Odd Even Investigators

Overview

Students investigate odd and even numbers by pairing counters, representing multiplication facts and noticing patterns in the ones digit. The lesson builds on prior knowledge of counting in equal groups, skip-counting by 2s, and reading two- and three-digit numbers.

Learning intentions

Students will:

• identify and classify numbers as odd or even;
• explain odd and even numbers using equal pairs and remainders;
• use the ones digit rule to classify larger numbers;
• connect odd/even patterns to multiplication and number sequences.

Success criteria

• I can make equal pairs to decide whether a number is odd or even.
• I can explain that an even number has no counters left over and an odd number has one left over.
• I can use the ones digit to classify a number.
• I can justify my answer using a model, number sentence or explanation.

Curriculum links

• Multiplicative relations: represent and use multiplication structures to 10 × 10 to solve problems.
• Multiplicative relations: use known facts, related multiples and number sequences.
• Place value: use the ones digit and the role of zero to represent numbers.
• Additive and multiplicative reasoning: explain and complete number statements using appropriate strategies.

Lesson structure (60 minutes)

1. 0–7 min · Hook and prior knowledge. Open with the odd and even investigation deck and display the question, “Is 27 even or odd? How could you prove it without counting every object?” Students make a quick individual prediction, then share a strategy with a partner. Ask: “What does it mean to make equal groups?” and “What happens when one is left over?”

2. 7–18 min · Explicit teaching and modelling. Use the odd and even investigation deck to model 8 counters arranged into pairs: 4 × 2 = 8, so 8 is even because there are no counters left over. Model 7 counters as 3 pairs and 1 left over, linking this to 3 × 2 + 1 = 7, so 7 is odd. Record the language “even = pairs with none left over” and “odd = pairs with one left over”. Demonstrate that the ones digit rule works for larger numbers: numbers ending in 0, 2, 4, 6 or 8 are even; numbers ending in 1, 3, 5, 7 or 9 are odd. Include 40 and 105 to highlight the role of zero and place value.

3. 18–33 min · Paired investigation. Give each pair counters or small classroom objects and distribute the odd and even investigation worksheet. Students choose or are given numbers from 1 to 50, build each number, arrange counters into pairs, record the number of pairs and any leftover counter, and classify the number. They then write a related number sentence, such as 12 = 6 × 2 or 13 = 6 × 2 + 1. Circulate and ask: “How do you know?” “Can you show it another way?” and “What do you notice when you count by twos?”

4. 33–43 min · Differentiated investigation tasks. Continue using the odd and even investigation worksheet with groups working at an appropriate level:

• Support: Use numbers 1–20, counters and a prepared two-column table labelled odd/even. Encourage students to draw pairs and use the sentence stem, “___ is ___ because ___.”
• Core: Classify two- and three-digit numbers, explain the ones digit rule, and complete number sequences such as 14, 16, 18, __, __ and 31, 33, 35, __, __.
• Extension: Find all odd and even numbers between 40 and 60 that satisfy a condition, such as “has a 5 in the ones place” or “is a multiple of 4”. Explain whether an odd number can be a multiple of 2 and justify the answer.

5. 43–53 min · Share, reason and address misconceptions. Invite pairs to present one model and one explanation using the odd and even investigation deck. Discuss why 20 is even although it ends in zero, and why 108 is even although its tens digit is odd. Address common misconceptions: odd does not mean “small”; even does not mean “the number is divisible by any number”; and an odd number has one left over when paired, not necessarily one object in total. Ask formative questions: “Is 34 odd or even? Prove it two ways.” “What can you tell me about 2, 4, 6, 8, 10?” “If 27 is odd, what happens to 27 + 1?”

6. 53–60 min · Exit ticket and reflection. Students complete the final questions on the odd and even investigation worksheet: classify 46 and 73, explain one answer using pairs or the ones digit, and complete 22, 24, 26, __, __. Students hand in their responses and finish the sentence, “I know a number is even when…”.

Resources

• the odd and even investigation deck
• the odd and even investigation worksheet
• Counters, linking cubes or small classroom objects
• Mini-whiteboards and markers
• Number cards from 1 to 100
• Pencils and erasers
• Large paper or board space for class models

Assessment

• Observe paired modelling and listen for accurate use of “pairs”, “left over”, “odd” and “even”.
• Use questioning to check whether students can justify classification rather than rely only on the ones digit.
• Use the exit ticket to identify students needing further work with pairing, the ones digit rule or number sequences.

Differentiation

• Provide counters, a number line, enlarged numerals, colour-coded pairs and sentence stems for students requiring support.
• Reduce the number range and work alongside a teacher or peer model before moving to the ones digit rule.
• Provide challenge through three-digit numbers, multiple conditions and explanations using multiplication or division language.
• For EAL/D learners, explicitly display and rehearse “pair”, “equal groups”, “left over”, “odd”, “even” and “ones digit”; accept oral, drawn or demonstrated explanations.
• Seat students for clear access to materials, offer pencil grips or reduced writing demands where required, and allow extra processing time.

Common misconceptions

• The size of a number does not determine whether it is odd or even.
• The ones digit, not the tens or hundreds digit, determines the classification.
• Odd numbers can be paired, but one counter remains unpaired.
• Counting by twos produces even numbers only when starting from an even number; starting from an odd number produces odd numbers.