What’s new in Maths Matters Resources?
LENGTH PHOTOGRAPHS – 14 new resources
We’ve been focussing on our length resources this week. Duffy is drawing 4 sports people (coming soon) and I’ve just uploaded 15 new Length Photographs. Many of these are items you use to measure both informal and formal length. Use them as part of your introductory discussion to a length unit. Many people are unfamiliar with the formal equipment. What can you use this item for? What has it got to do with length? Where do you start and finish your measurement? e.g. this photo shows a Diameter Gauge. Notice the measurments are smaller at the lower pointy end and larger at the wider section. This makes sense when you put this object into the top of an open container, such as a jar. It is one way to measure the inside diameter. Always encourage our students to estimate the diameter first, before they start to measure.
MATHS GRAPHICS – CREATURES – Alpaca and friends
Duffy has been hard at work creating 4 new farm animals for me to use on my new Algebra Animal Antics Level 1 Stage 3 activities. I just flick my fingers and demand a creature, then voila, they suddenly appear ready for all of us to use. He is SOOOO clever! Duffy’s favourite is the alpaca (he knows I love these in real-life too). My favourite is the duck. Which new creature do you like best?
NUMBER & ALGEBRA – Patterns & Algebra – Algebra Animal Antics S3
What a lot of animals. We’ve tried to help your students understand algebra concepts by substituting animals rather than just a geometric symbol to represent numbers in a number sentence.
Algebra Animal Antics STAGE 3 Level 2 is for your medium block students in Stage 3 (Grades 5/6/7). We’re calling these 2 dot or Level 2, for want of a better description. Each set has 4 cards that create the clues for one number puzzle. There are 4 sets like this to enable each group to practise this idea 4 times before they attempt to create some of their own. Once you (or your students) have photocopied each set and cut out the cards, you’re ready to go. Everything is there to help you, including sample solutions for those students who need the scaffold.
Bev is working on similar P&A cards for 1 dot Level 1 (high block students) and 3 dot Level 3 (low block students) right now. They should be ready some time soon.
MATHS GRAPHICS – 2D Shapes – Stars
Stars galore – and on the same night as the Oscars are announced in America!!
Lucy creates all our special technical designs and these stars are no exception. Beautiful bright colours and points from three to ten.
Use them to create patterns, discuss angle size and length measurements. And remember that these can fold to create magical multi-sided 3D pyramids.
MATHS GRAPHICS – SPECIAL OCCASIONS – Birthday Party
A birthday party is a good excuse for a maths discussion and further exploration. How many people do you want to invite? What do you need to say on the party invitation? What time should people arrive? How long will they stay? What do you need to provide for your guests? What is your budget? When do you need to get everything ready? Who will help you? We’ve just uploaded 3 new illustrations for our Birthday Party theme in Special Occasions.
How can your students use these as a stimulus for their mathematical thinking?
NUMBER – Place Value Graphics – Winner
Imagine you won the lottery. What extra good deeds could you do? You can use this latest “Winner” Maths Graphic from Duffy as part of a daily Mental Warm-up, as a focus for counting by 100s or as a stimulus for a lesson about Money.
Did you know that:
- There are over 170 different currencies in the world today.
- More Monopoly money than real money is printed each year in the USA – a Monopoly game has $15140.
- Our word “cent” comes from the Latin word “centum” – a hundred, a hundredth part.
- Cattle were the first form of money and the Latin word “caput” (head of cattle) eventually became our word “capital” in reference to money.
- The word “money” evolved from the old Roman goddess Juno Moneta. Roman coins were made in her temple.
- “Bankrupt” evolved from the medieval Italian “banca rotta” (broken bench). Moneylenders worked at a bench and when they ran out of money the bench was broken.
- “Pygg” was a type of clay in medieval England. It was used to make jars to store money. Today we have “piggy banks”.
- Hungary printed the highest denomination banknote in 1946. It was worth 100 quintillion pengoes. That’s 1 000 000 000 000 000 000 (18 zeroes).
- Obsolete bronze 1 and 2 cent Australian coins were melted down to create the Sydney 2000 Olympics medals.
- Australia was the first country to produce plastic polymer bank botes that are almost impossible to counterfeit.
- Fake $50 Australian notes can be discovered by scratching the clear window with a coin. If the star comes off your $50 banknote is a fake.
I wonder what mathematical discoveries and explorations you and your students will make using this graphic?
NUMBER & ALGEBRA – Patterns & Algebra – Metal Fish Patterns (F/1/2)
Younger students need to experience patterning every week. They need to see the rhythm, the sequencing, the various possibilities. They need to be able to describe a pattern, predict what the next item may be, identify an item that doesn’t belong in a pattern. They can explore patterns in buildings looking at window repetitions, brickwork. They can explore patterns at a fruit shop where the fruit & vegetables are often laid out in regular, repeated patterns in shapes & colours & textures.
