Hook:
Mental computation/Keys to Success
Make 20 (Addition/Subtraction)
Teacher calls two numbers (e.g., 7 and 12).
Students must quickly find what to add/subtract to reach 20.
Example: 7 needs 13, 12 needs 8.
Extension: Change target to 50, 100, or 1,000.
Mini Lesson:
Quick-fire: What’s the fastest way to make 100? (students shout out equations).
Add in rules (e.g., must use 3 numbers, must include a decimal, must include an odd number).
Independent/Guided:
Using any whole numbers (or decimals for extension), they must make the target using addition only.
Rules: they must use at least 4 numbers, and no number can be repeated.
Low floor: Students add simple numbers (e.g., 100 + 200 + 300 + 400).
High ceiling: Students explore decimals, fractions, and larger numbers (e.g., 999.5 + 0.25 + 0.25 + 0.0).
Reflection
Share different equations.
Discuss: What strategies made it easier to get close to the target?
Exit ticket: “What’s one clever addition strategy you used today?”
Hook:
Keys to Success
Mini Lesson:
Play Closest to Zero: Students start with 50 and subtract teacher-called numbers (e.g., subtract 7, subtract 12). Closest to zero without going negative wins.
Independent/Guided:
Each student gets a starting number (e.g., 500).
Roll a dice (or use random number cards 1–20, or random number generator). Students subtract that number from their total.
Aim: be the last person with a positive number.
Low floor: Students subtract simple single-digit numbers.
High ceiling: Allow subtraction with decimals or negative numbers, exploring what happens when their total goes below zero.
Extension:
Predict who might win by estimating differences.
Create a strategy: is it better to start with a higher or lower number?
Reflection
Class discussion: Was this more luck or strategy?
Quick journal: “How do you know if your answer is reasonable?”
Hook:
Keys to Success or Double & Halve (Multiplication)
Teacher calls a number (e.g., 24). Students double it, halve it, then say both answers out loud. Example: 24 → double = 48, half = 12. Extension: Push into fractions/decimals (half of 7.5, double 3.6).
Mini Lesson:
Multiplication Stretch: Teacher says a number, students give as many facts as possible (e.g., teacher: 36 → students: 6×6, 9×4, 12×3).
Independent/Guided:
Choose a factory number (e.g., 240).
Students must find as many multiplication equations as possible to make the number.
Low floor: Students use simple facts (e.g., 24 × 10 = 240).
High ceiling: Students explore factor pairs, arrays, prime factorisation (e.g., 2 × 2 × 2 × 2 × 3 × 5 = 240).
Extension:
Can they represent the number using area models?
Can they find the longest multiplication chain possible (e.g., 2 × 2 × 2 × 2 × 3 × 5)?
Reflection
Share most interesting solutions (e.g., prime factorisation chains).
Exit slip: “What did you notice about factors today?”
Hook:
Keys to Success or Teacher fires rapid questions:
“What’s 36 ÷ 6?”
“What’s 100 ÷ 4?”
Students answer as fast as possible.
Extension: Include remainders (e.g., 37 ÷ 6).
Mini Lesson:
Pose quick division questions with remainders: “17 ÷ 5 = ?” Discuss: What could the remainder mean in real life?
Independent/Guided:
Pose real-world problems: “You have 137 lollies to share equally between 6 friends. How many does each get?”
Students must work out answers and decide what to do with remainders (discard, share differently, cut into pieces, etc.).
Low floor: Divide simple numbers with small remainders.
High ceiling: Division with large numbers, decimals, or fractions.
Extension:
Give open tasks: “Make up a division story problem where the answer has a remainder of 3.”
Challenge them to represent the same division problem using different models (repeated subtraction, arrays, equations, fractions).
Reflection
Share student-created problems.
Class discussion: When is a remainder important? When is it not?
Hook:
Teacher says two numbers (e.g., 8 and 3).
Students must give four equations using those numbers:
8 + 3 = 11
8 – 3 = 5
8 × 3 = 24
8 ÷ 3 ≈ 2 r2
Extension: Challenge with larger numbers or decimals.
Mini Lesson:
Make 24 Game: Given 4 numbers (e.g., 2, 3, 4, 6), students try to make 24 using +, –, ×, ÷.
Independent/Guided:
Students get 4 random numbers (e.g., 3, 7, 8, 25).
Their challenge is to combine the numbers using any of the four operations to make a target number (e.g., 100).
Low floor: Students attempt simple combinations (25 × 4 = 100).
High ceiling: Students try to use all four operations in one solution (e.g., (8 × 25) – (7 × 3) = 100 – 21 = 79, then +21).
They may also invent multiple solutions or explain why some targets are impossible.
Extension:
Introduce decimals, fractions, or exponents.
Challenge: Make the biggest number and the smallest number possible with their 4 numbers.
Reflection
Students share their solutions on the board.
Discuss strategies: Which operations worked best?
Exit slip: “Today I learned that _____ is a clever operation to use because _____.”