CBSE Class 5 · Mathematics
The Dairy Farm
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 “The Dairy Farm” 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
1Multiplication facts hide in arrays of pouches
3 rows of 6 pouches is 3 \times 6 = 18. The array is the fact you can see.
A scattered pile is not an array until you make rows.
Figure. Twelve buttermilk pouches sit as 3 rows of 4. The array is the multiplication sentence 3 × 4 = 12, not twelve separate counts.
How it works
- Make equal rowsSame count each.
- Count rows and row-size3 and 6.
- Write the product18 pouches.
2The same product can be many groupings
18 = 3 × 6 = 2 × 9 = 1 × 18. Same pouch-count, new grouping.
A new grouping is not 18 extra pouches.
Figure. The same twelve pouches can be 2 rows of 6 or 3 rows of 4. The product stayed; only the grouping changed.
How it works
- Fix the total18.
- Find another pair of factors2 and 9.
- Check the productStill 18.
3Place digits to get a product near a target
Using 3, 4, 5 you might try 34 × 5 = 170 or 45 × 3 = 135. Near a target means compute, then compare.
Arranging digits without multiplying is a decoration.
Figure. Digits 2, 4, 6, 8 can sit in different houses. 64 × 28 = 1792 sits nearest the 1800 target; 46 × 28 undershoots; 82 × 46 overshoots.
How it works
- Hear the targetNear 150.
- Form a product with the digitsOne try.
- Compute and see the gapNear, or far.
4A two-digit mystery number needs every clue
Tens-digit even, product with 4 is 72: ones and tens must both satisfy. Drop a clue and many numbers fit.
One clue is not the mystery solved.
Figure. A two-digit mystery needs every clue. Tens digit 4, even, ones digit 8 — only 48 sits on the 40–50 line and keeps all three.
How it works
- List the cluesEvery one.
- Try a candidateDoes it pass all?
- If one clue fails, drop itKeep searching.
5Equal groups of buttermilk pouches
5 crates of 8 pouches are 5 groups of 8. Multiplication names that.
Crates of mixed counts are not one equal-group story.
Figure. Equal groups of buttermilk pouches: three crates, four pouches in each crate. 3 × 4 = 12 is the groups sentence, not a new count.
How it works
- Name groups5 crates.
- Name size8 each.
- Multiply40 pouches.
Crates of pouches
6 crates, 8 pouches each. How many pouches?
- Groups6
- Size8
- Product6 × 8 = 48
Pro tip. Equal groups. Check: 48 ÷ 8 = 6 crates.
6Estimate a product
6 × 8 is near 5 × 8 = 40 or 6 × 10 = 60. Estimate by nearby facts, then compute exactly.
The estimate is a neighbour.
Figure. 48 × 21 is near 50 × 20. The estimate 1000 sits on the dashed rule; the exact product 1008 is a hair taller. Estimation is a nearby product, not a guess.
How it works
- Round a factor8 → 10, or 6 → 5.
- Use a known factA neighbour product.
- Then compute exactly48.
7Check by splitting the groups
6 × 8 = (5 × 8) + (1 × 8) = 40 + 8 = 48. A split rebuilds the product.
A split that loses a group is a broken check.
Figure. Split 14 into 10 and 4. Then 6 × 14 = 6 × 10 + 6 × 4 = 60 + 24 = 84. The stacked bar and the check bar are the same length.
How it works
- Split one factor6 = 5 + 1.
- Multiply each part40 and 8.
- Add48, or redo.
8The dairy is the story; the arrays are the maths
Pouches and crates are the picture. Factors and products are the maths.
Do not invent a dairy-only times.
Figure. The farm is the story; the array is the maths. Twenty-four pouches at the dairy become a 4 × 6 grid you can count by rows or by columns.
How it works
- Keep the settingA farm.
- Compute on the arrayRows × columns.
- Use ordinary ×The farm is not a new rule.
3 rows of 6 pouches are
- 18 pouches
- 9 pouches
- 36 crates
3 × 6 = 18.
Notes
- The official chapter title is “The Dairy Farm”. 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
- Rows \times row-size = product.
- Same product, new grouping: 18 = 3\times 6 = 2\times 9.
- Check: (a+b)\times c = a\times c + b\times c.
Recap
Hold these pegs from the official chapter “The Dairy Farm”. The wording is ExamMaster’s teaching, not a textbook recap.
- Multiplication facts hide in arrays of pouches
- 3 rows of 6 pouches is 3 \times 6 = 18. The array is the fact you can see.
- The same product can be many groupings
- 18 = 3 × 6 = 2 × 9 = 1 × 18. Same pouch-count, new grouping.
- Place digits to get a product near a target
- Using 3, 4, 5 you might try 34 × 5 = 170 or 45 × 3 = 135.
- A two-digit mystery number needs every clue
- Tens-digit even, product with 4 is 72: ones and tens must both satisfy.
- Equal groups of buttermilk pouches
- 5 crates of 8 pouches are 5 groups of 8. Multiplication names that.
- Estimate a product
- 6 × 8 is near 5 × 8 = 40 or 6 × 10 = 60. Estimate by nearby facts, then compute exactly.
Practise The Dairy Farm
Reading is free and needs no account. Practice, mocks and progress live in the app.
- A 4-question practice set that ends the chapter
- 1 quick check with worked explanations
- Timed mocks scored with the real marking scheme
- Readiness tracked per topic, kept on your device