These metal fish are just one way to expose your students to looking for patterns in real-life. Which way do the fish face? Is there one of a kind or two or three? How do you know how many fish you need to put down before it is a recognisable and describable pattern? If one piece in your pattern is covered up, is it easy to see what this hidden part must be so that the pattern sequence is continued? There are no black and white answers to these questions but your students need to see this for themselves.
Metal Fish Patterns provides you with 36 small metal fish pieces and 6 sample pattern cards. All suitable for your 5-7 year olds.
NUMBER & ALGEBRA – MONEY ACTIVITIES – Stage 3 What’s Today’s Rate?
Investigating currency rates around the world is an effective way to practise multiplying and dividing decimal numbers by 10, 100 and 1000. Use this activity, What’s today’s rate? as a Mental Warm-up with your Stage 3 students at least once a week. Your students will become proficient at collecting online data and multiplying and dividing decimals in their head.
They challenge a partner to answer random questions related to the data they collect. They will see how each week our currency is worth more or less or may even stay at the same exchange rate. The decimal differences will make sense rather than just being a number on a screen or a page in a workbook.
GEOMETRY – 3D PHOTOGRAPHS – Edible Triangular Prism
How many 3D objects can your students name that are delicious to eat? Here is a slice of lemon tart from Tillerman’s Restaurant at Tea Gardens. Yum. It is definitely an edible 3D object. What is the mathematical name of this object? Can you describe at least 3 properties or facts about this object? e.g.The top and bottom (the bases) have the same shape, (a triangle), the sides are rectangular, two slices side by side still look like a triangular prism (just wider).
What shape are student sandwiches? What shape could these be? How can you describe fruit that your students bring to school? Students could also investigate the 3D Objects they discover for dinner tonight. You could then draw and graph the objects the next day to find out which object is the most common edible 3D dinner object.
GEOMETRY – POSITION PHOTOGRAPHS – Wooden Ball Triangular Pyramid
It’s quite difficult for us to imagine what something looks like from different viewpoints. Yet this is a wonderful skill we can try to develop in each of our students. A part of your daily mental Warm-ups, hold up a 3D object and ask your students to imagine what this looks like from on top or below of from the back. You might even ask them to sketch it on some scrap paper and then compare their sketches with a partner. Here is a triangular pyramid, for example, made from wooden balls.You can see it from 3 different angles.
These balls demonstrate tetrahedral numbers too. The first 5 tetrahedral numbers are 1, 4, 10, 20 and 35. This one is made from 20 wooden balls stacked together. The base starts with 4 balls on each side.You need 35 wooden balls to make a triangular pyramid with sides 5 balls long. You need only 4 balls to make a triangular pyramid with sides 2 balls long at the base. One ball doesn’t really look like a triangular pyramid but the idea is there!!! By the way, in the Song “The 12 Days of Christmas my true love sent to me …” the total number of gifts is 364 – the twelfth tetrahedral number!
VOLUME & CAPACITY PHOTOGRAPHS – 200 mL juice
Measurement makes no sense when it is isolated from everyday events. When you study Volume and Capacity with your students always link your discussion to real life examples. Before investigating millilitres, for example, ask each student to bring in an empty plastic litre container, preferable a transparent one. Use your school’s marked litre and millilitre resources to measure and then mark out where multiples of 100 mL come to in each container. Ask your students to compare what these multiples look like in different-shaped containers. Can they then predict where it will come to in a new container?
Encourage them to visualise, to imagine where the finish line will be. Look at where 200 mL orange juice comes up to in this marked container, for example. You need your eye to be level with the line to get an exact measure.
Duffy has created a very cute Christmas Card for you this year. We often visit Hawks Nest (a small sea-side town in NSW) which is famous for its small endangered koala population so Duff was inspired to have a koala as the central motif. Other Christmas characters can be found in Graphics – Special Occasion. You can also find links to useful Christmas Tree facts in the Maths Cafe.
GEOMETRY – POSITION PHOTOGRAPHS – Willow reads a map
Willow has only just turned 3 years old and she loves to read the Taronga Zoo Kids Map to discover her favourite animal spaces. She loves the giraffes in particular and carries her toy giraffe with her wherever she goes.
Map reading is an effective skill we use in our daily lives e.g. to read a transport map to figure out which station, stop or ferry wharf we need to get out at. You need to know which way is to the left and right on your map, even if you don’t have the words “left” and “right” fully understood. You need to understand that specific symbols refer to paths, areas and directions.
If Willow can maneuver herself and her Grandma around a zoo when she is three years old, imagine what she will be able to do when she is 5 and in Kindergarten. Current technology presents us with Google Maps, locations of holiday houses, shops and a friends house at the flick of an ipad or iphone.
What do we need to do in our schools to make map reading a relevant part of our maths sessions?
MATHS PHOTOGRAPHS – CREATURES – Butcher Bird
I have just been serenaded for 30 minutes by this magnificent butcher bird. He seems to show no fear of humans and let me take his photograph at close range.
