Make a table strategy

Quick answer

When you have a problem with many possible answers, make a table to help you keep track of everything. You put the possibilities in rows and columns so you can see them clearly and find the right answer.

Learning outcome

By the end of this page, you will be able to use a table to solve a problem by listing all the possible answers in rows and columns.

• You can write down all the options for a problem in a clear way
• You can check your list to make sure you haven’t missed anything
• You can find the answer by looking at your table
• You can use this strategy for problems with many choices

Why this matters

When you have a problem with many choices, like "How many ways can you make 10p using coins?", it can be easy to forget some options or get confused. Making a table helps you keep everything straight. This strategy is used in many real-life situations, like planning a party, deciding what to eat for lunch, or even in games and sports. Learning to make tables helps you think clearly and find the right answer.

How it works

When you make a table to solve a problem:

1. First, you work out what you are trying to find.
2. Then, you think about what things can change or be different.
3. You make a table with rows and columns to show the different combinations.
4. You fill in the table one row at a time, checking each possibility.
5. Finally, you look at your table to find the answer.

Examples you can see

Let’s look at a simple example. Say you want to know how many ways you can make 10p using only 1p and 2p coins.

Now you can see all the ways to make 10p. There are 6 different ways.

Try it as a mini adventure

Adventure: The Cookie Party

You are planning a cookie party for your class. You have 3 types of cookies: chocolate chip, oatmeal, and sugar. You also have 2 types of frosting: vanilla and chocolate. How many different cookie combinations can you make?

Make a table like this:

How many combinations did you find? There are 6 different cookie combinations.

Common mistakes

• Mistake: Forgetting to check all the possibilities.
  Why it happens: It’s easy to get excited and forget to write down every option.
  Fix: Go through your table one row at a time and double-check that you’ve listed everything.
• Mistake: Writing the same combination twice.
  Why it happens: When you are working quickly, you might repeat a row.
  Fix: Read through your table after filling it to make sure you didn’t repeat anything.
• Mistake: Mixing up rows and columns.
  Why it happens: Sometimes it’s hard to keep track of what goes where.
  Fix: Label each row and column clearly so you know what each part of the table shows.

Parent and carer guide

Helping your child use the “make a table” strategy is easy and fun. Here’s how:

• Start simple: Begin with a problem that has only a few choices, like “How many ways can you make 5p using 1p and 2p coins?”
• Use real objects: Let your child use coins or counters to model the problem before making the table.
• Ask questions: Ask your child, “What are the things that can change?” or “Did you check all the ways?”
• Keep it light: Don’t make it feel like a test. Make it more like a game or puzzle.
• Be patient: It might take a few tries to get the hang of making tables, but that’s okay.

Practice questions

1. How many ways can you make 6p using 1p and 2p coins? Show your table.
2. You have 2 types of fruit: apples and bananas. You have 3 types of drink: water, juice, and milk. How many different fruit and drink combinations can you make?
3. How many ways can you make 8p using 1p, 2p, and 5p coins?
4. You have 3 shirts (red, blue, green) and 2 pairs of pants (black, white). How many outfits can you make?
5. How many ways can you make 12p using 1p and 2p coins?

Answers:

1. There are 4 ways. Table: 0 two-p coins, 6 one-p coins; 1 two-p coin, 4 one-p coins; 2 two-p coins, 2 one-p coins; 3 two-p coins, 0 one-p coins.
2. There are 6 combinations. Table: Apple with water, Apple with juice, Apple with milk, Banana with water, Banana with juice, Banana with milk.
3. There are 5 ways. Table: 0 five-p coins, 0 two-p coins, 8 one-p coins; 0 five-p coins, 1 two-p coin, 6 one-p coins; 0 five-p coins, 2 two-p coins, 4 one-p coins; 0 five-p coins, 3 two-p coins, 2 one-p coins; 1 five-p coin, 1 two-p coin, 1 one-p coin.
4. There are 6 outfits. Table: Red shirt with black pants, Red shirt with white pants, Blue shirt with black pants, Blue shirt with white pants, Green shirt with black pants, Green shirt with white pants.
5. There are 7 ways. Table: 0 two-p coins, 12 one-p coins; 1 two-p coin, 10 one-p coins; 2 two-p coins, 8 one-p coins; 3 two-p coins, 6 one-p coins; 4 two-p coins, 4 one-p coins; 5 two-p coins, 2 one-p coins; 6 two-p coins, 0 one-p coins.

FAQ

What is the make a table strategy?

The make a table strategy is a way to solve problems by writing down all the possible answers in rows and columns. This helps you keep track of everything and find the right answer more easily.

When should I use a table to solve a problem?

You should use a table when there are many possible answers or choices, and it’s hard to keep them all straight in your head. It helps especially when you are trying to find all the combinations of two or more things.

Can I use this strategy for anything?

Yes! You can use this strategy for many things, like planning a party, choosing what to eat, planning a game, or even working out how many ways you can arrange your toys.

Is it okay to make mistakes when making a table?

Absolutely! Making mistakes is part of learning. The important thing is to check your table and fix any errors. You can always go back and correct your work.

How can I make my table look nice?

Make sure your rows and columns are clearly labelled. Use a pencil or pen so you can erase and correct if needed. You can even draw little pictures or use stickers to make your table more fun!