Lesson 08 — Writing and Evaluating Simple Expressions

Learners write simple expressions with a variable for real situations (n apples per basket plus loose ones → 3n + 2), and evaluate them by substituting a number for the variable. They interpret what the expression means in the situation.

D05 P3: Intellectual & Cognitive Awareness D05.S2 45 minutes Draft

Objectives

D05.S2.05.02 Write and evaluate simple expressions and interpret what they mean in a real situation.

Essential question

How do I write a simple expression for a real situation and find its value?

expressionvariableevaluatesubstituteoperationsparentheses

Materials

Standard materials

Expression cards · 1 set per group Cards pairing a real situation (n apples per basket plus loose ones) with its expression
Variable substitution chart · 1 per learner A chart for evaluating an expression for several values of the variable
Expression recording page · 1 per learner A page to write expressions for situations and evaluate them

Low-tech / no-cost

Cups and counters Use a cup as the variable (unknown amount) and stones or seeds as counters; build the expression with real objects
Voice patterns Chant the situation ("three baskets of n plus two loose") and substitute numbers aloud, acting it out

Enriched / lab & device

A simple spreadsheet · 1 per group A spreadsheet with a formula cell that evaluates an expression for different values of a variable, where devices allow
An expression-match game · 1 per group A game matching situations to expressions and to their values for given variable amounts

Works in different contexts

large-group Model writing and evaluating one expression on the board, then have groups match situations to expressions and share one
multi-age Younger learners substitute numbers into a ready-made expression while older learners write the expression from the situation
self-directed A learner works the recording page alone, writing and evaluating expressions and checking against the worked example
level-grouped Learners ready to extend write expressions with two operations and parentheses, and evaluate for a table of values
outdoor-only Use a cup or basket as the variable and real objects outdoors to build and evaluate each expression

An expression diagram for 3n + 2. Three circles each labeled n, plus two loose dots, equal a box labeled 3n + 2. Below, an evaluation shows substituting n = 5: 3 times 5 plus 2 equals 17. Labels, counts, and shapes, not color alone, carry the meaning so it prints clearly in grayscale.

Lesson 8 — Writing and Evaluating Simple Expressions

Summary

Learners write simple expressions with a variable for real situations (n apples per basket plus 2 loose → 3n + 2) and evaluate them by substituting a number for the variable. They interpret what the expression means in the situation and check that the answer makes sense.

Objectives

Write a simple expression for a real situation and evaluate it by substituting a value for the variable. (D05.S2.05.02)

Connection

A market seller packs n mangoes into each box. If you take 3 boxes plus 2 loose mangoes, how many do you have? You cannot count them yet because you do not know n — but you can write 3n + 2. The moment someone says “each box holds 5,” you substitute: 3 × 5 + 2 = 17. A variable is a box that can hold any number, and an expression is a recipe that tells you what to do with it. Cooks, builders, and shopkeepers use such recipes every day.

Materials

Expression cards
Variable substitution chart
Expression recording page

Preparation

Copy expression cards for groups and the recording page for each learner.
Copy the variable substitution chart.
Have a worked example ready: 3 boxes of n mangoes plus 2 loose → 3n + 2; n = 5 → 17.

Facilitator note

This lesson is written to the learner (“you”). The ideas to land: (1) a variable is a letter that stands for an unknown or changing amount; (2) an expression combines numbers, variables, and operations (3n + 2 means “three times n, then add 2”); and (3) to evaluate, you substitute a number for the variable and do the operations in order. Model a worked example first (Kirschner, Sweller & Clark, 2006), then guide a second before independent work. Two common slips: treating “3n” as “3 + n” (it means 3 × n), and doing operations out of order. Retrieval: ask learners to recall the coordinate relationship y = 2x from last lesson — that is itself an expression, now given a name. The algebra here is evidence; the habit of writing a rule clearly so anyone can follow it is an egalitarian value (clear rules are shareable rules, docs/philosophy.md §4). Note: variables are a human convention — different traditions use different symbols, but the idea of “a number you do not know yet” is universal.

Procedure

Gather (5 min). Last time you saw the relationship y = 2x on a grid. Today you write such rules yourself — using a variable, a letter that stands for a number you do not know yet.
Meet variables and expressions (10 min). A seller packs n mangoes per box. “Three boxes plus 2 loose” is written 3n + 2: the 3n means “3 times n,” and the + 2 means “plus 2.” This whole rule is called an expression.
Worked example — write (10 min). Write an expression for: “5 baskets of n oranges plus 3 loose.” That is 5n + 3. What about “n cookies shared by 4”? That is n ÷ 4.
Worked example — evaluate (10 min). Evaluate 3n + 2 when n = 5. Substitute: 3 × 5 + 2. Multiply first: 15, then add 2: 17. So 3 boxes of 5 mangoes plus 2 loose is 17 mangoes.
Practice with a partner (10 min). Take your expression cards: match each situation to its expression, then evaluate it for the value given. Check each other: did you multiply where it says multiply, and do operations in order?
Close (5 min). A variable is a box that can hold any number, and an expression is the recipe for what to do with it. Write the recipe first, then substitute the number — that is the whole skill.

Differentiation

Support: Use only expressions like n + 3 and 4n (no two operations at first); keep the substitution chart with one clear value. Describe each step aloud and use cups/counters so learners with low vision can follow by touch.
Extension: Write expressions with parentheses and two operations (2(n + 3)) and evaluate for a table of several values.

Assessment

Formative (observation/self): Can the learner write an expression for a real situation and evaluate it correctly by substitution?
Self-check: The learner asks, “Does my expression match the situation word for word, and did I substitute and operate in the right order?”

Home connection

Find a situation at home with an unknown amount (a bag with n things, a recipe for n people) and write an expression for it; then pick a number and evaluate it.

Resources

Variables and simple expressions are standard in elementary mathematics; see John A. Van de Walle, Elementary and Middle School Mathematics (10th ed., 2019). The note that variables are a human convention used across traditions is a factual observation; the value that clear rules should be shareable by everyone is a commitment (docs/philosophy.md §4).