ sign in our working.

Book: **12**

Toy Car: 12 - 7 = **5**

Altogether: 12 + 5 = **17**

(Both)

The numbers in this question are too big for us to draw pictures so we use tally marks instead.

- Draw 12 marks for the book.
- Draw 7 fewer marks for the toy car.
- Now count all the marks.

- Draw a rectangle for the book. Cut the rectangle into 2 parts.
- Write the number 7 in the second part. Write the number 12 above the rectangle.
- Draw another rectangle for the toy car. The size of this rectangle must be the same size as the first part of the book.

From the model, we can see that:

Book: **12**

Toy car: 12 - 7 = **5**

Total = 12 + 5

= **17**

Micky is 4 years younger than Tom. Their ages combined is 18. How old is Micky?

Answer: 7

First we draw models. Since Micky is 4 years younger than Tom, the difference in their ages is 4.

Now we list the combinations of pairs of numbers that total 18. (We don't have to make a complete list.)

- 8 + 10
- 9 + 9
- 10 + 8
- 11 + 7
- 12 + 6

Now we find the difference between the numbers listed. The pair we want must have a difference of 4.

Difference

- 8 + 10 10 - 8 = 2
- 9 + 9 9 - 9 = 0
- 10 + 8 10 - 8 = 2
- 11 + 7 11 - 7 = 4 .... Eureka!!
- 12 + 6

Since Micky is younger, his age is the smaller number, which is 7.

Sam bought some fruits. There are 5 more apples than oranges. There 7 fewer pears than apples. If there are 6 pears, how many fruits did Sam buy altogether?

Answer: 27

This question is complicated so we have to solve it a small part at a time. We start with the number we know, which is the number of pears.

Pears: **6**

Apples: Since there are fewer pears than apples, the number of apples must be bigger than the number of pears.

6 + 7 = **13**

Oranges: Since there are more apples than oranges, the number of oranges must be smaller than the number of apples.

13 - 5 = **8**

Altogether: 6 + 13 + 8 = **27**

- Start by drawing 6 marks for the pears.
- There are fewer pears than apples, so draw 7 more marks for the apples when compared to the pears.
- There are more apples than oranges, so draw 5 fewer marks for the oranges than for the apples.

Now do the working:

Pears: **6**

Apples: 6 + 7 = **13**

Oranges: 13 - 5 = **8**

Total: 6 + 13 + 8 = **27**

- Draw the pears.
- Draw the apples. Break it into 3 parts as shown. One part to compare with the pears and one part to compare with the oranges.
- Draw the oranges.

Do the working:

Pears: **6**

Apples: 6 + 7 = **13**

Oranges: 13 - 5 = **8**

Total: 6 + 13 + 8 = **27**

Please let us know if you have any questions or comments on these explanantions.