# Hopper

Students explore patterns and sequences and develops estimation, counting, addition, subtraction and multiplication skills with whole numbers and decimals. The objects introduce algebraic thinking in an engaging, non-threatening way, using words and visualisation rather than symbolic notation.

### Teacher notes

• Using a number grid, students estimate the answer to a word problem (the jump plan). They watch a frog (the Hopper) dynamically complete the jump plan on a number line and observe the pattern produced on the number grid. The jump plan is a rule or expression that promotes algebraic thinking.
• Each completed jump plan is shown to the students in three ways: as the written rule, on the number line and highlighted on the number grid
• Following each jump, students select the problem, from a choice of three, which matches the jump pattern they have just used
• In the Hopper subset of learning objects there is additional scaffolding where the patterns are represented on non-numerical grid patterns to assist visualisation of the pattern.

### Learning objects

 Hopper: whole numbersStudents select a jump size between 1 and 10 and the starting point is generated randomly on a grid of whole numbers between 0 and 999 Hopper: tenthsStudents select a jump size between 0.1 and 1 and the starting point is generated randomly on a grid of numbers expressed as tenths between 0 and 99.0 Hopper: hundredths Students select a jump size between 0.01 and 0.1 and the starting point is generated randomly on a grid of numbers expressed as hundredths between 0 and 9.99. Hopper: ultimateStudents are presented with randomly selected problems from each of 'Hopper: whole numbers', 'Hopper: tenths' and 'Hopper: hundredths'. Hopper challenge: whole numbersStudents select a jump size between 1 and 10, the end point is generated randomly on a grid of whole numbers between 0 and 999. Hopper challenge: tenthsStudents select a jump size between 0.1 and 1 and the end point is generated randomly on a grid of numbers expressed as tenths between 0 and 99.0. Hopper challenge: ultimateStudents are presented with randomly selected problems from each of 'Hopper challenge: whole numbers' and 'Hopper: tenths'.