# Doug's Tablecloth Years 4 - 8

### Preparation

 Ask someone to help you find, measure and cut a piece of thin cloth to 36cm (exactly) x 72cm (approximately). The back of an old shirt would work. You will need a ruler for the activity too. Print this Tablecloth Drawer and cut it to make two copies. You have the second copy in case someone wants to try this puzzle with you. Write the title of this challenge and today's date on a fresh page in your maths journal.

### Getting Started

 Open this Doug's Tablecloth Starter. You can read it on screen or print it. It's okay to work with a partner. Two (2) heads might be better than one (1). The first challenge is to read the first part of the card and try Question 1. Keep trying until you can do it, then draw and write in your journal to explain your success. Instead of writing and drawing you could make a video with your phone to explain to someone else. Remember, it only has to fit exactly into the depth of the draw. When it is inside the drawer, there might be space beside it. Have fun exploring Doug's Tablecloth. Hints If you are only folding in halves all the time, stop. It won't work. You know one measurement of the cloth for certain. You are aiming to fit just one of the measurements of the drawer. Could those measurements give you a hint? Have you tried imagining the cloth already in the drawer and imagining what the last fold could have been that got it in? When you have Question 1 figured out, try the Challenge on the Starter. What you have learnt from Question 1 should help you with this.

You can learn other things from Doug's Tablecloth too.You can keep going now if you want to
or you can put a note in your journal to come back and try these another time.

### Tablecloth Fractions

This problem has been about a whole piece of cloth that is folded into equal parts. Whenever there is a whole thing with equal parts the language of fractions can be used. Fraction language - half, third, quarter, fifth, sixth, seventh and so on - is the language of parts of whole. The language tells you the number of parts.
• Find a whole piece of blank A4 paper.
• Put it in front of you on the table the landscape way.
• Pretend it is Doug's Tablecloth and fold it the way you did to get it into the drawer. Press each fold down hard.
• Sketch the unfolded paper in your journal and dot in the fold marks.

Open up the paper and keep it landscape. Rows of boxes (also called cells) go across your tummy. Rows always go across your tummy.

• Hold your pencil across the top row.
• Slide it down counting the rows as you go ... 1, 2, 3, 4.
• There are four rows.
• The rows divide the whole piece of paper into 4 equal parts.
• In fraction language, the rows divide the whole paper into quarters (or fourths).
• Hold your pencil across the top row again.
• This time slide it down and count by quarters ...
1 quarter
2 quarters (or one ...)
3 quarters
4 quarters (or ... or ...)
Rows go across your tummy. Columns go the other way.
• Hold your pencil up the left column.
• Slide it across counting the columns as you go ... 1, 2, 3, 4, 5, 6.
• There are six columns.
• The columns divide the whole piece of paper into 6 equal parts.
• In fraction language, the columns divide the whole paper into sixths.
• Hold your pencil up the left column again.
• This time slide it across and count by sixths ...
1 sixth
2 sixths (or one ...)
3 sixths (or one ...)
4 sixths (or two ...)
5 sixths
6 sixths (or ...)
You can count the cells across or down. Answer these questions in your journal.
• How many cells are there in the whole piece of paper?
• The cells divide the whole piece of paper into ... equal parts.
• Each cell has the same fraction name. Each is one ... of the whole.
Touch your pencil in the top left cell. Count all the cells by twenty-fourths.

Beside the sketch of your folded paper write all the fraction equations you can find in your diagram.

Different Fractions

• Fold a piece of A4 paper so it shows halves and thirds.
• Sketch it and write all the fraction equations you can find in it.

• Fold a piece of A4 paper so it shows thirds and fourths.
• Sketch it and write all the fraction equations you can find in it.

### Folds & Creases

You will need someone to help you with this activity because you have to close your eyes and imagine while they read out the instructions.
• Print this Investigation Guide.
• Work through the questions. You might discover some patterns. A mathematician is always looking for patterns.
• You can write on the sheet then stick in your journal. Or you can write the answers straight into your journal.

### Just Before You Finish

• Add a speech bubble that tells what you learnt.
• Read your Working Like A Mathematician page again and write two or more sentences explaining how you worked like a mathematician in this activity.