Decimals (ACMNA079) MAG 4.4.5
Draft-This is a work in progress. MAG writing project 2013
Australian Curriculum YR 4
ACMNA079 Recognise that the place value system can be
extended to tenths and hundredths. Make connections
between fractions and decimal notation.
Prerequisite Knowledge● Fractions as part of a whole (whole/part model)
with continuous and discrete models.
● Fractions as an equal share or measure using
discrete models.
● Fractions have equal sized parts.
● The more you share amongst, the smaller the
part and the larger the fraction name.
● Link to known number patterns e.g. half of a half
is a quarter, a third of a third is a ninth.
[Continuous units - e.g. area of paddocks, pieces of cake,
lengths of ribbon and a can of soft drink. Discrete units e.g. separate articles; sets of people, pebbles, chips]
Key Ideas● Extend the place value system to tenths and
hundredths (build on existing knowledge of the
number system).
● Decimals are fractions that pertain only to the
tenths, hundredths, thousandths etc., all other
fractions need to be converted into these to be
represented as a decimal.
● The patterning of fractions can extend to the
multiplicative relationship when partitioning e.g.
tenth of a tenth is a hundredth, tenth of a
hundredth is a thousandths.
● Linking decimals to measurements for length,
capacity and mass is more difficult as there is not
a direct unit of measurement for the tenths as
there is for the hundredths (e.g. cm) and
thousandths (e.g. mm).
●
●
Cutting, folding and manipulating needs to be done
comprehensively before colouring/shading
representations.
When colouring/shading or using common shapes to
represent decimal fractions, colour in a variety of
different ways including non-standard
representations.
Resources ● FISH problem solving kit
● Number lines
● Blue number line mat
● Paper Plates
Activity Process
1 - counting forwards and backwards from any given
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
Use previously made pizzas from fraction lessons to
review counting patterns with various fractions.
Steps 1 & 2 explain this procedure and may need a
separate lesson to make.
1. On a paper plate, each child draws a pizza and cuts it into
half. Use these to count in halves.
2. Repeat the procedure, cutting pizzas into thirds, quarters,
fifths, sixths, eighths, ninths and tenths. Use these to become
fluent in counting in mixed fractions especially e.g. ⅓, ⅔, 1, 1
⅓, 1 ⅔, 2 etc.
3. Make the link with the learners, that our number system is a
base 10. When we cut one whole into ten pieces we get tenths,
then when we cut the tenths into 10 - hundredths, and cut
these into 10 - thousandths. [Don’t worry about equivalent
fractions such as 5/10 = ½ at this point in time]. Point out the
similarity to tens, hundreds, thousands. What is the difference?
‘ths’ Everything pivots around the 1 (1 whole) - the numbers to
the left of 1 get larger. Where would it make sense to put
numbers that are smaller than one? ‘to the right’ When we do
this, it just looks like we’re making a bigger number - that’s why
they’ve put the decimal point next to the one - everything on
the right hand side of the decimal point means it is smaller than
one.
4. Share representations and investigate if this is consistent.
5. Using the fraction pizzas (10th’s only), show 1/10 and ask
how would we write this as a decimal? Are there any whole
pizzas? No, so we must put the 0 in the ones and put the one in
the tenths place to the right of the decimal point. Continue
putting out the fraction pizza pieces (parts of the whole) and
writing down the corresponding decimal representation,
emphasising the change from the 0 to 1 at one whole pizza etc.
Ones
.
Tenths
0
.
1
1
Activity Process-2
1. Revise the term decimal; (the word decimal means based on
10 from the Latin ‘decima’ a tenth part) discuss how it is similar
to a fraction, that a decimal shows parts of a whole.
2. Write up the current place values students know onto a
display
th
th
whole and 100 are smaller parts than 10 . Why?
6. Continue giving students fractions to shade and record as a
written fraction and as a decimal.
3. The first decimal place is tenths. Write place value onto the
place value chart. Explain that the whole numbers are
separated with a “decimal point” from the decimal values.
Activity 31. Revise the term decimal, fraction, and parts of a whole.
What is the decimal place value we have already looked at?
How do we show it as a fraction, a decimal and say it? Practice
write and saying different tenth fractions.
2. The first decimal place was tenths the next is hundredths.
Add heading to the place value chart.
5. Continue giving students fractions to shade and record as a
written fraction and as a decimal.
