Materials ;
 Student “think cards”.

Calculators.

Decimal place value mats.

Number line and decimal tickets.

Blue tack.
Outline:
 Tutors working in pairs / threes discussing “student think” cards.
Groups record ideas and report back to larger group.

Look at the use of manipulatives to reinforce decimal understanding.
-
Modelling decimal place value using ‘place value mats’. i.e. model 1.34
- Place these decimals on the number line below;
0.5, 1.3, 0.2, 2.7, 1.9, 3.08, 1.75, 2.6
0 1 2 3 4
- Practice Your Estimation Skills
•
Estimate the answer to each of these questions. Discuss how you arrived at your estimation.
1.2 + 3.95
4.75 + 2.25
3.4 - 1.97
2.2 x 4
5.3 x 0.5
6 ÷ 1.5
 Share ‘teaching points’ sheet.

Think Cards about decimal misconceptions:
Share out and discuss in small groups. Report back to class.
Bill worked out that:
2.4 x 5.9 = 10.36
Sarah thought;
150 is ten time larger than 15,
* Is the answer reasonable? So 1.50 must be ten times larger than1.5
* Explain Bill’s thinking? What are the misconceptions?
What teaching would you do?
Paul thought;
023 is the same as 23,
Therefore 0.023 must be the same as 0.23.
Mere carried out the following calculation;
3.7
+ 2.8
6.4
11.19
What are the misconceptions? What are the misconceptions?
Sam thought; Jenny thought;
The decimal equivalent to a half is 0.2. Which is bigger; zero point five or zero point
What are the misconceptions? twenty-seven?
“Zero point twenty-seven.”
What are the misconceptions?

Decimal Mats: Introduce the model.
1 whole one-tenth one-hundredth.
Show students the “one whole”, then the “one-tenth”.

How many of these to make one whole? (list answers)

How do we write one tenth – as a fraction and as a decimal. (If students don’t know how to write one-tenth as a decimal, show them).
Pass out a set of equipment to groups of 2 or 3 students.
Set comprises: 4 wholes, 16 tenths.

Could you model me 3-tenths? How would I record this as a decimal?

Model 6-tenths and 8-tenths, recording the fraction and decimal.

How many more tenths do you need to make 1 whole?

Which is the same as a half; 0.2 or 0.5? Have them model 0.2 at one end of the holder and 0.5 at the other end. Becomes very obvious 0.5 equals a half.
Try 0.8 to make sure they don’t think it is ⅛.

Model for me 1.2. Discuss what the 1 and the 2 stand for. (one whole and 2 tenths).
Continue with 1.3, 1.4 etc. Target “NE” thinkers.
This would be a good time to reintroduce the place value chart.
Discuss where the number 7 would go on the chart hundreds tens ones
7
What happens when we move the 7 from the ones place to the tens place?
(Number has got ten times bigger) What happens if we moved it to the hundreds column?
(Number has got ten times bigger)
Reverse the process so the 7 is in the ones column. (Each move to the right the number gets ten times smaller)
What would happen if we divided 7 by 10 again? It becomes 0.7.(students may wish to use a calculator to confirm this). hundreds tens ones
0 tenths
7

Ask students to:
 model 0.12. Initial responses will be to use the 1 whole as a tenth and 2 tenths as the hundreds. (Can’t change the model) Next they will try using 12 tenths. It is important for students to come to the realisation the “2” refers to something ten times smaller that a tenth.

Handout the hundredths and discuss what it is called and why.

Introduce the hundredths column to the place value chart. hundreds tens ones tenths hundredths
0 1 2
 discuss what the different numbers on the chart mean. (0 means no ones, 1 means one tenth, 2 means two hundredths).

Ensure students are reading the decimals correctly – 0.12 is said zero point one two, not zero point 12.

Have students model other decimals; o.43, 0.78, 0.25, 1.82.

Focus on the problem area of 0 as a place holder. Model 0.21, 0.2, 0.20. Which is larger?
The decimal point never moves. It stays in the same place separating the whole number from parts of a whole number.
Have students place the decimals on a number line as shown below.
0 1 2
0.2 0.3 0.35
0.4 0.5 0.67

0.7 0.82 0.9
1.3 1.37 1.4
Handout copies of the worksheet below:
Place these decimals on the number line below;
0.5, 1.3, 0.2, 2.7, 1.9, 3.08, 1.75, 2.6
0 1 2 3 4
Practice Your Estimation Skills
•
Estimate the answer to each of these questions. Discuss how you arrived at your estimation.
1.2 + 3.95
4.75 + 2.25
3.4 - 1.97
2.2 x 4
5.3 x 0.5
6 ÷ 1.5

Some points to think about:

Start with place value – the understanding that a bigger unit can always be broken into ten smaller units of the same size. I.e. 1 whole = ten tenths.
 Understanding that the decimal point indicates where the ‘ones place’ is – to the right of the decimal point.

Zero as a place holder indicating there are no items of that value in the column. Avoid the idea that zero means nothing.

In the decimal system numbers either get ten times bigger or ten times smaller
(including multiples of ten). It is the number or digits that move, rather than the decimal point as many of us were taught.

Emphasis the importance of having the same number of digits after the decimal point when adding and subtracting decimals. Students need to know about putting extra zeros as place-holders where necessary.

Emphasis the idea that when multiplying and dividing decimals works in the opposite way to multiplying and dividing whole numbers. Let students explore this with sequences of division on a calculator.

Focus on the importance of checking the reasonableness of an answer to a calculation by using approximation.

Students should explore equivalences between fractions and decimals, using calculators where necessary. Encourage students to learn by heart some of the common equivalences, such as
½ = 0.5, ¼ = 0.25, ⅓ = 0.333, ⅕ = 0.2, ¾ = 0.75

When exploring (teaching) decimals it is important to use decimal place value mats and number lines.