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Battleship Numberline - GameUp - BrainPOP.

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Battleship Numberline - GameUp - BrainPOP.

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Battleship Numberline - GameUp - BrainPOP.

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In this free online math game, students explore fractions, decimals, and other number concepts by estimating their place on a number line.

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Battleship Numberline - GameUp - BrainPOP.

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Battleship Numberline - GameUp - BrainPOP.

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Battleship Numberline - GameUp - BrainPOP.

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In this free online math game, students explore fractions, decimals, and other number concepts by estimating their place on a number line.

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Drag the decimals in the right order. There are different levels of difficulty.

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Scale matters: range of numbers - (TLF L1997 v6.0.0)

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Scale matters: range of numbers - (TLF L1997 v6.0.0)

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Scale matters: range of numbers - (TLF L1997 v6.0.0)

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KS2 Maths activities, games, tests and notes on numbers including addition, subtraction, multiplication, division fractions and decimals

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Counting on - fractions, Mathematics skills online, interactive activity lessons

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Counting on - fractions, Mathematics skills online, interactive activity lessons

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Counting on - fractions, Mathematics skills online, interactive activity lessons

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Free access to help you learn Mathematics skills online using over 1000 interactive activity lessons, games, worksheets and videos

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Learn about fractions with fraction bars at MathPlayground.com!

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ABCya! | Play math games, reading games and more!

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ABCya! | Play math games, reading games and more!

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Can't see the game? Try turning off adblocker.

Equivalent Fractions BINGO is a fun educational game for children to practice equivalent fractions. The game has two modes: Easy & Challenge. Easy mode of play displays a pie graphic to represent the fraction. The denominator is represented by the total number of slices and the numerator is represented by the colored slices. Challenge mode displays only the numerical fraction at first. If the student needs help it will introduce a pie graphic representing only the denominator. If they need further help it will display the shaded slices representing the numerator. Challenge points are awarded based on how much help the student needed to correctly answer the question. Less help = more points!

Trouble Playing This Game?

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Can't see the game? Try turning off adblocker. Equivalent Fractions BINGO is a fun educational game for children to practice equivalent fractions. The game has two modes: Easy & Challenge. Easy mode of play displays a pie graphic to represent the fraction.

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Adding Fractions with Like Denominators | ABCya!

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Adding Fractions with Like Denominators | ABCya!

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ABCya! * Adding Fractions with Like Denominators

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Adding fractions is a fun game for kids to practice adding fractions with like denominators.

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1/32 Fraction | Thirty Second Fraction | DK Find Out

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1/32 Fraction | Thirty Second Fraction | DK Find Out

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DK Find Out! | Fun Facts for Kids on Animals, Earth, History and more!

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Visit DK Find Out! to learn about dinosaurs, space, animals, nature & more. Fun learning activities for kids with videos, quizzes & galleries at DKFindOut.com

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Drawing an analogue clock face / Number lines / Misunderstandings / Patterns / Topdrawer / Home - Topdrawer

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Drawing an analogue clock face / Number lines / Misunderstandings / Patterns / Topdrawer / Home - Topdrawer

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Drawing an analogue clock face / Number lines / Misunderstandings / Patterns / Topdrawer / Home - Topdrawer

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Find Math games to practice every skill.

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Learn math the fun way with our free educational games! With animation, music, and lots of fun- kids can enjoy practicing math and increase their math skills and math memory.

Topics include: addition, subtraction, multiplication, division, fractions, decimals, numbers, geometry, shapes, early math, integers, time, measurement and much more!

Game types involve puzzles, action games, arcade style, driving games, swimming, matching, memory and many more varieties for all kinds of learners and abilities.

You can also find math videos and math game demonstrations at our math channel on youtube:

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Fraction and Decimal Games | MathPlayground.com

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Fraction and Decimal Games | MathPlayground.com

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Practice fractions with our popular math games. Learn about equivalent fractions, adding and subtracting fractions, multiplying fractions and more.

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Fraction, Decimal & Percent Tiles | ABCya!

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Fraction, Decimal & Percent Tiles | ABCya!

