week 4 year 5 and 6 mathematics all packages

| NSW Department of Education - Parents and carers guide

Week 4 - Package 1 - Year 5 and 6 Mathematics - Mystery spinner

Things you need Have these things available so your child can complete this task.

Ideal ● pair of compasses ● card ● toothpick ● blue, yellow and red coloured pencils or textas ● pencil ● scissors ● paper

Back up

● You can draw around the bottom of a glass twice. Once on a piece of paper and once on a piece of card. Cut out both circles. Fold the paper circle into quarters so you can find the centre of the circle. Put the paper circle exactly on top of the card one and use a sharp object such as a needle to poke through the paper circle and mark the centre of the card circle.

● Card from a cereal box or other packaging is fine. ● A matchstick or sturdy twig from the garden will do, but you will need something

sharp to make a hole to put the stick through. ● Other coloured pencils - you will need three and you will need to insert the names of

the new colours correctly into the problem.

education.nsw.gov.au

Before you start This is a reasoning activity and is expected to take some time. Try to encourage your child to solve the problem without stepping in to help too quickly. Depending on how dextrous your child is you may need to help them create the circular spinner from the card, especially if they are using a pair of compasses. If a younger sibling is joining in the activity they will definitely need help with the compasses. See above for an alternative way of drawing a circle and finding the centre. Give your child time to practise spinning the spinner even though there are no coloured sections on it yet and check that the spinner is reasonably well balanced. It may be useful to have a chat about how sections are marked on a spinner. Below is an example. Remember it is not time to colour the spinner yet.

What your child needs to know and do This problem requires some understanding of chance or probability. It will give your child an opportunity to talk about fairness and about fair testing. Your child will need to understand language such as more likely, twice as likely, twice the chance, half the chance, half as likely and least likely. It is worth checking that they know this language before you start. Your child will also need to know about fractions of a whole circle.

Here is the problem they will be trying to solve:

If I spin the Mystery Spinner it is twice as likely to land on a blue section as a yellow section and half as likely to land on a yellow section as a red section.

What could the Mystery Spinner look like? Is there more than one possibility? Can you explain your answer?

© NSW Department of Education 1

What to do next Before your child starts figuring out the problem please check that they have both read and understood it. If reading is an issue for your child please read the problem for them. This is not a reading activity. Once your child has read the problem ask them to tell you the problem in their own words.

Your child may then want to try experimenting by drawing some spinners on paper and colouring in different sections. If they really like to be neat you can find a template here but this is not really necessary.

Once your child has at least one solution to test they can colour their spinner. If they have two solutions they can flip the spinner and colour the other side too.

At this point it is important that your child has an opportunity to test their solution. They should spin their spinner 10 times to see what happens. They could record their solution in a table and count how many times the spinner landed on blue, yellow or red. If your child does not get the desired result, ask them if they think that is because their solution is incorrect or could there be other issues?

Some ideas your child could come up with are:

● The spinner is not well balanced – check. ● A round spinner is hard to read as it may land where two colours meet – find a

way to have a flat edge to each section. Do the flat edges all need to be the same length? Why? How can that be done?

● 10 spins is not a large enough sample to test – keep spinning!

Talk to your child about their solutions. Were there other possibilities? What were they? Why were there more possibilities?

Here are some more questions that will help your child engage deeply with the reasoning:

● What is the least number of sections in total that the spinner could have? ● What fraction of the spinner should be blue? ● What fraction should be yellow? ● What fraction should be red? ● If your spinner had ten equal sections how many tenths would be red? ● If your spinner had 20 equal sections how many twentieths would be red? ● What about the other colours?


https://commons.wikimedia.org/wiki/File:Circle_and_its_center.svg

https://commons.wikimedia.org/wiki/File:Circle_and_its_center.svg

Options for your child

Activity too hard?

Your child could work out the solution using coloured LEGO blocks before embarking on the spinner activity. Start by asking them to show you twice as many green blocks as blue blocks.

Activity too easy?

Ask your child to explain how this activity relates to equivalent fractions. Ask them to draw a table to illustrate their explanation. Ask questions such as ‘What if the Mystery Spinner was 4 times more likely to land on yellow?’

Extension/additional activity To extend the learning your child could make up their own Mystery Spinner for someone else to solve. Play Mystery Spinner here.


http://www.scootle.edu.au/ec/viewing/L2384/index.html#


Week 4 - Package 2 - Year 5 and 6 Mathematics - Inside Seven Squares

Adapted from NRICH maths.


Ideal ● Pencil ● Dotty grid paper (square dots) ● Ruler ● A square or A4 piece of paper

Back up

● Pen or texta ● Grid paper such as that in your child’s mathematics book.

