Adding and Subtracting Fractions
- Investigate strategies to solve problems involving addition and subtraction of fractions with the same modelling and
- solving addition and subtraction problems involving fractions by using jumps on a number line, or making diagrams of fractions as parts of shapes denominator
- solving addition and subtraction problems involving fractions by using jumps on a number line, or making diagrams of fractions as parts of shapes denominator
Decimals
Focus:
AC: Students order decimals and locate them on number lines.
CM: Recognise that the place value system can be extended beyond hundredths (ACMNA104)
CM: Compare, order and represent decimals (ACMNA105)
AC: Students order decimals and locate them on number lines.
CM: Recognise that the place value system can be extended beyond hundredths (ACMNA104)
CM: Compare, order and represent decimals (ACMNA105)
Counting Decimals:
Focus: students to say the counting sequence when using 0.1, 0.2, up to and over whole numbers (e.g. 3.7, 3.8, 3.9).
Zero
Invite students to decide when zero is and is not said when saying a range of numbers. For example, have students sort a range of numbers—including 103, 9.05, 80, 800, 0.8, 270, 2703, 2.500—according to whether the zero is said or not. Make up a rule to share so it will be easy to decide next time. Ask: If your rule is ‘whenever’ there is a decimal point you say the zero, does it still apply to $1.05?
Car Odometer
Extend the Middle Sample Learning Activity (‘Bicycle Odometer’, page 44) to more places by adding more strips to the odometer with decimals.
Place Invaders
Extend ‘Wipeout’ (see Key Understanding 5, Middle Sample Learning Activities), so that numbers can only be wiped out from the ones place. Discuss with the students how they may need to multiply by 10s (if tenths are present) or 100s (if two decimal places) to remove the decimal first. For example, for the number 256.37, multiply the number by 100 to make 25637 and then subtract 7. Ask: How do you know what to multiply or divide by to get the digit into the ones place? Packs: Ask students to use an extended place-value table that includes decimal places. (See Key Understanding 4.) tens of thousands, thousands, Hundreds, tens, ones, tenths, hundredths,
Measuring Heights:
Focus: Have students work out what is different about the way we say the digits
on either side of the decimal point. For example, ask students to use
tape measures, then record their heights in metres and centimetres
(e.g. 1 m 53 cm) and metres (e.g. 1.53 m). Discuss: What is different
about how we say these numbers? Why doesn’t it make sense to say ‘one point fifty-three’? Plot students’ heights on a graph for a classroom display. Revisit this graph later in the year, so students can gauge how much they have grown and practise saying decimal numbers.
1.67 // 1.67m // 1 meter and 67 cms
What is the difference in these three (3) numbers?
What do these decimals show?
How would you read these tape measures? When would you need to use decimals?
Decimal Fractions
Use decimetre squares of 1 millimetre grid paper as units to show how successive division by 10 relates to the places. Cut the grid paper into ten pieces, take one-tenth and write 0.1; cut that piece into ten pieces and take one-tenth, then write 0.01, and so on. Cut a square into two pieces, keeping to grid lines, and calculate the decimal fraction of each piece. Ask: If you are using a calculator to add the two numbers together, why must the result be 1?
0 or 0.1 or 0.10 or 0.01 or 1?
Task: Compare a decimal in the tenths and the hundredths using the same digit. e.g. 0.4 VS 0.04
0.8 + 0.2 = ? /// 0.08 + 0.02 = ?
Will this give you the same answer? How do you know?
Will this give you the same answer? How do you know?
Counting by Decimals:
Decimal Number Line:
Decimal Number Line : Hang a long piece of string across the classroom. Set up a decimal number line, with a card labelled ‘2’ on the extreme left of the line and a card labelled ‘3’ on the extreme right. Write ‘2.5’ on another card and ask where it should go. When students answer correctly, peg the number card in position on the line. Ask students to write another number to add to the line and to explain why they have placed their card in that position. Later, extend the activity to thousandths and decimals with different numbers of places.