Students come to appreciate the power of algebra for generalising results from arithmetic. They connect arithmetic operations with algebraic notation and visualisations. Each lesson commences with an observation made using arithmetic that students then justify and extend using algebra.

This sequence is designed to consolidate skills in algebra, including collecting like terms and expanding and factorising using the distributive law. The resources emphasise the importance of algebra for generalising and justifying arithmetic results. It is assumed that students have some familiarity with algebraic notation.

### Lesson 1: Mathematical Mind Reading

This lesson uses algebra to explain results in arithmetic by expressing two- and three-digit numbers in the general form 10*a *+ *b* or 100*a* + 10*b* + c. Students examine a well-known 'trick' involving reversing digits and explain it using algebra. They extend the activity to three-digit numbers and sustain their learning using algebra to predict what will happen in a related activity.

### Lesson 2: Reverse and Add

This lesson extends from the first lesson in the sequence. Students use algebra to explain results in arithmetic by expressing two- and three-digit numbers in the general form 10*a *+ *b* or 100*a* + 10*b* + *c*. Students start by reversing the digits of a two-digit number, adding it to the original number and observing that the result is always a multiple of 11. Links are made to ideas in statistics by randomly generating a large sample of two-digit numbers.

Last updated June 21 2020.