**Level:** Year 9

**Author:** Marcus Garrett

**Description:**

In this unit you’ll be introduced to the calculation of simple interest, as a starter for learning about the more widely used compound interest in Year 10. You’ll learn about a range of ways in which interest generally is used and applied in the real world and then use the formula for calculating simple interest to solve borrowing, saving and investment problems.

This unit includes an *AMSI Interactive* called ‘Simple Interest’.

**Australian Curriculum (Mathematics) Outcome/s:**

Solve problems involving simple interest (ACMNA211

**For any questions or queries please contact: ****choosemaths@amsi.org.au**

**Level:** Year 7

**Author:** Leanne McMahon

**Description:**

This unit investigates the idea of representing patterns algebraically in the year 7 classroom. According to the Australian Curriculum, by the end of Year 7, students should be introduced to the concept of variables as a way of representing numbers using letters. They should also be able to create algebraic expressions and evaluate them by substituting a given value for each variable. This series of lessons/ideas gives physical patterns and explains the 5 ways of representing these patterns:

- As a diagram
- In a verbal description
- As a chart
- As an algebraic formula
- In graphical form

**List of Resources:**

**For any questions or queries please contact: ****choosemaths@amsi.org.au**

**Level:** Year 9

**Author:** Marcus Garrett

**Description:**

In this unit you’ll identify and describe everyday examples of direct proportion such as when as the number of hours worked increases, earnings also increase. You’ll explore everyday examples of inverse (indirect) proportion, such as when as speed increases, the time taken to travel a particular distance decreases.

The unit will help you to recognise direct and inverse proportion from graphs, distinguish between positive and negative gradients when using a graph and to use the equation ** y = kx** to model direct linear proportion (where

This unit includes a *GeoGebra* graphing file to model tables of values and to graph equations representing linear direct proportion.

**Australian Curriculum (Mathematics) Outcome/s:**

- Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208)

**For any questions or queries please contact: ****choosemaths@amsi.org.au**

**Level:** Year 8 and Year 9

**Author:** Marcus Garrett

**Description:**

In this unit you’ll investigate the concept of irrational numbers. You’ll examine some examples of commonly used irrational numbers such as Pi (), , the ‘Golden Ratio’ and the natural logarithm ‘** e**’ and explore where irrational numbers have applications in the real world. You’ll then take a closer look at the nature of both Pi and irrational roots or surds and how they work.

The unit includes an *AMSI Interactive* unit called ‘Investigating Irrational Numbers’

**For any questions or queries please contact: ****choosemaths@amsi.org.au**

**Level:** Year 6

**Author:** Leanne McMahon

**Description:**

According to the Australian Curriculum by the end of Year 6 students should be able to select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers. This is a skill that requires a great deal of practice and should be taught throughout the year, rather than as a designated unit. The following suggestions include a list of popular strategies for problem solving and some age-appropriate problems for students to work on.

**List of Resources:**

- Year 6 Problem solving AMSI
- Problem solving strategies with Examples

**For any questions or queries please contact: ****choosemaths@amsi.org.au**

**Level:** Year 4, Year 5 and Year 6

**Author:** Cassandra Lowry

**Description:**

Helping children learn more about factors and multiples can help them better understand multiplication and division.

**Factors**are the numbers we multiply together to get another number, for example, 3 x 4 = 12 so 3 and 4 are both factors of 12**Multiples**are what we get as a result of the multiplication, for example, 3 x 4 = 12, so 12 is a multiple of 3 and a multiple of 4

Playing games and activities that require children to identify factors and multiples will help children become more familiar with these terms. This understanding will support children’s ability to solve problems, including knowing how to add fractions with different denominators.

**List of Resources:**

**NRICH**Factors and Multiples Game**NCTM Calculation Nation**Factor Dazzle**Math Playground**Factor Pair Up**ABCYA**Number Ninjas – Multiples- 1-100 Counting chart
- 1 cm grid paper

**This activity covers the following Australian Curriculum – Mathematics Content:**

- Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075)
- Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098)

**For any questions or queries please contact: ****choosemaths@amsi.org.au**

**Level:** Year 4, Year 5 and Year 6

**Author:** Cassandra Lowry

**Description:**

Estimation is a skill that many of use on a regular basis, think of cooking or driving a car, but we often do not say “I estimate…”. At school, estimation is part of the curriculum from the beginning. Early on children are encouraged to estimate the number of objects in a collection, then later check the total. By the end of Year 5, children are encouraged to use estimation to help them make reasonable guesses at solutions and to check the accuracy of their calculations.

Basically, estimation is about finding an answer to a problem (often quickly) that is “close enough” to the right answer to help us. For example, if we only had $20 to buy food and we knew that the four items we wanted to buy were each less than $5 we could quickly estimate (as 4 x 5 = 20) that we would have enough money.

Estimation can also help children to check whether their calculations are valid. For example, if we wanted to find 19 x 5, we might think that 20 x 5 is 100, so 19 x 5 must be less than that. Here we have “rounded” 19 to the nearest ten. This process of rounding numbers can assist with making quick calculations and estimates.

