Suppose we have two types of measuring tools. The first, measures 1 cm, and the second measures \(x\) cm. Now suppose there is some length we wish to measure, and it just so happens that the length is not a whole number. We find that by placing some number of \(x\) cm lengths, and some number of \(1\) cm lengths, that we reach a more precise measurement. Teaching measurement with an unknown unit of length would be interesting, because it frames variables somewhat concretely, as an unknown unit of measure. We could provide problems which give results of \(ax + b\) and \(ax - b,\) where \(a\) and \(b\) are whole numbers.

Watch these Khan Academy videos:

- Order of operations examples: exponents
- Writing basic expressions with variables
- Evaluating expressions with two variables
- Terms, factors, & coefficients
- Expression value intuition
- Writing expressions with variables
- Evaluating an expression with one variable
- Evaluating expressions with variables: temperature
- Evaluating expressions with variables: cubes
- Evaluating expressions with variables: exponents
- Writing basic expressions word problems

Do these Khan Academy exercises:

- Order of operations
- Writing basic expressions with variables
- Evaluating expressions with multiple variables
- Parts of algebraic expressions
- Expression value intuition
- Writing expressions with variables
- Evaluating expressions with variables word problems
- Evaluating expressions with multiple variables: fractions & decimals
- Evaluating expressions with one variable
- Writing basic expressions word problems

Next, give your students these challenges:

- Bugs in the Garden by NRICH
- Stringy Quads by NRICH

Conclude by leading this investigation:

Integral Centrifuge (multiplication of +/-1)

by MathPickle

6.EE.A.2: Write, read, and evaluate expressions in which letters stand for numbers.