Before you start This is a reasoning activity adapted from nrich.maths and is expected to take some time. Try to encourage your child to solve the problem without stepping in to help at the first hurdle.

Your child will need to be able to draw lines accurately with a ruler using the dotty grid paper or ordinary grid paper as a guide. Drawing lines accurately is an important mathematics skill but is not necessary for the reasoning part of the activity. Your child will also need to know the basic properties of squares and right-angled triangles so you may want to do some research before you get started. In addition, your child will need to understand that area is the amount of space inside the boundary of a two-dimensional shape and can be measured in square units.


https://nrich.maths.org/2132

https://www.printablepaper.net/category/dot

https://nrich.maths.org/2132/note


What your child needs to know and do

The problem

Seven squares are set inside each other. The centre point of each side of the outer square is joined to make a smaller square inside. This is repeated each time a square is drawn until there are 7 squares.

The centre square has an area of 1 square unit.

What is the total area of the four outside right-angled triangles (the ones in red)?


What to do next A useful way to get your child thinking about this problem is to make the beginning of the design by folding a square piece of paper. Using concrete materials is an important mathematical skill at all levels of learning. Remind your child that this is a tool for learning.

An A4 piece of paper can be made to represent a square as follows:

The following folding activity will help your child consider where the problem came from. It is really helpful to ask what they notice at each step of the process.

1. Once you have your square piece of paper fold it along both diagonals to find the centre.


2. Fold each right angle carefully into the centre.

3. Open out and use the folds to draw the next square.

4. Fold in again and then fold the next four right angles into the centre of the new square. At this point the paper is going to start looking like a Chatterbox. Making a Chatterbox would be a lovely fun activity to do after the maths! It is a great way to practise accurate folding.


5. Open out again and draw the next square.

6. Your child can continue this activity until it becomes too hard to fold the paper. I wonder whether 7 times really is the limit for folding a piece of paper? The folds will become less and less accurate as the paper gets thicker. (You might even like to view an old episode of Myth Busters about this!)

Next you will need the dotty paper or squared paper from your child’s maths book, a pencil and ruler.

It would be wonderful if you could do the activity alongside your child or if they could work with a sibling to share ideas. Make sure you give your child a chance to think about and discuss where on the paper they will start, what size square to start with, and whether to start with the largest or the smallest square. There may be a few trial runs.

Once all of the squares have been drawn it is important to remember that the problem asks you to find the combined area of the four outer triangles (the red ones in the diagram). There will be a number of ways to explain this. All strategies are good strategies and it is worth brainstorming as many ways as possible.


       


Activity too hard?

If the drawing activity is too difficult there is still a lot of learning in the folding activity. Ask your child how much bigger the area of the original square is than the square created by the folds. Ask them how they know.

Activity too easy?

Ask your child to determine how many times bigger the area of the outside square than each of the successive squares.

Ask if they can predict the area of the square outside the largest one they have drawn. Can they create a table that shows the areas of each square so they can predict the areas of both smaller and larger squares?

Can they add perimeter to their table or length of each side to discover the relationship between the perimeters of the squares and their areas?

Extension/additional activity

A lovely extension activity that everyone can try also involves manipulating squares. The activity is called Fitted. From NRICH maths.

The problem

Nine squares with side lengths 1,4,7,8,9,10,14,15 and 18 cm can be fitted together with no gaps and no overlaps, to form a rectangle.

What are the dimensions of the rectangle?




Week 4 - Package 3 - Year 5 and 6 Mathematics - Totality


Ideal ● Watch the video from NRICH maths. ● Print out of the game board. ● 1 counter.

Back up

● Follow typed instructions below. ● Draw your own game board. ● 1 coin.

Before you start This is a strategic game of addition. It is played with 2 players. It offers the opportunity to think strategically by considering several moves in advance, and practise working with addition at the same time!

What your child needs to know and do Your child needs to have strategies for solving problems with addition.



https://nrich.maths.org/content/00/01/game1/Totality.pdf

What to do next Play the game!

Students slide the shared counter across several adjacent numbers, adding them up as you go to make a 'running' (or cumulative) total. The goal is to be the first player to make the final slide so that the chosen target is reached exactly. Making the total go above the target loses you the game.

How to play

1. Player 1 chooses a target to reach. This is the total both players try to make. 2. Player 2 places their counter on the game board over one of the numbers and says

that number. 3. Player 1 moves the same counter in any direction along a line segment to a

neighbouring number and announces the total of the two numbers. 4. Player 2 moves the same counter to cover a neighbouring number, adds on that

number, and announces the 'running' total of the three numbers. 5. Players take it in turns to slide the counter to cover a neighbouring number and to

add that number to the 'running' total. 6. Players must move when it is their turn. 7. No 'jumping' is allowed.