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ABCya! * Virtual Manipulatives - Fraction, Percent & Decimal Tiles

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Virtual Manipulatives: Fraction, Decimal & Percent Tiles is a fun way for students to explore and understand how parts make up a whole. Let Dottie the Worm help kids better comprehend various math concepts while working with colorful blocks and tiles!

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Interactive Fraction Wall explore Fractions Percentages and Decimals

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Interactive Fraction Wall explore Fractions Percentages and Decimals

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Fraction walls are a great way to teach about fractions and in particular equivalent fractions. In a fraction wall each row or layer of the wall represents one whole number. The layers are divided into a number of bricks and hence each brick represents a fraction whose denominator is equal to the number of bricks in that layer. Each brick can be turned on or off by clicking it. This wall also allows the display of decimal and percentage values. To the right of the wall are boxes which can be hidden, the value of each box is fraction of the wall that has been turned on.

Selecting different walls

When you launch this interactive teaching program the initial wall is a mixed one showing 3 distinct fraction families. Change the wall by using the mode control. 'Large' displays a wall in which the layers are split 1,2,3 up to 12. The others split the wall along 2s, 3s or 5s. The 5s also includes a lower wall of 100 bricks, this naturally works quite well in explaining percentages since each brick represent ¹⁄ ₁₀₀ or 1%.

Fractions, decimals or percentages

Use the display type control to display decimals (rounded to 2dp), percentages (rounded to 1dp), fractions or none.

The equivalent fraction control

Normally when you click a brick to turn it on or off, only that brick is affected. However if you turn on the equivalent fraction function by clicking the 'Eq' toggle button. Now when a brick is clicked the other layers will turn on bricks if they can match an equivalent fraction. Note, this is not always possible, in fact if you select the primes wall it is never possible to show an equivalent fraction. In this case all the other layers have bricks turned off.

Least Common Multiple

Also known as 'the lowest common multiple' or 'smallest common multiple' is crucial when adding, subtracting or comparing fractions. This button will calculate the LCM based on the rows that have active bricks. Pressing the LCM button will create a new wall that contains the originally selected fraction but also a new layer with the number of divisions equalling the least common multiple of the denominators of the other rows. Sounds complicated, but it really just means that it is always possible to create an equivalent fraction in the LCM row from the other rows.

Other controls

The other controls are

'On' button when clicked will turn on all the bricks

'Off' button when clicked will turn off all the bricks

'Random' button creates a randomized wall in which roughly half the bricks are on. Usually you would hide the totals before pressing this and then the class can work out each fraction in the random wall.

' < ' button will align all the bricks to the left hand side of the wall. This is often pressed after using the randomize function. Fractions can then be compared by considering the length of each row of on bricks.

hide totals click to hide all the totals. The individuals total can then be clicked to show the value.

show totals reveal all the totals.

Advanced Section

To show or hide the advanced section click the advanced toggle button

When the advance controls are on, each layer of the wall has a dedicated slider, move this to change the number the number of bricks in that layer.

Automatic 1 button when clicked create a new wall by dividing the top layer by all its ascending prime factors. So for example if you move the top slider so the top layer has 42 bricks and then click the button. The primefactors of 42 are 2,3 and 7. So the second layer will have 42÷2=21 bricks, the third layer will have 21÷3=7 bricks and the final layer will have 7÷7= 1 brick.

Automatic 2 is similar but creates a layer for every factor of the top layer value.

Add Layer adds a new layer to the bottom of the wall.

total type select control will change the type of total to display. The default is to match what the wall shows, so in this case if the wall is showing fraction the total will be a fraction. But using this control it is now possible for fractions to be shown in the wall but the total to be given as a percentage.

Further fractions

Closely related to this activity is the percentage fraction and decimals grid, which can be used to display a square or circle fraction representation.

Other activities that can be used to teach fractions are the clock activity which uses the clock face to show the fraction of minutes passed in an hour. Launch the activity and select the fractions mode, this mode also show equivalent fractions for example ³⁰⁄ ₆₀ = ¹⁄ ₂. The number explorer activity can show the fraction resulting from division of a number.

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Interactive Fraction Wall | online fraction | percentage | decimal | visnos

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Fraction walls are a great way to teach about fractions and in particular equivalent fractions. In a fraction wall each row or layer of the wall represents one whole number. The layers are divided into a number of bricks and hence each brick represents a fraction whose denominator is equal to the number of bricks in that layer.

