Evaluating expressions – Grade 6 math lesson
Lesson 17 of 26 in the Grade 6 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 6 (ages 11–12) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 6 (ages 11–12)
- You need
- Paper, a pencil and this page
- Graded
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “If x = −2, what is x² − 3x? Explain each step.”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Writing 3a as 34 when a = 4. Put in the multiplication sign: 3 × 4.
- Squaring a negative without parentheses. Write (−3)² = 9.
Tip for home: Use a formula to convert temperatures or cooking times together.
What your child will learn
Learning goal: substitute numbers into expressions and formulae.
Success looks like
- I can substitute into expressions.
- I can use formulae.
- I can substitute negative numbers.
Key words
- substitute
- replace a letter with a number
- formula
- a rule that links quantities
- evaluate
- work out the value
- expression
- terms joined by + or −
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use a formula from real life, such as cooking time = 20 × mass + 20, and substitute different masses.
The big ideas (for the adult)
Substituting means replacing each letter with its number, then working it out.
Remember the hidden multiplication: if a = 4, then 3a = 3 × 4 = 12, not 34.
Take care with negatives and powers: if x = −3, then x² = 9 but −x² = −9. Use parentheses when you substitute.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.
More practice
More Grade 6 math lessons
- Solving word problems
- Fractions, decimals and percentages
- Ratios
- One quantity as a fraction or percentage of another
- Percent
- Proportional relationships
- Rates and unit rates
- Unit prices and best buys
- Converting units
- Negative numbers and temperature
- Integers and absolute value
- Operations with multi-digit decimals
- Operations with fractions
- Greatest common factor and least common multiple
- Square and cube numbers
- Writing expressions
- Simplifying expressions
- Solving equations
- Inequalities
- Writing equations for situations
- 3-D shapes and nets
- Coordinates
- Volume and surface area
- Mean, median and mode
- Box plots and interquartile range
Curriculum
Common Core State Standards 6.EE.A.2.c: “Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s³ and A = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.