Focus of activity: Understanding place value in numbers with 3 decimal places.
Working together: conceptual understanding • Give each child a 1s, 0.1s, 0.01s and 0.001s place value grid (see child instructions). Remind
children that we can write tenths as 0.1s or 1/10s, and hundredths as 0.01s or 1/100s. Explain that we write thousandths as 0.001s or 1/1000s. These are really tiny! There are one thousand thousandths in one whole. There are one thousand grams in a kilogram, so one gram is one thousandth of a kilogram.
• Show children the decimal place value chart (see child instructions). Point out the column ofones, the column of tenths, the column of hundredths and the column of thousandths. Ring onenumber in each column to make a number, e.g. 2.467. Write this number so children can see it.Ask them to write this number in their place value grid. What is the digit 4 worth in this number?And the 6? And the 7?
• Ring a different number in each column and ask children to write the number in their place valuegrids, e.g. 7.341. Ask what each digit is worth. Point out that the decimal point separates thewhole part of the number and the decimal parts.
• Repeat for other numbers with three decimal places (no zeros).• Ring only three numbers to make 0.524. Point out that this time there are no whole parts to the
number so children write 0 before the decimal point to let us know this. This number is less than1.
Up for a challenge? Ring only three numbers to make 8.079. We need to write a 0 in the 0.1s column to show that there are not tenths. Say that we are using zero as a place holder, otherwise the number would look like 8.79 – seven tenths and nine hundredths instead of seven hundredths and nine thousandths. Repeat for 9.001.
Now it’s the children’s turn: • Children play in pairs. One child writes down a number with three decimal places without
showing their partner, and use one coloured pencil to colour in numbers on the place valuechart to make this number. The other child looks at the coloured numbers and writes thecomplete number. The first child reveals the written number. Do their numbers match?Children swap roles and repeat, using a different coloured pencil to colour numbers in theplace value grid. Numbers already coloured in cannot be used.
• Go round the group and observe them as they play the game. You may wish to make notes asa record.
S-t-r-e-t-c-h: If children cope well, ask them to ring numbers in only three or even two columns to make numbers with three decimal places which use 0 as a place holder.
Things to remember Remember that the decimal point separates the whole parts of the number from the decimal parts, the fraction parts of the number. The value of a digit depends on its place in a number. Write 4.444 and ask what each digit represents. Ask a child to read a number from their work. The rest of the group write down the number. Have they written it correctly? You may want to add something that has emerged from the activity. This may refer to misconceptions or mistakes made.
Resources • 1s, 0.1s, 0.01s and 0.001s place value
grids (see child instructions) • 1s, 0.1s, 0.01s and 0.001s place value
chart (see child instructions) • Coloured pencils
Outcomes 1. Children know the value of each digit in numbers
with three decimal places. 2. Children begin to use zero as a place holder in
Things you will need:• Nine different coloured pencils• A place value chart• A pencil
What to do:
• Without showing your partner, write down a number with three decimal places likethis:
Use a coloured pencil to shade numbers on the place value chart which add to makeyour number.
• Show your partner the chart.
• Your partner looks at the shaded numbers and writes the completed number.
• Does what they have written, match your number?
• Swap roles and repeat.Use a different coloured pencil to shade numbers on the place value grid. Numbersalready shaded cannot be re-used.
Deduce the decimal Activity 1
Learning outcomes:• I know the value of each digit in numbers with three decimal places.• I am beginning to use zero as a place holder in numbers with three decimal places.
S-t-r-e-t-c-h:Ring numbers in only three or even two columns to make numbers with three decimal places which use 0 as a place holder.
Focus of activity: Multiplying and dividing by 10, 100 and 1000.
Working together: conceptual understanding • Show children an A3 copy of a 100s, 10s, 1s, 0.1s, 0.01s and 0.001s place value grid (see child
instructions). • Ask a child to place digit cards in the place value grid to show 346. What is 300 divided by 10?
Which way do the digits move? Move all the digit cards one place to the right and ask a child toread the answer. Record 346 ÷ 10 = 34.6.
• We’re going to divide by 10 again! What is 30 divided by 10? Ask a child to move the digits in thecorrect direction and then read the answer. Record 34.6 ÷ 10 = 3.46.
• Say that you will now divide the number by 10 once more. Ask a child to move the digits in thecorrect direction and then read the answer. Point out that we need to put a 0 before the decimalpoint to show that there are no whole parts to the number. Record 3.46 ÷ 10 = 0.346.