Rounding is where we change numbers slightly to make calculations easier to complete mentally. For example, if I wanted to estimate a solution to the problem 33 + 66, I might round both these numbers to the nearest 10, then in my head calculate that 30 + 70 is 100. If my solution to 33 + 66 is too far away from my estimate, then I will know I may have made a calculation error.

More information on estimation and rounding can be found in the document below.

**List of Resources:**

- Estimation
**MathGames**by**TeachMe**have several estimation and rounding activities with different levels of challenge- More estimation and rounding activities can be found on the
**Sheppard Software**site - For further tips to help children with rounding, check out this video by
**MuchoMath**

**For any questions or queries please contact: ****choosemaths@amsi.org.au**

**Level:** Year 3 & Year 4

**Author:** Cassandra Lowry

**Description:**

Helping children learn their addition facts does not need to be a chore. In fact, there are many games and activities that are fun to play that allow children to improve their addition skills.

Regular practise of addition facts can help children build their confidence in maths and help them in other areas, including multiplication, measurement and interpreting data.

**List of Resources:**

- Bunny Ears
- ROWCO
- Yohaku Number Puzzles
- Open Middle Tasks
- Totality (a two player addition game from NRICH)

**This activity covers the following Australian Curriculum – Mathematics Content:**

- Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)
- Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)

**For any questions or queries please contact: ****choosemaths@amsi.org.au**

**Level:** Foundation and Year 1

**Author:** Janine Sprakel

**Description:**

This activity is about discovering shapes and objects in the home environment. Opportunities to name, describe, sort two-dimensional shapes and three-dimensional objects using their features are provided.

**List of resources needed:**

- Pencils and paper OR a copy of this table for each child
- Optional: A device to take digital photos

**Objective:** To name, describe and sort two-dimensional shapes and three-dimensional objects.

**What to do:**

- Print the worksheet, or the child could copy and answer each item on paper.
- Some students will need an adult or older child to read the task to them.
- Modify to suit your child. They may need more paper for drawing and writing.
- Encourage the child to say the names and describe the shapes and objects out loud as they go.

**Notes for parents: **

- Drawing shapes is hard at this age. Allow them the freedom to use a large piece of paper if needed. Naming and describing can also be a challenge for young students but it’s important that they start using the correct language from an early age. The ways in which they sort shapes and objects according to features they identify can also be interesting!
- Your mindset is as important as your child’s. Foster a growth mindset. Instead of thinking “I can’t do this”, encourage them to say, “I can’t do this, yet!”
- Let the child do their best. Keep it light and fun. They do get better at things with more practice.

**We want children to:**

- Name two-dimensional shapes
- Name three-dimensional objects
- Describe two-dimensional shapes according to their features. Some features may include: they are flat, have no thickness, the number of sides, number of corners etc.
- Describe three- dimensional objects according to their features. Some features may include that three-dimensional objects have length, width and height, faces, edges etc.

**(Not all students will be able to demonstrate all the above but will be working towards these understandings.)**

**This activity covers the following Australian Curriculum – Mathematics content:**

Sort, describe and name familiar two-dimensional shapes and three-dimensional objects in the environment (ACMMG009)

Recognise and classify familiar two- dimensional shapes and three-dimensional objects using obvious features (ACMMG022)

**For any questions or queries please contact: ****choosemaths@amsi.org.au**

**Level:** Foundation and Year 1

**Author:** Janine Sprakel

**Description:**

The purpose of counting is to find ‘how many’ we have altogether. The focus of this activity is for students to count a variety of objects in their home environment, and write the number for each.

**List of resources**

- Pencils and paper OR a copy of this worksheet for each child
- Clock with a second hand (or a stopwatch, or stopwatch app on a phone)

**What to do:**

Print the mind map, or draw your own

**Instructions:**

- Print the worksheet, or the child could copy and answer each item
- Encourage counting out loud. It is OK to touch and count
- The child records the number for each set of objects counted. There is no single, correct answer
- Students should complete as many as they are able

**We want children to:**

Use the language of counting.

Assign numerals to the quantities they count.

Record the numeral for the quantity counted correctly.

Explain that the purpose of counting is to find how many we have altogether.

**Notes for parents: **

- Writing numbers is hard at this age, students often mirror the numbers. See this webpage for a suggested way to write numbers. Children do get better at writing numbers with more practice.
- Encourage the child to count out loud as they go. Your mindset is as important as your child’s. Foster a growth mindset. Instead of thinking “I can’t do this”, encourage them to say, “I can’t do this, yet!”
- Ask your child what they do when they count.
- Some children will need an adult or older child to read these items to them.
- Modify to suit your child. For example, if you live in an apartment and don’t have a back door… change it to How many … steps from your front door to your television?
- Let the child do their best and keep it light and fun.

**This activity covers the following Australian Curriculum – Mathematics Content:**

**Foundation**

Number and Place Value. Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point (ACMNA001)

Number and Place Value. Connect number names, numerals and quantities, including zero, up to 10 and then beyond (ACMNA002)

** **

**Year 1**

Number and Place Value. Count to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero (ACMNA012)

Number and Place Value. Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line (ACMNA013)

Count collections to 100 by partitioning numbers using place value (ACMNA014)

**For any questions or queries please contact: ****choosemaths@amsi.org.au**