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Summary of key words used to describe fractions and working with fractions.

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To develop explanation and justification solution strategies for problems involvingmultiplication, division and proportion. 

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To develop explanation and justification solution strategies for problems involvingmultiplication, division and proportion. 

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Specific Teaching Focus:To introduce place-value ideas and strategies for tenths and hundredths; make, name,record. 

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Specific Teaching Focus:To introduce place-value ideas and strategies for tenths and hundredths; make, name,record. 

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developing the halving, thirding,
fifthing strategies, and establishing how to use this knowledge to construct fraction
diagrams and representations for common fractions and decimals.

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Description of LAB

Linear Arithmetic Blocks - our concrete model of choice for teaching decimals!

Numbers are represented by length of pieces of plastic pipe. The longest piece, representing "one" is just over a metre long. Thispieceisshowntothestudents first. Discuss cutting into 10 equal pieces. Ask students to use their hands to indicate how long the new piece will be, and what name it should have (a tenth).

Now show the students a tenth piece and discuss cutting it into 10 equal pieces. Again, ask students to predict the length of the new piece and a name (a hundredth).

Now show the students the hundredth piece and discuss cutting it into 10 equal pieces. Again, ask students to predict the length of the new piece and a name (a thousandth).

Now show the students the thousandth piece. Use washers for thousandths because it is too hard to cut such thin pieces of plastic pipe. Then discuss cutting the washer into 10 equal pieces, to make ten-thousandths and beyond to smaller and smaller pieces so that students understand the process that creates the endless base ten chain. In practice, we make nothing smaller than thousandths.

LAB pieces can be arranged randomly in piles or in a long line. In the photos below, the pieces are laid end to end to confirm that:

10 tenths have the same length as the one piece

10 hundredths have the same length as the tenth piece

10 thousandths have the same length as the hundredth piece

Features of LAB as a model

LAB represents numbers by the quantity of length, not by units of length such as millimetres. This is an important distinction because using units of length may perpetuate misconceptions that the decimal point simply separates one whole-number quantity (the number of metres) from another (the number of millimetres). It happens that the unit piece is approximately one metre long, but this is only a consequence of the size of suitable materials.

How to make LAB

Linear Arithmetic Blocks (LAB) can be made at home or at school from ordinary washers and PVC pipe of a similar diameter. To make LAB, first purchase the washers (thousandths). The next pieces (hundredths) are then made by cutting small lengths of plastic tubing to exactly to the length of 10 washers. Then make tenths (medium size lengths of tubing ) cut to match 10 hundredths. Lastly, the one (whole) is cut to match 10 tenths and is a rather long piece of tube, probably over a metre long (as the washer may well be more than 1 mm thick). Note that it is very important that you do not introduce the materials to the students in this order, as they will automatically assign the value of 1 to the washer and 1000 to the longest piece. Also note that you should not mark any of the pieces, (for example mark the one with lines to show it is the same as 10 tenths) as then the one rod will stop looking like a 1, and look like a 10.

A good set for classroom demonstration requires about 7m of 25 mm diameter plastic pipe and contains

about 40 thousandths

about 30 tenths and hundredths

at least two ones.

Using LAB as a model of the number line

In the pictures below, the LAB pieces representing the decimals have been laid linearly instead of in a random pile. This allows us to compare the total length of the pieces and hence the size of the decimals they represent.

LAB clearly shows that 0.2 is larger than 0.13 and not the other way around! Many children think that 0.13 is larger than 0.2 (as 13 is larger than 2).

It also shows other properties clearly including:

equivalence of 0.2 and 0.20 (2 tenths and 20 hundredths)

equivalence of 0.13 (13 hundredths) with 0.1 + 0.03 (one tenth and 3 hundredths)

density of decimal numbers (that there are other decimals between 0.24 and 0.25 or between 0.247 and 0.248 etc)

LAB can be used to round decimal numbers. For example, to round 0.27 to the nearest tenth, make several numbers using only the tenths pieces (1 tenth, 2 tenths, 3 tenths, 4 tenths) and compare. Children can see that the number 0.27 is between 2 tenths and 3 tenths and closer to 0.3.

