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### Algebra prompts

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Algebraic expressions and proof
im Number line inquiry

im Steps inquiry

im Squaring numbers inquiry
 402 = 39 x 41 + 1

im Difference of two squares inquiry
 42 - 32 = 4 + 3

Substitution
im  a2 < a + b < ab < b2

Sequences

im Intersecting sequences inquiry

im The difference, sum and product of two numbers are the first three terms of a sequence.

Equations
im Solving equations inquiry

im Simultaneous equations inquiry

Formulae
im Formulae inquiry
l2 + h= n
Coordinates
im Coordinates inquiry

Graphs
im  y - x = 4

im Intersecting lines inquiry

im Distance-time graph inquiry

Matrices
im Matrices inquiry

Algebra prompts for year 7 (grade 6)

Billy Adamson is developing a scheme of learning based on inquiry. The algebra prompts, designed for six weeks of lessons, cover expressions, factorisation, use of brackets and substitution. The prompts offer the potential for creative and rich inquiry that can help students develop a deep understanding of the use of symbols and the manipulation of algebra.

Collecting like terms
These templates can be used for pages 9 to 16 of Billy's prompts. Students can start an inquiry by placing terms or expressions at the vertices of the triangle and sum them to find the cells on the edges and then in the middle. In the next phase, they might work backwards from an expression in the middle cell. Is it always possible to find a solution? How many? Another pathway sees students using multiplication instead of addition.