Butcherbirds are Australasian songbirds with a complex range of beautiful songs. They get their name from hanging their prey by a twig hook or in a tree crevice. They often live in dense forests but can also be found in suburban backyards. They are quite large with bodies between 30 – 40 cm long and they have a heavy hook-tipped beak. Females lay between 2 – 5 eggs in the nest in a fork of a tree about 10 m from the ground. They breed from August to December and live together in family groups of up to 10 birds. Young birds leave the nest at about 4 weeks old.
MATHS GRAPHICS – 3D OBJECTS – 6 new solids
Duffy has been hard at work creating lots of new graphics. These are his latest – six 3D Objects for your students to compare, discuss and describe. They replace our earlier versions on the activity for Stage 1 students 3D Objects Mental Warmup Cards, where previously Bev had used just simple diagrams from Microsoft Word. Hmm … Duffy’s are heaps better! So professional.
GEOMETRY – 3D OBJECTS – What 3D Object am I?
We live in a beautiful 3D world and your students need to explore, talk about, describe and sort 3D objects – real life ones, whenever possible. But they also need to interact with photographs, pictures and diagrams of 3D objects too. These 3 new activities, What 3D Object am I ? and What 3D Object am I? PICTURE CARDS and Sorting 3D Objects for your Stage 1 students provide photocopiable resources using photographs and diagrams for pairs and small groups to use over and over again. They can close their eyes while a partner reads out some verbal clues. Can they visualise which object is being described? Or can they give their own verbal description based on just looking at a diagram of a 3D object. We’ve provided everything you need, even suggested ANSWERS and sample definitions. Plenty here to keep your 3D maths sessions full of discussion.
For example, Duffy is wearing a hat shaped like a cone. A cone has one curved surface that meets at a point. It also has one flat surface shaped like a circle. It has no straight edges. It has no corners.
Did you know that corners are formed only when 2 or more straight lines or faces meet. There are no straight edges or faces to form a corner in a cone. The point is created by a curved surface. This point is called an apex.
Fractions Decimals Percentages PHOTOGRAPHS – Discount Signs
Shopping is a fantastic way to talk about real-life mathematics. These 4 Shopping Discount signs can be used in a multitude of ways in your classroom. For example, use a real store catalogue with one of these signs. What is the current price? What will it be with another 40% off? What strategy will you use to work this out? Is there more than one way? Does one strategy work better than another for you?
Or use one of our 1000s of maths photographs and allocate a range of prices for these items. Next select one of the shopping discount photographs and discuss what this means. Will the prices be higher or lower with this discount? Is it more than half price of less than half price?
Or your students can draw their own shopping items and then allocate prices. Swap drawings with a partner, select a shopping discount and work out the sale prices for each item.
MATHS SESSION – MENTAL WARM-UPS – Measurement “What do I know?”
Real-life maths is all around us. But often your students sit on mathematical information without fully thinking about it. These activities grew out of an analysis of NAPLAN data over 10 years ago. We discovered that across Australia students looked at information with a one track mind. For example, 2 cakes cost $1.50 – they read it at face value. Yes, two cakes cost $1.50. They didn’t follow through with any other implication. For example, 4 cakes cost $3, 20 cakes cost $15, 1 cake costs 75 cents. If they were half price the original cost for 2 cakes was $3, and so on.
These 5 Measurement Mental Warm-ups “What do I know?” cover Length, Area, Mass, Volume & Capacity and Time – with 10 suggestions for each sub-strand. They are included in the Grades 3/4 section but will apply across a wider range of students.
In just one minute can your students brainstorm with a partner everything they can think of that has a mathematical link to what is shown. Don’t just limit yourself to the sub-strand either, try to create as many mathematical connections as you can, by discussing and sharing ideas as a whole class.
We want students who can think for themselves without us breathing down their necks all the time. We need independent thinkers who can stand on their own two feet and see mathematics all around them. We need students who go out into the adult world thinking mathematically.
NUMBER & ALGEBRA – FRACTIONS – Pizza Slices Challenge 3456
Yesterday Duffy and I had lunch at our local cafe and were surprised to see that our pizza had been cut in quite an unusual way. Here it is as Pizza Slices Challenge for your low block Grades 3 and 4 students, or for Grades 5 and 6 to tackle as well.
We have left it as quite an open challenge so that your students can solve it using a variety of strategies. It would be best if they worked with a partner so that they can discuss and explain their thinking. But we know you prefer to see at least one sample solution, so we have included that also in quite a lot of details as the concepts are not always easy to understand instantly.
Keep on the lookout for other real-life maths problems. They are all around you!
MATHS PHOTOGRAPHS – MULTIPLICATION – 4 bread & butter puddings
Food seems to be a recurring theme this week! How delicious – 4 bread and butter puddings straight out of the oven from Cafe M at Tamarama. What an effective way to focus on groups of 4 as part of your multiplication & division activities.
Use the photo as a Mental Maths Warm-up by challenging your students to count by 4s for as far as they can. Link to money by giving these puddings a price e.g. 4 for $16 so some students can count by 16s as they count off groups of 4 puddings. Link to division by talking about larger groups e.g. The cafe baked 48 muffins for a party and sold them for $144. How much will 4 cost?