Many children and even some adults are confused by number lines. Building a number line is the ideal way to help students understand the important ideas involved.

Why we prefer LAB to MAB

Research conducted at the University of Melbourne ( Stacey et al , 2001) has demonstrated that LAB has a number of advantages over MAB. Two teaching experiments involving 30 matched students indicated that LAB is considerably more "accessible" for students. There are three reasons for this:

students get confused with MAB simply because it has been used before with the "mini" representing one;

LAB models number with length whereas MAB models number with volume and many students in upper primary do not yet have a strong grasp of volume;

the various pieces of MAB seem to be of different dimensions (1-D, 2-D, 3-D ) and this makes generalising to more place value columns difficult.

Use of LAB was associated with more activeengagement by students and deeperdiscussion. Both models show how the size of numbers depends on the digits and the place value columns and they both can be used to demonstrate various operations with decimals. However, a significant difference between the two models is that LAB, with pieces laid end to end, has structural similarity to the number line so is better able than MAB to model number density (the property that between any two decimals, a third decimal can always be inserted). LAB is therefore better able to demonstrate the principles of rounding.

References

This page is published with permission from Steinle, V., Stacey, K. & Chambers, D. (2006) Teaching and Learning about Decimals. ( Version 3.1 ) Faculty of Education, University of Melbourne . (CD-ROM). See also http://extranet.edfac.unimelb.edu.au/DSME/decimals

Stacey, K., Helme, S., Archer, S., & Condon, C. (2001). The effect of epistemic fidelity and accessibility on teaching with physical materials: A comparison of two models for teaching decimal numeration. Educational Studies in Mathematics, 47, 199-221.

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Linear Arithmetic Blocks - our concrete model of choice for teaching decimals! Numbers are represented by length of pieces of plastic pipe. The longest piece, representing "one" is just over a metre long. Thispieceisshowntothestudents first. Discuss cutting into 10 equal pieces.

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Scaffolding Numeracy in the Middle Years: Learning Plans

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From Term 1 2017, Victorian government and Catholic schools will use the new Victorian Curriculum F-10. Curriculum related information is currently being reviewed and may be subject to change.

For more information on the curriculum, see:
The Victorian Curriculum F-10 - VCAA

Indicator of progress

Success depends on students realising that it is the digits with the highest place value that contribute the most to the size of a number. This is especially difficult for decimal numbers.

Young students often think that the size of a decimal number is related to the length of the decimal, because they draw false analogies with whole numbers. For example, they might think that "1576 is larger than 742 as it is contains more digits" and so conclude that "8.1576 is bigger than 8.742 as it is longer". Understanding decimal numbers requires a deeper understanding of place value.

Illustration 1: Why comparison is a revealing task

The activities below use the task of comparing decimal numbers of different length to reveal students' misconceptions about place value. Whilst the ability to compare numbers is of importance in itself and is closely connected to number sense, the comparing tasks used here are a way to highlight fundamental aspects of place value and make them an object of class discussion.

The process of comparing decimal numbers is actually exactly the same process for comparing whole numbers, although students might not appreciate this to be the case. Instead of focusing on place value, students might be distracted by the 'length' of the whole numbers, and hence base their perception of the relative size of whole numbers on the relative number of digits involved. For example, they might say that "1576 is larger than 742 as it is contains more digits" or "1576 is bigger than 742 as it is longer". While this strategy will provide correct answers for whole numbers, this lack of focus on place value is likely to lead to similar (but incorrect) strategies for comparing decimal numbers. For example, some students think that long decimals are usually large numbers, and surprisingly, some think that long decimals are usually small numbers.

The fact that these incorrect strategies sometimes result in correct answers leads teachers to over-estimate the student's understanding of the size of decimal numbers. It is important that the teacher provides examples that will reveal a student's incorrect strategy so that this student will appreciate that they do, in fact, have something more to learn.

Illustration 2: Longer-is-larger students

Many students beginning to learn about decimals have longer-is-larger misconceptions.

