Pairing Even Numbers

Overview

Students investigate even numbers as quantities that can be grouped into pairs with none left over. Through teacher modelling, pictorial representations and written examples, they identify even numbers from 0–1000, notice the ones-digit pattern, and connect even numbers to multiplication by 2. The lesson prepares students to contrast even and odd numbers in the following lesson.

Learning intentions

Students will:

• represent even numbers by making equal groups of two;
• identify even numbers to 1000 using the ones digit;
• connect doubling and multiplication by 2 to even numbers;
• explain how they know a number is even.

Success criteria

• I can show or explain how an even number makes pairs with none left over.
• I can identify even numbers to 1000.
• I can explain why numbers ending in 0, 2, 4, 6 or 8 are even.
• I can write an even-number fact using multiplication by 2.

Vocabulary

Even, pair, group of two, equal groups, none left over, ones digit, multiple, double, multiplication, product.

Curriculum links

• Multiplicative relations: represent and use multiplication structures to solve problems.
• Multiplicative relations: complete multiplication and division number sentences with missing values.
• Place value: use the ones digit and the role of zero to represent numbers to at least tens of thousands.
• Additive and multiplicative reasoning: explain and justify strategies using mathematical language.

Prior knowledge

Students should be able to count forwards and backwards, recognise two-digit and three-digit numbers, identify the ones digit, make equal groups, and recall some multiplication facts for 2.

Lesson structure (60 minutes)

1. 0–7 min · Hook and diagnostic. Display a visual of 14 counters arranged as pairs and 15 counters with one unpaired; ask, “What is different?” Model a quick prediction and invite students to share what “even” might mean. Record existing ideas without correcting them immediately.

2. 7–17 min · Teacher modelling: pairing. Model drawing pairs for 8, 11 and 20 on the board. Explicitly state: “An even number can be grouped into pairs with none left over.” Think aloud while recording each number as “pairs made” and “left over”. Use guided questions such as “What do you notice?” and “How do you know?” Students copy one worked example and complete two short written examples in their books.

3. 17–27 min · Visual representation and pattern. Draw paired dots or arrays for 6, 12 and 18, then write 2 × 3 = 6, 2 × 6 = 12 and 2 × 9 = 18. Guide students to examine the ones digits of a sequence of even numbers: 0, 2, 4, 6, 8, 10, 12, 14… Students complete 22, 24, 26, __, 30 in their books and explain the pattern. Emphasise that the tens and hundreds do not determine evenness; the ones digit does.

4. 27–39 min · Guided written practice: Even or not? Display numbers from 0–1000 one at a time. Model circling the ones digit and classifying the first examples, then students independently classify the remaining numbers on a worksheet or in their books. Ask selected students to justify answers with a paired-dot sketch or multiplication-by-2 fact. Pause for a hinge check: display 307, 418 and 560; students write E or not E and explain their choice. Use the pattern and hinge-question slides to support discussion.

5. 39–51 min · Teacher-led worked examples and questioning. Model a range of two- and three-digit examples, including zero and numbers ending in 1, 3, 5, 7 or 9. Think aloud while sorting them on the board into “even” and “not even”, then invite students to suggest where each example belongs and why. Work through three even numbers in two ways: a paired-dot or array drawing and a multiplication sentence using 2. Students complete parallel examples independently and finish the sentence “I know ___ is even because…”. Address the misconception that size determines evenness.

6. 51–56 min · Abstract consolidation. On the board, model related facts such as 2 × 17 = 34, 17 × 2 = 34 and 34 ÷ 2 = 17. Students complete missing-value sentences independently: 2 × __ = 46, __ × 2 = 80 and 72 ÷ 2 = __. Link the answers to the pairing model, not just recall. Use the multiplication connection and plenary slides.

7. 56–60 min · Independent exit task and preview. Students complete an individual exit ticket: (a) circle the even numbers: 205, 316, 427, 590; (b) explain why 316 is even; (c) complete 2 × __ = 316. Collect responses and preview: “Next lesson we will investigate numbers that leave one unpaired. What might their ones digits be?”

Resources

• the complete even-numbers teaching deck
• the even-number investigation worksheet
• Board or interactive display
• Prepared board examples or visualiser materials
• Mini-whiteboards, markers and erasers for hinge checks
• Pencils and highlighters
• Exit-ticket slips or exercise books

Assessment

• Question students during teacher modelling and written examples for accurate understanding of pairs and “none left over”.
• Review written classifications and paired-dot, array or multiplication justifications for accuracy.
• Use whiteboard hinge questions to check whether students use the ones digit rather than the number’s size.
• Review the individual exit ticket, especially the explanation and missing multiplication value, to identify students needing further modelling or written support next lesson.

Differentiation

• Support: begin with numbers to 100, provide paired-dot templates, highlight the ones digit, and offer the sentence starter “___ is even because ___”.
• For students needing additional support, rehearse counting in twos through teacher-led board examples and use a place-value chart to locate the ones digit. Accept oral explanations or annotated drawings before requiring a number sentence.
• EAL/D support: display visual examples for pair, equal groups, left over and even; model complete sentences and provide key vocabulary during guided questioning.
• Extension: students create a three-digit even number that satisfies a condition, such as “greater than 500 and ending in 6”, then write a related multiplication and division fact.

Teacher notes

Keep zero in the investigation and explicitly confirm that zero is even: it makes zero pairs with none left over. Avoid saying that even numbers are only numbers that can be divided; anchor the definition in the teacher-modelled equal-pairs representation first. During the final discussion, record the even ones digits in order—0, 2, 4, 6 and 8—so the next lesson can compare them with the ones digits of odd numbers.