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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
im  a2 < a + b < ab < b2

im Intersecting sequences inquiry
im The difference, sum and product of two numbers are the first three terms of a sequence.
im Solving equations inquiry

im Solving advanced equations inquiry
im Simultaneous equations inquiry
im Quadratic equations inquiry

im Formulae inquiry
                         l2 + h= n
im Coordinates inquiry
im  y - x = 4
im Intersecting lines inquiry
im Distance-time graph inquiry
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.

Billy Adamson is the Head of Mathematics at Thurston Community College (Bury St Edmunds, UK). You can follow Billy on twitter @Billyads_47.