Students who say that "1576 is larger than 742 as it is contains more digits" or "1576 is bigger than 742 as it is longer" are likely to say that "4.11 is larger than 4.9 as it is longer". While this is incorrect, it is a very understandable belief, as they are treating the digits after the decimal point as a separate number. We often use a point to separate a pair of whole numbers. For example, students might note that an Australian Rules football team with 4 goals and 9 behinds, which then scores another 2 behinds, now has 4 goals and 11 behinds. The difficulty is when this is recorded as a pair of whole numbers separated by a dot: 4.9, 4.10, 4.11, which now look like decimal numbers. This clearly supports the idea that 4.11 is larger than 4.9, and hence supports the incorrect generalisation that 'longer numbers are larger'. Inspect any textbook with numbered sections (or an agenda of a long meeting) and you will find that after section 4.9 (perhaps the 9th section in Chapter 4) comes section 4.10 then 4.11, etc. Students without a good understanding of place value are surprised when the teacher states that 4.11 is smaller than 4.9, or that the result of adding 4.9 and 0.2 is 5.1 (when they are expecting 4.11). Research indicates that the majority of students make this error when first encountering decimal notation; the concern is that some students retain this misconception of decimal numbers for many years.

Note that these students are likely to order these numbers correctly: 0.34, 0.35, 0.36, 0.37, as they have the same number of digits after the decimal points. In order to identify these students, we need to ask them to order numbers involving different numbers of digits after the decimal points (called "ragged decimals") as the correct answer cannot be obtained by a student who is treating the digits after the decimal point as another whole number. For example, if we ask them to order this set of numbers: 0.3, 0.4, 0.38, 0.39, 0.312, they might write 0.3, 0.4, 0.38, 0.39, 0.312 (instead of the correct order: 0.3, 0.312, 0.38, 0.39, 0.4).

Counting sequences - here you can see how a longer-is-larger student would place numbers between 1 and 2.

Illustration 3: Shorter-is-larger students

Another incorrect strategy that students use to order decimal numbers, is to choose the 'shorter' number (i.e. fewer digits) when asked to choose the larger number. The students incorrectly believe, for example, that 0.4 is larger than 0.87. There are various reasons. Some of them confuse decimals with fractions and argue that "if we share the cake among 4 people we get more than if we share it among 87", effectively treating 0.4 as 1/4, and 0.87 as 1/87. Note that it is desirable that students do link fractions and decimal numbers, but this has not been done correctly by these students.

Other students also incorrectly believe that 0.4 is larger than 0.87, but for a different reason. They argue that "tenths are bigger than hundredths, so 0.4 is bigger than 0.87". This incorrect statement is based on a partial truth "one tenth is bigger than one hundredth". Such students are also likely to incorrectly order fractions with different denominators like this: 1/8, 2/8, 3/8, 5/8, 1/4, 2/4, 3/4 (i.e. firstly the eighths, then the fourths).

As above, we can find these students by providing 'ragged decimals' to order. They might write 0.312, 0.38, 0.39, 0.3, 0.4 (or possibly 0.312, 0.39, 0.38, 0.4, 0.3) instead of the correct order (0.3, 0.312, 0.38, 0.39, 0.4).

Shorter-is-larger misconception remain prevalent amongst older students, whereas longer-is-larger misconceptions tend to be dispelled by later experiences.

Counting sequences - here you can see how a shorter-is-larger student would place numbers between 1 and 2.

Teaching strategies

The teaching strategies here are to use a diagnostic test so that instruction can be targetted where it is needed, to use open-ended tasks so that misconceptions can be revealed, discussed and eliminated, and to support instruction on decimals by a concrete model which is easy for students to understand.

Activity 1: Diagnostic test takes students only a few minutes to complete and provides useful information to teachers about likely misconceptions regarding decimal numbers.

Activity 2 and Activity 3 are open-ended tasks that require students to compare decimal numbers with different numbers of digits after the decimal point. They should be encouraged to find more than one solution for each task, because it is in the pattern of solutions that they start to see the importance of place value in determining the size of numbers.

Activity 4: Linear Arithmetic Blocks provides instructions for a simple concrete model. Students need access to a good physical model that will assist them to develop their place value understanding and hence construct meaning for decimal numbers. The model can also be used to explain arithmetic operations on decimals.

