3A · Chapter 4 · Lesson 6
Odd and Even Numbers
Recognize even numbers as numbers that can be paired with no item left over.
Today's challenge
Is 121 + 86 odd or even? Explain using pairs. Try your own method, then compare it with a model.
What you'll learn
- Recognize even numbers as numbers that can be paired with no item left over.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Groups of two and division with remainder.
Prerequisite competency: PREREQ-PRIOR-EQUAL-GROUPS
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Draw 2 groups of 3 counters and find the total.
Show answer and reasoning
Answer: 6
2 equal groups with 3 in each group make 2 × 3 = 6. This is prerequisite equal-group reasoning.
- E2
Draw 3 groups of 6 counters and find the total.
Show answer and reasoning
Answer: 18
3 equal groups with 6 in each group make 3 × 6 = 18. This is prerequisite equal-group reasoning.
Learn the concept
Words to know
- even number
- a whole number that can be arranged into pairs
- odd number
- a whole number with one unpaired item
Recognize even numbers as numbers that can be paired with no item left over.
An even number forms complete pairs; an odd number leaves exactly one unpaired item. Combining two odd collections pairs the leftover items.
Why this works
An even number can be paired with no counter left over. An odd number has one unpaired counter. When two odd collections are joined, their two leftovers form a new pair, so odd + odd is even. Three odd collections leave three counters; two pair up and one remains, so the sum is odd.
Check the meaning
Verify statements using concrete pairs or number expressions, not merely last-digit patterns.
Concrete → Pictorial → Abstract
- Build: Use counters, grid paper, or labeled bundles to represent the story or quantity.
- Draw: Sketch an array, place-value exchange, or equal-unit bar; label what is known.
- Calculate: Write an equation matching the representation and solve.
- Verify: Use an inverse operation or a second strategy to check.
For advanced students: if you can already explain this concept, start with the independent or challenge set.
Worked examples and immediate checks
Explain each step aloud or in writing. Work the fresh question before revealing its solution.
Worked example 1
Reason and verify
Is 121 + 86 odd or even? Explain using pairs.
- An even number forms complete pairs; an odd number leaves exactly one unpaired item. Combining two odd collections pairs the leftover items.
- 121 is odd, 86 is even; their sum 207 is odd because 207 leaves 1 unpaired item.
- Verify statements using concrete pairs or number expressions, not merely last-digit patterns.
Result: odd
Understanding check 1 — your turn
Is 145 + 88 odd or even? Explain using pairs.
Reveal reasoning
Answer: odd — 145 is odd, 88 is even; their sum 233 is odd because 233 leaves 1 unpaired item.
Worked example 2
Reason and verify
Is 138 + 17 odd or even? Explain using pairs.
- An even number forms complete pairs; an odd number leaves exactly one unpaired item. Combining two odd collections pairs the leftover items.
- 138 is even, 17 is odd; their sum 155 is odd because 155 leaves 1 unpaired item.
- Verify statements using concrete pairs or number expressions, not merely last-digit patterns.
Result: odd
Understanding check 2 — your turn
Is 162 + 19 odd or even? Explain using pairs.
Reveal reasoning
Answer: odd — 162 is even, 19 is odd; their sum 181 is odd because 181 leaves 1 unpaired item.
Worked example 3
Reason and verify
Is 155 + 28 odd or even? Explain using pairs.
- An even number forms complete pairs; an odd number leaves exactly one unpaired item. Combining two odd collections pairs the leftover items.
- 155 is odd, 28 is even; their sum 183 is odd because 183 leaves 1 unpaired item.
- Verify statements using concrete pairs or number expressions, not merely last-digit patterns.
Result: odd
Understanding check 3 — your turn
Is 34 + 30 odd or even? Explain using pairs.
Reveal reasoning
Answer: even — 34 is even, 30 is even; their sum 64 is even because 64 leaves 0 unpaired item.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Is 34 + 15 odd or even? Explain using pairs.
Show answer and reasoning
Answer: odd
34 is even, 15 is odd; their sum 49 is odd because 49 leaves 1 unpaired item.
- G2
Is 51 + 26 odd or even? Explain using pairs.
Show answer and reasoning
Answer: odd
51 is odd, 26 is even; their sum 77 is odd because 77 leaves 1 unpaired item.
- G3
Is 68 + 37 odd or even? Explain using pairs.
Show answer and reasoning
Answer: odd
68 is even, 37 is odd; their sum 105 is odd because 105 leaves 1 unpaired item.
- G4
Is 85 + 48 odd or even? Explain using pairs.
Show answer and reasoning
Answer: odd
85 is odd, 48 is even; their sum 133 is odd because 133 leaves 1 unpaired item.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Is 104 + 15 odd or even? Explain using pairs.
Show answer and reasoning
Answer: odd
104 is even, 15 is odd; their sum 119 is odd because 119 leaves 1 unpaired item.
- I2
Is 121 + 26 odd or even? Explain using pairs.
Show answer and reasoning
Answer: odd
121 is odd, 26 is even; their sum 147 is odd because 147 leaves 1 unpaired item.
- I3
Is 138 + 37 odd or even? Explain using pairs.
Show answer and reasoning
Answer: odd
138 is even, 37 is odd; their sum 175 is odd because 175 leaves 1 unpaired item.
- I4
Is 155 + 48 odd or even? Explain using pairs.
Show answer and reasoning
Answer: odd
155 is odd, 48 is even; their sum 203 is odd because 203 leaves 1 unpaired item.
- I5
Is 172 + 59 odd or even? Explain using pairs.
Show answer and reasoning
Answer: odd
172 is even, 59 is odd; their sum 231 is odd because 231 leaves 1 unpaired item.
- I6
Is 44 + 70 odd or even? Explain using pairs.
Show answer and reasoning
Answer: even
44 is even, 70 is even; their sum 114 is even because 114 leaves 0 unpaired item.
- I7
Is 61 + 81 odd or even? Explain using pairs.
Show answer and reasoning
Answer: even
61 is odd, 81 is odd; their sum 142 is even because 142 leaves 0 unpaired item.
- I8
Is 78 + 92 odd or even? Explain using pairs.
Show answer and reasoning
Answer: even
78 is even, 92 is even; their sum 170 is even because 170 leaves 0 unpaired item.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
Explain using pairs why any odd number added to another odd number gives an even number.
Show answer and reasoning
Answer: Even
Each odd collection leaves one unpaired counter; the two leftovers make a complete pair.
- C2
Does the sum of three odd whole numbers have to be odd? Show why using pairing.
Show answer and reasoning
Answer: Yes
Each odd number contributes one unpaired counter. Three leftover counters form a pair and one leftover: odd.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Is 99 + 15 odd or even? Explain using pairs.
Show answer and reasoning
Answer: even
99 is odd, 15 is odd; their sum 114 is even because 114 leaves 0 unpaired item.
- E2
Is 116 + 26 odd or even? Explain using pairs.
Show answer and reasoning
Answer: even
116 is even, 26 is even; their sum 142 is even because 142 leaves 0 unpaired item.
- E3
Is 133 + 37 odd or even? Explain using pairs.
Show answer and reasoning
Answer: even
133 is odd, 37 is odd; their sum 170 is even because 170 leaves 0 unpaired item.