6. Students can still find it difficult to differentiate between
th
th
10 and 100 when written as a decimal. Remind learners that
as we move further to the right, every place gets 10 times
smaller (one tenth as big) Provide multiple opportunities for
students to practice identifying, writing and drawing a mixture
of decimals from different place values.
Activity Process 4 - Regrouping Game
1. Give children 5 squares approx 5cm x 5cm, that have been ruled
into 10 columns. Ask them to cut them into strips and place all of the
strips in a collective pile. Make the link that they have cut one whole
(square) into tenths.
4. Provide students with a laminated hundred chart. Ask
students to divide the chart into 10 equal parts and shade in
1/10 on the chart.
3. Provide students with a laminated hundred chart. Advise
students we have divided the whole shape into 100 equal
parts and ask to colour 1/100 on the chart. Discuss the
th
th
difference between 10 and 100 .
2. Using a decimal place value chart, children take it in turns to roll the
dice and collect the relevant number of tenths to place onto their
laminated chart. They record their number on the chart with a
whiteboard marker. The first person to reach 5 whole squares is the
winner.
* When children have 10 tenths, they may swap/trade/regroup it for 1
whole square from an uncut pile.
Q: At any stage of the game ask, “How many do you still need to make
5 whole or the next whole number?”
·
·
·
5. Advise this fraction can also be written as a decimal and will
be recorded as 0.1. Write fraction onto the place value chart.
Ask students –
How many wholes do we have?
How many parts do we have?
How many 10ths do we have?
·
Ensure students understand that decimals are part of a whole.
·
·
4. Advise this fraction can also be written as a decimal and will
be recorded as 0.01.
Write fraction onto the place value chart.
Ask students –
How many wholes do we have?
How many parts do we have?
How many 100ths do we have?
Activity Process 4 - Investigating ½, ⅓, ¼ as a decimal
1. Even though our decimals are tenths and hundredths only,
can we still write a half as a decimal, or a quarter, a third etc.?
Yes - how? Prove it/show it.
2
* Allow children to discuss and investigate either
individually or in groups. If necessary prompt with
question stem such as, “Is there more than one way of
representing the same fraction?” Equivalent fraction.
Extensions and Variations- Digital Learning
Word Wall
Review
decimal point, eighths, equal, equivalent, fifth, flat, four point two,
group, half, halves, hundredths, long, mixed number, none, naught
point five three, other part, out of a (or one) hundred, place value,
quarter, remaining, share, short, sixths, tenths, thirds, thirteen
hundredths, whole, zero point zero seven
L7901 Swamp Survival: hundredths counting
Help the boy cross the dangerous swamp by making a path of
stepping stones. Place the decimals in an ascending order, counting
by either tenths or hundredths to form the path. Compare the
decimal fraction on each stepping stone to the others to see if it is
larger or smaller. Look for a counting pattern. Put the decimals in
order from smallest to largest. Test the sequence by sending the boy
across the swamp.
Activity Process 5 - Comparing Decimals
1. Game - two teams. Each person pulls out two decimal
cards and runs to put them in the correct position either
side of a greater than or less than symbol. The first
person to accurately do this receives a point for their
team.
* Level 1 - tenths; Level 2 - hundredths; Level 3 - mixed
L7903 Swamp Survival: hundredths challenge
Assessment
A number of activities in this MAG are ideal for teacher observation.
While teachers’ typically observe learners at work and interact with
them, it is recommended that teachers in this instance nominate a
particular observation emphasis.
Background
A decimal fraction where the denominator (the bottom number) is a
power of ten (such as 10, 100, 1000, etc.).
You can write decimal fractions with a decimal point (and no
denominator), which make it easier to do calculations like addition
and multiplication.
Help the boy cross the dangerous swamp by making a path of
stepping stones. Place the decimals in an ascending order to form the
path. Compare the decimal fraction on each stepping stone to the
others to see if it is larger or smaller. Look carefully at whole numbers
and the tenths or hundredths. Put the decimals in order from
smallest to largest. Test the sequence by sending the boy across the
swamp.
iPad App - Chicken Coop Fractions Game (FREE)
Links to other MAGs
Year 4 Part Whole 4.4.2
Year 4 Tens & Hundredths 4.4.3
Year 4 Partitioning 4.4.4
The first team to get ten points wins the round
In this educational game you will be shown a fraction and your job is
estimate the decimal equivalent by placing a nest on a number line.
Our hens are mathematical experts and they will fire their eggs
towards the correct answer. If your estimate is good the eggs will be
caught in
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