Many more activities are available on Teaching and Learning about Decimals

Activity 1: Diagnostic Test

The test will determine which students are longer-is-larger thinkers and which are shorter-is-larger thinkers. Print the Decimal Comparison Test (pdf - 2.8kb) which asks students to choose the larger decimal number from each pair. This test can be completed by students in about 10 minutes. Print the Decimal Classification (pdf - 9.06kb) sheet to see if any of your students match the samples provided.

The test will determine which students are longer-is-larger thinkers and which are shorter-is-larger thinkers. Note that it is the pattern of choices throughout the test (rather than an overall score) that is important for diagnosing students who are using either of the incorrect strategies ( longer-is-larger or shorter-is-larger) mentioned above. In other words, we can detect students who do not understand the place value properties of decimal numbers.

Once misconceptions have been identified, teachers can make sure their instruction and examples address the students' problems. The first important idea to note is that the above incorrect strategies reveal that the students do not understand decimal numeration; they are resorting to these incorrect strategies as they do not have a full place value understanding on which to base their choices. They are unable to say, for example: "0.38 is less than 0.4, as 0.38 is 3 tenths and 8 hundredths which is less than 4 tenths". While, at first, it seems reasonable to quickly 'solve the problem' by providing students with a rule or algorithm to follow (eg 'write zeros at the end and then compare as whole numbers', or 'compare from left-to-right'), it is clear that giving students rules to follow is not a substitute for teaching for understanding. Indeed, while there are likely to be gains in the short-term, in the long-term students tend to forget rules that are not supported by understanding.

NOTE: It is possible for students to choose the correct answers on the test if they correctly use a rule. The activities below are useful to determine which of these students who can correctly compare numbers really have a good understanding of place value.

Activity 2: Decimal numbers between

Open-ended task
Ask students to write down 15 numbers between 3.1 and 3.4
Some students will claim that there are only two numbers 3.2 and 3.3, while others will appreciate that 3.18 is between 3.1 and 3.2. Encourage students to share their answers and to explain why their numbers are between 3.1 and 3.4, using models and diagrams to support their explanation. It is essential that students have a model to refer to which will resolve any disputes. Linear Arithmetic Blocks (LAB) is a model which has proven to be very useful in assisting students to improve their conceptual understanding of decimal notation. (Instructions are provided for making this model from washers and tubing which are inexpensive to buy and available from any hardware store.)

Number Between: Classroom Game and Computer Game

Number Between is a good game and is also available as a computer game for individuals and pairs (see References and Acknowledgements).

The teacher writes a pair of numbers far apart on the board (smallest on the left) and calls on a student to write a number in between the pair.

If a correct answer is given (it does not have to be the midpoint), another student is called on to write a number between the new number and one of the earlier endpoints. A dice could be thrown to decide whether it is to be larger or smaller than the new value, or you could have a simple rule - eg alternate between the larger and smaller sides, always go for the smaller etc.

Continue as the number line is divided into smaller and smaller segments. Stop when interest wains.

Dividing the students into teams, to take turns writing a number and to challenge the correctness of the answers of the other teams, creates a competition if desired.

Activity 3: Less than - more than

Ask students to fill the boxes with some of the digits 0, 1, 2, ...8, 9 to make the following true. The digits do not have to be the same and can be reused.

Task 1

Task 2

These are open-ended tasks with many correct answers. Encourage students to describe the range of answers in general terms. For example, in the first case, if the digit in the ones place (in the number on the left) is 0, 1 or 2, then the digits in the next two places (tenths and hundredths) can be anything (because it is always true that 0.XX < 3.X, and 1.XX < 3.X, and 2.XX < 3.X). However, if the digit in the ones place (in the number on the left) is 3, then the digits in the tenths place need to be considered carefully; the tenths digit on the left needs to be smaller than the tenths digit on the right.

It is important to review the students' answers carefully, as those students using incorrect strategies such as longer-is-larger or shorter-is-larger, need to know that they have something to learn.

Activity 4: Linear Arithmetic Blocks

Linear Arithmetic Blocks are a simple model for decimal numbers, which can be purchased commercially or made from simple materials. The size of a decimal number is modelled by length, which is conceptually simpler than other material such as multi-base arithmetic blocks (MAB) which represent size by volume.

Linear Arithmetic Blocks can be used to compare numbers, as well as to demonstrate arithmetic operations in a similar way to MAB.

