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Earning, spending, saving

Ratio, rates and money · level 2, lesson 6 of 6

A question to start

Noor wants a pair of roller skates that cost 30 dollars. She gets 5 dollars a week for helping at home. How many weeks until she can buy the skates?

Now a second question. On Saturday Noor looks in her wallet and finds only 6 dollars. She is sure she had more. Where did the money go?

The first question is about saving. The second is about keeping track. Grown-ups do both all their lives, and many find it hard. In this lesson you will learn a simple tool, the money diary, that answers both questions, and you will see why steady saving always gets you there.

The idea

Three things money can do

  • Earning is getting money: an allowance, a gift, money for doing a job like raking leaves.
  • Spending is giving money away to buy something.
  • Saving is keeping money for later.

Some families also talk about sharing: giving some money to help others, like a food bank or a friend in need. A popular idea is to keep three jars: one to spend, one to save and one to share. Each time you earn money, you split it between the jars.

The money diary

A money diary is a list of every time money comes in or goes out. Each line has the day, what happened, the money in, the money out, and how much you have after it.

Here is Noor's diary for one week. She starts the week with 4 dollars.

Day What happened Money in Money out Money I have
Sunday start of the week 4 dollars
Monday allowance 5 dollars 9 dollars
Tuesday snack after school 2 dollars 7 dollars
Thursday helped wash the car 3 dollars 10 dollars
Saturday comic book 4 dollars 6 dollars

Now we can answer the second question. Noor had 10 dollars on Thursday. Then she bought a comic book for 4 dollars. 10 take away 4 is 6. The money went on the comic! Without the diary she would just feel that money "disappears".

Why the diary always works

Every line follows one simple rule:

  • Money in: what you have goes up by that much.
  • Money out: what you have goes down by that much.

Money never appears or vanishes by magic. Every change has a line in the diary. So if you start right and write every line, the last number must be right.

You can also check the whole week at once. Noor earned 5 and 3, which make 8 dollars in. She spent 2 and 4, which make 6 dollars out. She started with 4. Then 4 and 8 make 12, and 12 take away 6 is 6. That matches the last line of the diary. Two ways, one answer: the diary is right.

Saving toward a goal

A savings goal is an amount you want to reach, for something you want to buy. Noor's goal is 30 dollars for the skates.

If she saves all 5 dollars every week, her savings grow like this:

51015 202530 week 1week 2week 3 week 4week 5week 6 goal: 30 dollars

Each week is one step up, and every step is the same height: 5 dollars. After 6 steps she reaches the goal line. So Noor needs 6 weeks.

Why the steps are equal

Noor saves the same amount every week: 5 dollars for every week. That is a "for every" rule, just like 2 lemons for every 5 cups of water in Ratio tables. You can even write it as a ratio table:

Weeks Dollars saved
1 5
2 10
3 15
6 30

The 6-weeks row is double the 3-weeks row: twice as many weeks, twice as much money.

Three ways to reach a goal sooner

Look at the staircase. There are only three ways to reach the goal line sooner.

  1. Start higher. If Noor already has some money saved, her staircase starts partway up.
  2. Take bigger steps. Save more each week, by earning more or spending less.
  3. Pick a lower goal. A cheaper thing, or a used one.

Every money plan in the world, even a grown-up's plan to buy a house, uses these same three ideas.

Worked examples

Example 1. How many weeks? Noor wants the 30-dollar skates and saves 5 dollars a week. She is starting with 0.

  1. Count by fives, one jump per week: 5, 10, 15, 20, 25, 30.
  2. That is 6 jumps. 6 weeks.

Example 2. Starting higher. What if Noor already has 10 dollars saved?

  1. Start the count at 10, then add 5 each week: 15 (week 1), 20 (week 2), 25 (week 3), 30 (week 4).
  2. 4 weeks. The 10 dollars she already had are worth 2 weeks of saving, because 10 is 2 groups of 5.

Example 3. Earning and spending. Sam earns 8 dollars a week and spends 3 dollars of it on treats. He saves the rest for a 30-dollar game. How many weeks?

  1. Each week he saves what is left: 8 take away 3 is 5 dollars a week.
  2. Count by fives to 30: 5, 10, 15, 20, 25, 30. 6 weeks.
  3. If Sam spent nothing on treats, he would save 8 a week: 8, 16, 24, 32. 4 weeks, with 2 dollars over. The treats cost him 2 extra weeks of waiting.

Example 4. Finding a missing number. Ella's diary for one day is smudged. She started with 12 dollars, spent something on a gift, and has 7 dollars left. How much was the gift?

  1. The money went down from 12 to 7.
  2. Count up from 7 to 12: 8, 9, 10, 11, 12. That is 5.
  3. The gift cost 5 dollars.
  4. Check: 12 take away 5 is 7. Yes.

Try it

  1. You start with 2 dollars. You earn 5 dollars, then spend 3 dollars. How much do you have now?
  2. You save 4 dollars a week for a 20-dollar puzzle, starting from 0. How many weeks?
  3. Noor wants the 30-dollar skates. She has 15 dollars already and saves 5 a week. How many weeks?
  4. Ben wants the 30-dollar skates too, but he can only save 3 dollars a week. How many weeks?
  5. Kai earns 7 dollars a week and spends 2. He is saving for a 25-dollar helmet. How many weeks?
  6. A diary says: start 10 dollars, then money in 6 dollars, then money out (smudged), and at the end 12 dollars. How much was the money out?
  7. Plan A: save 5 dollars every week. Plan B: save 2 dollars in week 1, 4 in week 2, 6 in week 3, and 2 more each week after that. Which plan reaches 30 dollars first?
  8. Ava saves 4 dollars a week for the 30-dollar skates. How many weeks? How much will she have left over after buying them?
Answers
  1. 4 dollars. 2 and 5 make 7. 7 take away 3 is 4.
  2. 5 weeks. Count by fours: 4, 8, 12, 16, 20.
  3. 3 weeks. Start at 15: 20, 25, 30.
  4. 10 weeks. Count by threes: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. Ten jumps.
  5. 5 weeks. He saves 7 take away 2, which is 5 dollars a week. Count by fives: 5, 10, 15, 20, 25.
  6. 4 dollars. 10 and 6 make 16. Then the money went down from 16 to 12. Count up from 12 to 16: 4. Check: 16 take away 4 is 12.
  7. Plan B, by one week. Plan A: 5, 10, 15, 20, 25, 30, so 6 weeks. Plan B: the total after each week is 2, then 2 and 4 make 6, then 6 and 6 make 12, then 12 and 8 make 20, then 20 and 10 make 30. So 5 weeks. Plan B starts slowly but its steps keep getting bigger.
  8. 8 weeks, with 2 dollars left over. Count by fours: 4, 8, 12, 16, 20, 24, 28. After 7 weeks she has 28, which is 2 short. After 8 weeks she has 32. 32 take away 30 leaves 2.

Common mistake

Forgetting small spending. A snack here, a sticker there: small amounts are easy to forget, and they are exactly why money seems to "disappear". Write down every time money comes in or goes out, even 1 dollar.

Counting earning as saving. If you earn 8 dollars and spend 3, you did not save 8. You saved only what is left, 5. Use the saved amount, not the earned amount, to count the weeks to your goal.

Where it leads