• Write the four numbers under one another so that the digits align according to place value:3 4 6 3 4. 6
3.4 6 0.3 4 6
• Look at the pattern and discuss how the digits move one place to the right each time when wedivide by 10.
• Write 346 ÷ 100 and ask a child to place digit cards in the place value grid to show 346 again. Thistime we’re going to divide by 100. What is 300 divided by 100? Say that the digits will still moveto the right, but two places this time. Ask the child to move the digit cards two places to theright. Record 346 ÷ 100 = 3.46.
• Write 346 ÷ 1000. How many places to the right do you think the digits will move this time? Movethe digit cards three places to the right and record 346 ÷ 1000 = 0.346.
• Ask a child to use digit cards to show 0.278 in the place value grid. Say that now we are going tomultiply by 10. Which way will the digits move this time? Move the digit cards one place to theleft, and point out that we no longer need the zero card. Record 0.278 x 10 = 2.78.
• Repeat multiplying by 10 to give 27.8 and then by 10 again to give 278.• Write the four numbers under one another, aligning the digits as before and discuss the pattern.• Use the cards to multiply 0.278 by 100 and 1000 recording the multiplications each time.
Up for a challenge? Write 825 ÷ □ = 8.25. Has 825 been divided by 10, 100 or 1000? How do you know? Write 5.37 x □ = 53.7. Has 5.37 been multiplied by 10, 100 or 1000? How do you know?
Now it’s the children’s turn: • Children work in pairs to make a 3-digit whole number in the place value grid, then divide it
by 10, 100 and 1000. Repeat with two new 3-digit numbers. They then make a number lessthan 1 with three decimal places, i.e. of the form 0.□□□, and multiply it by 10, 100 and 1000.They record the divisions and multiplications each time.
• Go round the group and mark their divisions and multiplications as they do them, e.g. initiallyafter one group of each. Watch out for children who think that to multiply by 10 we add azero, and so write 0.673 x 10 = 0.6730 for example.
S-t-r-e-t-c-h: If children cope well, ask them to work out whether numbers have been multiplied/divided by 10, 100 or 1000:
0.378 x □ = 37.8 935 ÷ □ = 0.935
Things to remember As a group to write rules for multiplying by 10, 100 and 1000, and for dividing by 10, 100 and 1000, clarifying which way digits move and by how many places. If you can’t remember which way digits move, test out your thinking with easy numbers, e.g. 3 x 100 or 300 ÷ 100. You may want to add something that has emerged from the activity. This may refer to misconceptions or mistakes made.
Resources • 100s, 10s, 1s, 0.1s, 0.01s and
0.001s place value grid (see child instructions)
• 0 to 9 digit cards
Outcomes 1. Children can multiply and divide by 10, 100 and 1000 to
give whole numbers or numbers with up to 3 decimal places.
2. Children begin to solve problems involvingmultiplying/dividing by 10, 100 and 1000.
Things you will need:• A place value grid• 0 to 9 digit cards• A pencil
What to do:
• Use digit cards to make a whole three-digitnumber in your place value grid. This is yourstarting number.
• Move the digit cards to divide yourstarting number by 10. Write the division.
• Move the digit cards to divide your startingnumber by 100. Write the division.
• Move the digit cards to divide your startingnumber by 1000. Write the division.
• Repeat with two new starting numbers.
• Use digit cards to make a number less than1 with three decimal places like this:0. This is your starting number.
• Move the digit cards to multiply your startingnumber by 10. Write the multiplication.
• Move the digit cards to multiply your startingnumber by 100. Write the multiplication.
• Move the digit cards to multiply your startingnumber by 1000. Write the multiplication.
645 ÷ 10 = 64.5
645 ÷ 100 = 6.45
645 ÷ 1000 = 0.645
0.723 x 10 = 7.23
0.723 x 100 = 72.3
0.723 x 1000 = 723
Learning outcomes:• I can multiply and divide by 10, 100 and 1000 to give whole numbers or numbers with up to 3 decimal places. • I am beginning to solve problems involving multiplying/dividing by 10, 100 and 1000.
S-t-r-e-t-c-h:Work out whether these numbers have been multiplied or divided by 10, 100 or 1000: 0.378 x = 37.8 935 ÷ = 0.935
