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CBSE Class 5 · Mathematics

Animal Jumps

Official NCERT chapter from Math-Mela (book code eemm1). ExamMaster notes are original teaching at CBSE Class 5 depth.

This lesson follows the official chapter “Animal Jumps” in Math-Mela. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 5
  • Easy level
  • 8 concepts

1A mystery box multiplies what goes in

A box that “× 4” turns 5 into 20. The rule is multiply, not add, unless the box says add.

Guessing the out-number without the rule is not the box.

Figure. The mystery box multiplies. 7 goes in, the box is ×9, 63 comes out. That is 7 groups of 9, not a new kind of count.

How it works

  1. Read the box rule× 4, or another factor.
  2. Put a number in5.
  3. Write the product out20.

2Factors of a number make arrays that tile

Factors of 12 are numbers that make a rectangle of 12 tiles: 1×12, 2×6, 3×4. A 5-wide array does not tile 12.

A factor is a side that tiles, not a pretty number.

Figure. 20 tiles as 5 rows of 4. Those side counts are factors of 20. A leftover cell would mean the groups were not equal.

How it works

  1. Pick a candidate side3.
  2. See if it tiles 123 × 4 = 12.
  3. If it leaves a gap, it is not a factor5 does not tile 12.

3Common factors of several numbers

A common factor of 12 and 18 divides both. 6 divides both; 8 does not.

A factor of only one number is not common.

Figure. Factors of 12 and of 18. The shared marks are 1, 2, 3, 6. The greatest of those, 6, is the HCF.

How it works

  1. List factors of A12: 1,2,3,4,6,12.
  2. List factors of B18: 1,2,3,6,9,18.
  3. Keep the overlap1, 2, 3, 6.

4A multiple is a product of factors

Multiples of 4 are 4, 8, 12, 16, … — products 4 \times 1, 4 \times 2, \ldots. 14 is not a multiple of 4.

A factor and a multiple are different seats: 3 is a factor of 12; 24 is a multiple of 12.

Figure. 4 + 4 + 4 + 4 = 16. Each landing is a multiple of 4. 16 is also 4 rows of 4.

How it works

  1. Fix the number4.
  2. Skip-count by that number4, 8, 12, …
  3. Those landings are multiplesA miss is not a multiple.

5Twelve is a multiple of each of its factors

Because 3 × 4 = 12, 12 is a multiple of 3 and of 4. The product sits in both skip-counts.

12 is not a multiple of 5.

Figure. Four jumps of 3 land on 12, so 12 is a multiple of 3. The same 12 is also 6×2, 4×3, 3×4, 2×6, and 1×12.

How it works

  1. Take a factor of 123.
  2. See 12 in the ×3 skip-count3, 6, 9, 12.
  3. Call 12 a multiple of that factorYes.

Is 12 a multiple of 5?

Skip-count by 5: 5, 10, 15. Does 12 land?

  • Skip5, 10, 15
  • 12 in the list?no
  • Multiple of 5?no

Pro tip. A multiple must land on the skip-count. 12 lands on 3 and 4, not on 5.

6The number itself is always a factor

12 ÷ 12 = 1, so 12 is a factor of 12. 1 is also a factor. Do not forget the ends of the list.

A list that skips 1 and the number itself is incomplete.

Figure. Every number tiles as one row of itself. So the number is always a factor of itself, paired with 1.

How it works

  1. Include 11 × n = n.
  2. Include nn × 1 = n.
  3. Then list the middle tilesThe rest of the arrays.

7Make arrays to list factors

Build every rectangle that tiles n. Each pair of sides is a factor pair. That is the list.

A mental skip without a tile can miss a pair.

Figure. Three arrays that each hold 12 cells: 1×12, 2×6, 3×4. Same area, different side pairs — those sides are the factor pairs of 12.

How it works

  1. Start at 11 × n.
  2. Try 2, 3, … until sides meetStop at repeats.
  3. Write each pairThe factor list.

8The jumps name the tokens; the arrays are the maths

Animal jumps are the picture. Factors, multiples, and box-rules are the maths.

Do not invent a jump-only factor.

Figure. Seven equal jumps of 6 land on 42. The jump names the token; 7 rows of 6 is the same product.

How it works

  1. Keep the settingJumps.
  2. Compute on arrays and skip-countsFactors and multiples.
  3. Use school × and ÷The animal is not a new rule.
A common factor of 12 and 18 is
  1. 6 (among others)
  2. 8
  3. 5

6 divides both. 8 divides neither 12 nor 18 evenly in both.

Notes

  • The official chapter title is “Animal Jumps”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Formulas

  • If a\times b = n then a and b are factors of n, and n is a multiple of each.
  • Common factor: divides every number in the set.
  • Always include 1 and n in the factor list of n.

Recap

Hold these pegs from the official chapter “Animal Jumps”. The wording is ExamMaster’s teaching, not a textbook recap.

A mystery box multiplies what goes in
A box that “× 4” turns 5 into 20. The rule is multiply, not add, unless the box says add.
Factors of a number make arrays that tile
Factors of 12 are numbers that make a rectangle of 12 tiles: 1×12, 2×6, 3×4.
Common factors of several numbers
A common factor of 12 and 18 divides both.
A multiple is a product of factors
Multiples of 4 are 4, 8, 12, 16, … — products 4 \times 1, 4 \times 2, \ldots.
Twelve is a multiple of each of its factors
Because 3 × 4 = 12, 12 is a multiple of 3 and of 4.
The number itself is always a factor
12 ÷ 12 = 1, so 12 is a factor of 12. 1 is also a factor. Do not forget the ends of the list.

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