Image from NRICH.


https://nrich.maths.org/content/00/01/game1/Totality.pdf


Activity too hard?

Play the game to a small target number. Eg 20.

Activity too easy?

Play the game with a larger target number. Use multiplication and addition to reach a large target number.

Extension/additional activity Play the game using this game board. Add your own numbers.



Week 4 - Package 4 - Year 5 and 6 Mathematics - Sponge art transformations

From Youcubed.


Ideal ● Plain paper ● Kitchen sponge (old or new) ● Paint in different colours ● Containers for the paint ● Plastic gloves and clothes covering (you may get paint on you) ● Plastic table covering ● Scissors

Back up

● Card from old packages or boxes ● Paper or card from old packages or boxes, lids, cut potato stamps. ● Food colouring ● Paper plates ● An old shirt you don’t mind getting paint on ● Cut up plastic bag laid flat on a table ● Paper


https://www.youcubed.org/resources/sponge-art-transformations-k-10-video/

Before you start This task comes from YouCubed at Stanford University. Watch the video.

Cut out the sponge into different shapes like different geometric shapes such as quadrilaterals, triangles, pentagons, and so on.

Set up your equipment.

What your child needs to know and do Students will be exploring ideas around the movement of shapes. We use words like ‘translate’, ‘rotate’ and ‘reflect’ to describe these movements.

Translate is when a shape moves position without turning (sliding). Reflect is when a shape is flipped (flip). Rotate is when a shape is turned, like it has a pin through its centre (turn).

Rotational symmetry is when a shape has a centre point (like a pin through its middle) so that when it is rotated, it moves onto itself perfectly. E.g an equilateral triangle has a rotation of 120 degrees where it turns onto itself.


https://www.youcubed.org/resources/sponge-art-transformations-k-10-video/

What to do next 1. Talk to your child about the different shapes you could make and allow them to

make a range of different shapes. Then, get creating! 2. Try making prints of the shape by ‘translating’ (sliding) a two-dimensional shape.

3. You can also try reflecting (flipping).


   

4. And rotating (turning).

5. Have fun making some art using your maths skills!

You can upload a picture of your painting to Geogebra to explore different transformations!


Activity too hard?

● Draw around a two-dimensional shape and use that to make your stamps. ● Practise tracing shapes by sliding the shape across a blank piece of paper. ● Use a mirror to show the reflection of a two-dimensional shape by holding it up

against the shape on a table.

Activity too easy?

● Using a sponge shape, test whether the shape can be tessellated by stamping the shape several times with one side lining up with the other.

● Does the shape fit perfectly next to each other? ● Can you think of other shapes which can tessellate? ● Can you find things in your house which are tessellations? (bathroom tiles)


https://www.geogebra.org/?lang=en

https://www.geogebra.org/?lang=en

Extension/additional activity

Rotational symmetry

Using a sponge shape, test whether the shape has rotational symmetry by stamping the shape in a clockwise direction without overlapping the paint.

Does the shape complete a full circle (360 degrees) without overlapping?

How can you change the shape of the sponge so it does have rotational symmetry?

Can you find the ‘centre’ of rotation?



Week 4 - Package 5 - Year 5 and 6 Mathematics - All the digits From NRICH maths.


Ideal ● Blank paper for working out

Before you start Write out the equation below using boxes for unknown numbers. This task requires students to think about place value and the way that written strategies for multiplication work. Although the problem can be done by trial and improvement, it is solved more efficiently if worked through systematically. This will take some patience.

What your child needs to know and do This activity requires the ability to use multiplication facts.

What to do next Solve the problem! Here are your clues (and challenges):

● Put the numbers 0 to 9 once only into the squares so that the equation is correct. ● The 4-digit number contains three consecutive numbers, which are not in order. ● The third digit is the sum of two of the consecutive numbers. ● The first, third and fifth figures of the five-digit number are three consecutive

numbers not in order. The second and fourth digits are also consecutive numbers.




Activity too hard?

Use a multiplication grid or calculator to help with calculations.

Activity too easy?

Challenge your child to prove to you that there is only one solution. How many solutions would there be if the clues about consecutive numbers did not hold?

Extension/additional activity Consecutive numbers are numbers which follow one after the other. For example, 6, 7, 8, 9.

● Choose 4 consecutive numbers and write them in a row. ● Add a multiplication or division symbol between the numbers. E.g. 6 x 7 ÷ 8 x 9 =? ● Practise using different sets of consecutive numbers. ● Use a calculator to check your answers.


week 4 year 5 and 6 mathematics all packages

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