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Share your NRICH activity.

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AC9M1M01

compare directly and indirectly and order objects and events using attributes of length, mass, capacity and duration, communicating reasoning

Sizing them Up | NRICH

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Can you put these shapes in order of size? Start with the smallest.

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Approaching Midnight activity.

AC9M2M04 Year 2 Measurement

recognise and read the time represented on an analog clock to the hour, half-hour and quarter-hour

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This is a game for two players. Can you find out how to be the first to get to 12 o’clock?

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construct a grid coordinate system that uses coordinates to locate positions within a space; use coordinates and directional language to describe position and movement

(AC9M5SP02)

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Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

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Students learn to:

collect, sort and compare data represented by objects and images in response to given investigative questions that relate to familiar situations

(AC9MFST01)

Strategies:

Look for a pattern

Make a table or chart

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

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recognise the relationships between dollars and cents and represent money values in different ways

(AC9M3M06)

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Amy went into her local stationery shop. Her mum had given her £2.50 to spend.

Amy liked the look of some luminous pens, which cost 15p each, and some fancy pencils, which cost 10p each.

She bought four times as many pens as pencils and was given 40p change.

How many of each did she buy?

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Amy’s mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

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In this game students uses addition and subtraction skills, combined with some strategic thinking to calculate amounts up to 20.

Website: https://nrich.maths.org/problems/strike-it-out?tab=teacher

Strategy: Look for a pattern

Students would be encouraged to use part-part-whole knowledge of tens to add and subtract up to 20.

Australian Curriculum: Year 1

AC9M1N04: Add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies.

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Watch the video below which shows two people playing the first few turns of a game.

What do you notice?

What do you want to ask?

Watch the video a second time.

Can you work out how to play the game?

What do you think the rules might be?

How might someone win the game?

If you are unable to view the video, you could click through this powerpoint presentation, which also demonstrates how to play. Alternatively, the rules of the game are hidden below.

The aim of the game:

The player who stops their opponent from being able to go wins the game.

How to play:

The first player chooses two numbers on the line and crosses them out. Then they circle the sum or difference of the two numbers and they write down the calculation.

For example, the first player's turn could look like this:

The second player must start by crossing off the number that Player 1 has just circled. They then choose another number to cross out and then circle a third number which is the sum or difference of the two crossed-off numbers. Player 2 also writes down their calculation.

For example, once the second player has had a turn, the game could look like this:

Play continues in this way with each player starting with the number that has just been circled.

Once a number has been used in a calculation, it cannot be used again.

The game ends when one player cannot make a calculation. The other player is the winner.

It's your turn!

Try playing the game against someone else a few times to get a feel for it.

Do you have any good ways of winning?

Now it's time to work together with a partner, rather than against them.

Try to create a string of calculations that uses as many numbers as possible on the 0-20 number line.

Is it possible to create a string of number sentences that uses all the numbers on the 0-20 number line? Why or why not? How would you convince a mathematician?

Once you've had a good think about it, you may like to look at this proof that has been scrambled up.

Can you rearrange it into its original order?

If you would prefer to work away from a screen, you could print off, cut up and rearrange the statements. (This sheet includes three copies of each statement.)

What about the 1-20 number line? Is it possible to create a string of number sentences that uses all the numbers on the 1-20 number line? Why or why not? How would you convince a mathematician?

Again, once you have thought about it, you may like to look at this proof that has been scrambled up.

Can you rearrange it into its original order?

If you would prefer to work away from a screen, you could print off, cut up and rearrange the statements. (This sheet includes two copies of each statement.)

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Year 3:

AC9M3P02 -

conduct repeated chance experiments; identify and describe possible outcomes, record the results, recognise and discuss the variation.

Strategy:

Draw / Act it out.

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Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

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Year 6 Measurement - "Through the Window"

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Year 6 Measurement - "Through the Window"

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AC9M6M02

establish the formula for the area of a rectangle and use it to solve practical problems

Elaboration

investigating the connection between the perimeters of different rectangles with the same area and between the areas of rectangles with the same perimeter

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My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

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What is the time?

Ordering different times by ordering analogue clock faces.

Strategies that can be used:

draw it out: students draw the hands on the faces of the clocks.

rule: students will follow the rule of telling time by reading the hands different positions to order the clocks.

act it out: students act out something that they would at that time of day (at home or at school)based on what they read on the clock face.

Logical reasoning: based on students preconceived knowledge on reading time to o'clock, quarter past, half past and quarter to, they can then reason what time they think the clocks might display depending where the minute hand is.

Curriculum link:

AC9M3M04

describe the relationship between the hours and minutes on analog and digital clocks, and read the time to the nearest minute

https://v9.australiancurriculum.edu.au/f-10-curriculum/learning-areas/mathematics/foundation-year_year-1_year-2_year-3_year-4_year-5_year-6/content-description?subject-identifier=MATMATY3&content-description-code=AC9M3M04&load-extra-subject=MATMATFY_MATMATY1_MATMATY2_MATMATY3_MATMATY4_MATMATY5_MATMATY6&detailed-content-descriptions=0&hide-ccp=0&hide-gc=0&achievement-standard=b9806917-600f-43ca-b497-58265e4112dc&side-by-side=1&strands-start-index=0&subjects-start-index=MATMATY1%2CMATMATY2%2CMATMATY3&view=quick

https://nrich.maths.org/problems/what-time

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Can you put these times on the clocks in order? You might like to arrange them in a circle.

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Working systematically - Ratio and Proportion

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Working systematically - Ratio and Proportion

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(Suited for ages 7-11)

Students are required to systematically figure out how many mL of cordial from a 750mL bottle is to be distributed between an established number of 15 glasses.

This activity is built upon an authentic scenario (having a drink of cordial) and aligns best with the Year 7 Maths curriculum. (AC9M7N09)

https://nrich.maths.org/problems/orange-drink

If too complex for the students, the foundations of the exercise are found in http://nrich.maths.org/problems/blackcurrantiest, which looks at proportions.

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analyse the effectiveness of different displays or visualisations in illustrating and comparing data distributions, then discuss the shape of distributions and the variation in the data

(AC9M4ST02)

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Looking at the 2012 Olympic Medal table, can you see how the data is organised? Could the results be presented differently to give another nation the top place?

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Students can use strategies such as:

Visual

Act it out

Looking for a pattern

Year 1

recognise, continue and create repeating patterns with numbers, symbols, shapes and objects, identifying the repeating unit

(AC9M1A02)

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Well done to everybody who sent in their solutions to this problem. We received lots of good ideas about the number of different ways of doing this, but most children found it tricky to create a convincing argument for why their ideas would always be true.

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solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies

(AC9M5N05)

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This problem is designed to be done in a group. So, ideally, you need to find three or four other people to work with you.

Firstly, take some time to work on your own to find the answers to these calculations, without writing anything down. (Although it would be good to write down the answer itself so you don't forget it.)

$19 \times 24$

$198 + 997$

Half of $57.6$

$3841 - 665.3$

$5.2 \div 4$

$101 \times 16 \times 4$

Now, join together with the other people in your group and focus on the first question.

Do you all agree on the answer?

Give EVERYONE in the group time to explain how they worked it out.

As a group, decide whose method you think is most efficient and why.

Do the same for each of the six questions: give everyone the chance to explain their own method and then choose the most efficient for that calculation.

For the final bit of the challenge, you will need a set of these cards - one set for the group. Each card has another calculation on it.

As a group, decide on the most efficient method for each of the cards.

What did you decide and why?

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This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.