## An update on our new content for Australia (Jan to Mar 2018)

### Primary

*Year 4*

*Year 4*

In Number Patterns students in this year group begin to play with the idea of an unknown in a numer sentence. This new subtopic (Finding the unknown with add/sub), reminds students of number strategies such as fact families, bridge to 10, counting using objects and place value and has them use these strategies to complete number sentences with unknowns.

Continuing on our extensive coverage of the development of multiplicative strategies, Properties of Multiplication shows students how the commutative property works, and has them practice this using questions like this one.

Also applicable to this age group are the following new lessons in Measurement. All of them with explanatory videos for students to watch, or for teachers to use as stimulus for discussion.

- Shapes and fractions with area
- Comparisons using volume
- Measure, estimate, order and compare objects
- Comparisons using area
- Areas of Regular and Irregular Shapes

*Year 5*

*Year 5*

The distributive property for multiplication is introduced to students through the idea of the area model for multiplication. Students identify that the area of 9 x 27 is the same as the area for 9 x 20 and 9 x 7 added together. This becomes an effective strategy both for multiplication, as well as a foundational skill for distributive expansion in the high school years. Two subtopics of questions were set live this month related to these skills. Distributive property for multiplication and Use the distributive property

Continuing on from earlier years, in year 5 students start to apply the idea of an unknown to multiplicative statements. There are 3 new subtopics this month to enable familiarity with this idea. The first one utilises students basic facts, and combines this with notations involving pronumerals. The next 2, focus on 4 operations and on combining operations together.

Finally, in measurement a great lesson went live on Shapes and fractions — perimeter. The video here guides students to proportional thinking in identifying strategies for finding the fractions around the outside of a shape. This is based on an activity I used to run with my students in the classroom, starting easy like finding one third of the way around a triangle, up to harder ones like finding ⅕ of the way around a triangle. It’s a great activity to run with your class and encourage class discussion on their thinking and understanding.

#### Year 6

Number patterns at year 6 level moves to generate rules to describe patterns using decimals or fractions. We have 4 new sets of work to help students with this. We have scaffolded the work for decimal patterns in tenths followed by hundredths, and then fractions using tenths or hundredths and then finally a last set that combines this knowledge together.

At Mathspace we try to combine ideas and knowledge together, one example of this is in our new lesson on Addition and subtraction problems involving angles, found in the whole number addition and subtraction topic we combine here skills of adding 2 and 3 digit numbers together with the newly acquired understandings of putting a measure to a rotation and calling it an angle. This lesson has a number of simple geogebra applets to help consolidate this understanding.

Long division — do you teach it or not? It’s one of those topics in mathematics that has felt the swing of the pendulum,from its early days as an explicit part of the most curriculum documents, to the somewhat vague reference in the Australian Curriculum under “written methods”. If you do teach it, then Mathspace has a number of subtopics to help you explicitly.

Long division for 1 or 2 digit numbers (resulting in decimal)

Long division for 3 digit numbers (resulting in decimal)

Long division for 4 digit numbers (resulting in decimal)

Long division — divide decimals by 1 digit numbers

Long division — divide decimals by 2 digit numbers

Identifying and describing types of patterns from tables or graphs is a new lesson published this month as part of the Number Patterns topic. It is a precursor to the type of analytical thinking required in algebra and statistics. There are 4 short videos on this lesson. Another lesson in number patterns this month is Patterns using input and output tables. This lays the foundations for some higher order algebraic thinking that comes in high school years involving functions.

#### High School

Whilst there was no new live content in the high school (yrs 7–10) domain in January, I thought I would highlight a number of excellent lessons in Measurement.

Area of two dimensional shapes, whilst starting in primary school with the understanding of rectangular areas, is extended throughout high school. The fundamental underpinning is the understanding of the area of a rectangle: A = l x w. Once students really understand the array structures that support this, we take them on a journey to connect the area of other shapes back to the area of the rectangle. Most of these lessons have simple geogebra applets to demonstrate the connection

Triangles (half of the rectangle)

Parallelograms (almost a rectangle)

Trapeziums (similar to parallelograms, which are almost a rectangle!)

Kites (half of a rectangle)

Rhombus (yep, just like a rectangle!)

Circle (yes, we even relate a circle back to a parallelogram — which is like a rectangle!)

#### Senior Secondary

A real mixed bag of new live content in the senior secondary domain in January. Mostly relating to upper levels of mathematics such as Methods, Extension 1 in NSW and even a few that might be applicable to the Specialist Studies (Extension 2 in NSW).

- Circle Geometry > Congruence and Similarity of Circles
- Systems of Equations > Simultaneous lines and circles
- Limits > Evaluating Limits
- Calculus of Trigonometric Functions > Solids of revolution (sin/cos)

Have you seen our coverage of complex numbers? 28 lessons in the ebook so far, most with interactive questions. From basic operations of complex numbers, up to sketching circles and ellipses on the complex plane. This month the subtopic Factorising and Expanding Complex Numbers was set rounding out our basic operations of complex numbers.

Similarly our topic of Logic and Reasoning may be new to you as well. We have a number of lessons already in the ebook, and this month a new set of questions on Inductive Proofs for divisibility (2)

Absolute Value Functions is a topic that has been left in most states to be dealt with in the Specialist courses, however the new NSW curriculum for Advanced mathematics covers it to a little more depth. As part of our commitment to covering the new NSW courses better than any text book, this month we started releasing new content in this area. Graphing Linear Absolute Value Functions is the first of a few subtopics coming this year in this area.

Vectors in Mathspace is something that we are working hard on to bring you as fully interactive content. At the moment however, you can find amazing coverage of 46 lessons relating to Vectors in our eBook.