Activity 01
Pairs: Letter Balance Scales
Pairs use balance scales with numbered weights and cards labeled x or n. They create balanced equations by adding or removing items, then solve for the letter by testing values. Record expressions and share one solution with the class.
Explain how using a letter instead of a blank box changes the way we think about an equation.
Facilitation TipDuring Letter Balance Scales, circulate to listen for pairs explaining how adding or removing counters changes the balance, linking this to the expression’s value.
What to look forPresent students with a set of simple word problems. Ask them to write an algebraic expression for each, using a letter of their choice for the unknown. For example: 'Sarah has 7 apples and buys some more. How many does she have now?' (Expression: a + 7).
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Activity 02
Small Groups: Word to Expression Relay
Each group gets word problem cards. One student translates it to an expression with letters on a whiteboard, passes to next for solving, then next generates a similar problem. Groups compare final expressions.
Compare the use of symbols and letters to represent unknowns.
Facilitation TipIn Word to Expression Relay, stand close to the final group to observe how they translate the last word phrase into a correct algebraic expression using a chosen letter.
What to look forGive students an algebraic expression, such as 4y - 2. Ask them to write one sentence describing what the expression means in words and one sentence explaining what the letter 'y' represents.
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Activity 03
Whole Class: Symbol Sort Challenge
Project problems using boxes or letters. Class votes and sorts into categories, then discusses differences. Follow with quick partner sketches of personal examples using letters.
Construct a simple word problem that can be translated into an algebraic expression.
Facilitation TipFor Symbol Sort Challenge, provide only one set of cards per group so students must negotiate and justify their sorting decisions collaboratively.
What to look forPose the question: 'Imagine you have an equation like 5 + ? = 12 and another like 5 + x = 12. What is different about how we think about solving these?' Facilitate a class discussion comparing the use of a numerical placeholder versus a letter variable.
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Activity 04
Individual: Mystery Number Creator
Students write a word problem with an unknown, represent it algebraically, and solve. Swap with a partner to check and create a response expression.
Explain how using a letter instead of a blank box changes the way we think about an equation.
Facilitation TipWhen students work individually on Mystery Number Creator, ask each one to explain their chosen expression aloud before solving to reinforce verbal reasoning.
What to look forPresent students with a set of simple word problems. Ask them to write an algebraic expression for each, using a letter of their choice for the unknown. For example: 'Sarah has 7 apples and buys some more. How many does she have now?' (Expression: a + 7).
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Generate Complete Lesson→A few notes on teaching this unit
Teach this topic by letting students experience the instability of fixed answers before moving to variables. Use physical models like balance scales to show that the same expression can hold different truths depending on the letter’s value. Avoid rushing to formal procedures; instead, build comfort with trial and substitution so students see letters as flexible tools rather than mysterious symbols.
Successful learning looks like students confidently replacing blanks with letters, explaining how the letter’s value changes the expression’s outcome, and using inverse operations to check solutions. They should articulate why letters generalise thinking beyond a single number.
Watch Out for These Misconceptions
During Letter Balance Scales, watch for students assuming the letter always stands for 10 or another fixed number.
Ask pairs to swap their chosen letter with a different letter and recount the counters, showing that the same physical setup can be described with any letter, proving the letter’s value is not fixed.
During Word to Expression Relay, watch for students avoiding multiplication or division with letters, writing only addition and subtraction.
Circulate and prompt groups to include an expression like 3n or n/4, then ask them to explain what each part means using counters or drawings to justify the operation.
During Symbol Sort Challenge, watch for students treating 2x and x + 2 as equivalent because they contain the same symbols.
Have students test both expressions with a chosen value for x, such as 3, to see that 2x equals 6 while x + 2 equals 5, clarifying that order and operation placement change the expression’s meaning.
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