• illustrate the solutions process for a first-degree, single-variable equation, using concrete materials or diagrams

The equation 4x = 4 + 3x has been modelled with algebra tiles. Explain how you can use the tiles to justify an algebraic solution process.

Use algebra tiles to justify an algebraic solution to
3x -7 = -2x + 8

• solve and verify first-degree, single-variable equations of forms such as:
  ax = b + cx; a(x + b) = c; ax + b = cx + d where a, b, c, and d are integers, and use equations of this type to model and solve problems

A string measuring 50 cm in length is cut into three pieces. One piece is twice as long as the shortest piece, and the other piece is 10 cm longer than the shortest piece. Find the length of each piece of string.

Dennis has $25 and can save $2.80 per day. Jeena has $18 and can save $3.70 per day. Who will be the first to be able to buy a $72 tennis racquet?

Yutaka goes to the record store. Compact disks cost $14 for the first one and $13 for each additional one. If Yutaka buys M compact disks and spends D dollars, write an equation that represents the relationship between M and D.

C represents the number of compact disks, and C + C + 4 + 2C = 56. Using this information, write a problem.

*The cost of installing a fence is calculated by C = 7L+ 15p + 80, where L is the total length of the fence in metres, and p is the number of posts required. You have budgeted $3,025, and the fence has to cover a perimeter of 250 metres. How many posts can you afford?

• identify constant terms, coefficients, and variables in polynomial expressions

What is the numerical coefficient of -6a⁴b?

What is the constant term in the expression 4x - 3 = 2y?