Mathematics Worksheet: Patterns, Odd and Even (Preparatory Stage)
Based on NCERT “Let Us Count – Patterns Around Us” (demm103.pdf). Concepts, computation, and reasoning – each question has a hidden answer and a detailed solution.
Concepts
- What is a “pattern” in mathematics?
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Answer: A repeating sequence using numbers, shapes, or objects.Show Solution
Solution: Example: red, blue, red, blue,… or 2, 4, 6, 8,… - Group the numbers 2, 3, 5, 6 as odd or even.
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Answer: Even: 2, 6; Odd: 3, 5Show Solution
Solution: Even numbers pair up; odd numbers always have one left. - If 1 picture = 5 coconuts, how many for 20 coconuts?
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Answer: 4 picturesShow Solution
Solution: 20 ÷ 5 = 4 - Write the next three numbers in the pattern: 3, 6, 9, ___, ___, ___
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Answer: 12, 15, 18Show Solution
Solution: Pattern increases by 3 each time. - What makes a number “even”?
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Answer: Can be split into pairs with nothing left over.Show Solution
Solution: Even numbers always end in 0, 2, 4, 6, 8. - How many 5-rupee coins are needed to make 25 rupees?
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Answer: 5Show Solution
Solution: 25 ÷ 5 = 5 coins - What comes next: triangle, circle, triangle, circle, ___?
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Answer: TriangleShow Solution
Solution: Alternates back and forth – triangle after circle. - Arrange coins of 2, 5, 10 rupees in order from least to greatest value.
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Answer: 2, 5, 10Show Solution
Solution: Value increases: 2 < 5 < 10 - How many ways can you pair the numbers 1 to 6 into “even” pairs?
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Answer: 3 pairs: (2,4,6) are evenShow Solution
Solution: 2 with 4, 4 with 6, 2 with 6, etc.; all even numbers. - Is the number 11 even or odd? Prove with a model.
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Answer: Odd; if you pair up 10, 1 is left.Show Solution
Solution: Draw dot pairs: 11th dot stands alone.
Computational Skills
- How many coconuts from 7 trees if each has 5?
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Answer: 35Show Solution
Solution: 7 × 5 = 35 - If a tray has 4 rows of 3 laddoos, how many in total?
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Answer: 12Show Solution
Solution: 4 × 3 = 12 - If a pattern has coins of value 1, 2, 5, and 10, what is the total for 3 of each?
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Answer: 1×3 + 2×3 + 5×3 + 10×3 = 3 + 6 + 15 + 30 = 54Show Solution
Solution: Total = (number × value) for each, then add up. - Muniamma made 5 trays of 4 laddoos each; how many laddoos?
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Answer: 20Show Solution
Solution: 5 × 4 = 20 - Shiv’s coins are arranged in a triangle: first row 3, next 5, next 7. Total coins?
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Answer: 3 + 5 + 7 = 15Show Solution
Solution: Add each row to get total. - What is the sum of all even numbers between 1 and 10?
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Answer: 2+4+6+8+10 = 30Show Solution
Solution: Count and add each even number. - How many odd numbers between 1 and 20?
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Answer: 10Show Solution
Solution: Odd = 1,3,5,...,19: total is 10. - Write any two 2-digit numbers (using 1 and 6, no repeat) and state if they're even or odd.
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Answer: 16 (even), 61 (odd)Show Solution
Solution: Even end in 0,2,4,6,8; odd in 1,3,5,7,9. - Are all numbers in the 2-times table even? Why?
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Answer: Yes; all can be grouped in pairsShow Solution
Solution: Multiplying by 2 always produces an even. - Combine coins: If Shirley has two coins of 5 and Shiv has three of 2, who has more and by how much?
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Answer: Shirley: 2×5=10; Shiv: 3×2=6; Shirley has 4 moreShow Solution
Solution: Compare their totals.
Problem-Solving & Real World Modeling
- Draw and label: circle even numbers, square odd numbers from 1–10.
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Answer: Even: 2,4,6,8,10 (circle); Odd: 1,3,5,7,9 (square)Show Solution
Solution: Practice identifying and drawing. - Which is greater: sum of all odd numbers 1–10 or sum of all even numbers 1–10?
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Answer: Even sum = 30; Odd sum = 25; even is greater.Show Solution
Solution: Add each group, compare results. - Choose 5 numbers in a row. Do you have more even or more odd numbers? Try with 1–5 and 10–14.
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Answer: Always 3 odds, 2 evens (for odd start); always 3 evens, 2 odds (for even start)Show Solution
Solution: Try both examples, see pattern. - If you have 3 trays stacked with 8 laddu each, but remove 2 from 2 trays, how many left in all?
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Answer: (8+6+6) = 20Show Solution
Solution: Only 1 tray stays at 8, 2 have 6. - Make two 2-digit odd numbers using only the digits 3 and 7 (without repeating digits).
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Answer: 37, 73Show Solution
Solution: Both 37, 73 are odd (end with odd number). - Can you spot any pattern in the page numbers of your math book?
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Answer: Odd numbers on right, even on left.Show Solution
Solution: Check an open book to see the pattern. - True or false: Both numbers before and after an odd number are even. What about before/after an even?
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Answer: True for odd; yes for even (will be odd).Show Solution
Solution: Try examples: before/after odd is even; before/after even is odd. - Circle the odd numbers: 41, 32, 17, 54, 23, 80
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Answer: 41, 17, 23Show Solution
Solution: All numbers ending with 1,3,5,7,9. - Count: How many even numbers are there between 1 and 50? Write the first and last ones.
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Answer: 25, first: 2, last: 50Show Solution
Solution: 2 to 50, step of 2: (50-2)/2 + 1 = 25 - Challenge: Is there always one more odd number than even between 1 and n if n is odd? Check with examples.
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Answer: Yes; try: 1–5 (3 odds, 2 evens), 1–7 (4 odds, 3 evens)Show Solution
Solution: For n odd, always one more odd than even.