References and Acknowledgements

The descriptions of LAB and the diagnostic test are published with permission from Steinle, V., Stacey, K. & Chambers, D. (2006) Teaching and Learning about Decimals. ( Version 3.1 ) Faculty of Education, University of Melbourne . (CD-ROM). This CD contains many lesson ideas for students with identified misconceptions, as well as several interactive computer games for decimals, including Number Between. See Teaching and learning about decimals

Tromp, C. (1999) Number Between: making a game of decimal numbers. Australian Primary Mathematics Classroom, 4(3), 9 - 11. Tromp (1999) describes how he used this game in his classroom.

Further resources

Mathematics related interactive learning objects can be found on the FUSE Teacher Resources page.

To access the interactive learning object below, teachers must login to FUSE and search by Learning Resource ID:

Hopper Challenge: ultimate - Students help a frog to jump along a number line. Students estimate the exact finishing point on a number line, after adding or subtracting multiples of tenths or whole numbers to a starting number. For example, 29.5 + (12 × 0.2) = 31.9.

Learning Resource ID: E4ZXCZ

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From Term 1 2017, Victorian government and Catholic schools will use the new Victorian Curriculum F-10. Curriculum related information is currently being reviewed and may be subject to change. For more information on the curriculum, see: The Victorian Curriculum F-10 - VCAA Success depends on students realising that it is the digits with the highest place value that contribute the most to the size of a number.

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PVC pipe and washers for 1000ths

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Introducing and comparing decimal numbers can sometimes be a confusing concept for students, who still associate visually larger numbers as mathematically larger numbers. Students must be able to understand and work fluently with counting collections to 100 by grouping in tens, and counting the tens, and use place value to partition and regroup those numbers. When beginning their study of place value, students correctly state that 1789 is larger than 892 because it has more digits. However, the same is not true of decimal numbers, where 8.742 is larger than 8.1576.

Consider the following extract taken from the Department of Education and Early Childhood Development:

Success depends on students realising that it is the digits with the highest place value that contribute the most to the size of a number. This is especially difficult for decimal numbers. Young students often think that the size of a decimal number is related to the length of the decimal, because they draw false analogies with whole numbers. For example, they might think that '1576 is larger than 742 as it is contains more digits' and so conclude that '8.1576 is bigger than 8.742 as it is longer'. Understanding decimal numbers requires a deeper understanding of place value.

Linear Arithmetic Blocks (LABs) are thus an excellent tool for teaching young students about the components of decimal numbers. They provide a visual for ones, tenths, hundredths and thousandths. Students can use LABs as a visual to-scale model of decimal place value. The numbers are represented by increasingly smaller lengths of piping, with the largest pipe representing "one," and the smallest representing a "thousandth." Students are shown the largest section of pipe, depicting "one", first. They are then asked to discuss cutting it into ten equal pieces, or "tenths". The "tenth" piece of pipe is then shown to students, and students are asked to discuss cutting it into ten equal pieces. They are asked to predict the size of the subsequent pipe and to give a name for it - "hundredths." This continues until students are left with "thousandths".

The use of LABs is ideal as it uses the physical quantity of length to represent the size of a number. Students are thus able to see that digits with the highest place value contributes the most to the size of a number. For instance, the below visualisation of a LAB depicts the numbers 1.37 and 1.214. It is now clear to students that despite 1.214 having more digits, 1.37 is still the larger number.

Download AMSI's free Place Value presentation for more ideas and information on teaching place value, numeration, decimals and counting.

For additional information on comparing decimal numbers from the Department of Education and Early Childhood Development, The Department also has a post focusing specifically on LAB, which can be found here.

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Comparing Decimal Numbers and the use of LAB [Year 4+]

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Introducing and comparing decimal numbers can sometimes be a confusing concept for students, who still associate visually larger numbers as mathematically larger numbers. Students must be able to understand and work fluently with counting collections to 100 by grouping in tens, and counting the tens, and use place value to partition and regroup those numbers.

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Fractions and Unit Squares - Texas Instruments

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How to Teach Fractions with Pool Noodles! - We Are Teachers

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Pool noodle fractions make math fun! It's a great way to keep your elementary math students' interest afloat.

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Games

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Game