Reference / Curriculum / 3B / Chapter 11

3B · Chapter 11 · Lesson 6

Kilograms and Grams

Model mass and convert kilograms to grams and vice versa.

MATH-3B-C11-L06Independent and tutor-supported

Today's mathematical question

Express 8,650 g as kg and g.

Learning target

Model mass and convert kilograms to grams and vice versa.

Before starting: Prior lesson: Liters and Milliliters. Try the warm-up independently.

Prerequisite · 3 questions

Check earlier skills first

These are earlier ideas you need for today; revisit them if they are difficult.

  1. P1

    Convert 8 L 480 mL into mL.

    Reveal explanation

    Answer: 8,480 mL

    8 L = 8,000 mL; add 480 to make 8,480 mL.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  2. P2

    Express 7,040 mL as L and mL.

    Reveal explanation

    Answer: 7 L 40 mL

    Partition 7,040 into 7 full groups of 1,000 plus 40.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. P3

    Convert 6 L 875 mL into mL.

    Reveal explanation

    Answer: 6,875 mL

    6 L = 6,000 mL; add 875 to make 6,875 mL.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Learn and understand

Mass measures how much matter an object contains. One kilogram equals 1,000 grams, so 3 kg 85 g is 3,085 g. A bag of flour and a bottle of juice can use different units; choose the unit appropriate to the question. Add or subtract only after the units match. One kilogram has 1,000 grams. A parcel of 2 kg 80 g weighs 2,080 g. Avoid treating 80 g as 800 g; each digit has a place value.

Represent it three ways

  1. Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
  2. Pictorial: Use full-kilogram and leftover-gram boxes. Exchange one kilogram for 1,000 grams when necessary.
  3. Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.

Important vocabulary

kilogram
metric mass unit equal to 1,000 g
gram
smaller metric mass unit
mass
quantity measured with a balance

Fully worked examples and checks

Try each new understanding check before revealing the explanation.

Worked example 1

Explore, calculate, verify

Express 8,650 g as kg and g.

1 kg1000 g each=1,000 g
One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  1. Identify the whole, the units, and what the question asks.
  2. Partition 8,650 into 8 full groups of 1,000 plus 650.
  3. Check that the answer uses the right units and makes sense.

Answer: 8 kg 650 g

Check your understanding 1

Express 6,480 g as kg and g.

Reveal answer and explanation

6 kg 480 g — Partition 6,480 into 6 full groups of 1,000 plus 480.

1 kg1000 g each=1,000 g
One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Worked example 2

Explore, calculate, verify

Convert 8 kg 250 g into g.

1 kg1000 g each=1,000 g
One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  1. Identify the whole, the units, and what the question asks.
  2. 8 kg = 8,000 g; add 250 to make 8,250 g.
  3. Check that the answer uses the right units and makes sense.

Answer: 8,250 g

Check your understanding 2

Convert 3 kg 480 g into g.

Reveal answer and explanation

3,480 g — 3 kg = 3,000 g; add 480 to make 3,480 g.

1 kg1000 g each=1,000 g
One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Worked example 3

Explore, calculate, verify

Express 2,875 g as kg and g.

1 kg1000 g each=1,000 g
One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  1. Identify the whole, the units, and what the question asks.
  2. Partition 2,875 into 2 full groups of 1,000 plus 875.
  3. Check that the answer uses the right units and makes sense.

Answer: 2 kg 875 g

Check your understanding 3

Express 8,040 g as kg and g.

Reveal answer and explanation

8 kg 40 g — Partition 8,040 into 8 full groups of 1,000 plus 40.

1 kg1000 g each=1,000 g
One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Guided · 5 questions

Guided practice

Keep the model and earlier examples visible while practising.

  1. G1

    Convert 2 kg 65 g into g.

    Reveal explanation

    Answer: 2,065 g

    2 kg = 2,000 g; add 65 to make 2,065 g.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  2. G2

    Express 4,250 g as kg and g.

    Reveal explanation

    Answer: 4 kg 250 g

    Partition 4,250 into 4 full groups of 1,000 plus 250.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. G3

    Convert 3 kg 125 g into g.

    Reveal explanation

    Answer: 3,125 g

    3 kg = 3,000 g; add 125 to make 3,125 g.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  4. G4

    Express 3,375 g as kg and g.

    Reveal explanation

    Answer: 3 kg 375 g

    Partition 3,375 into 3 full groups of 1,000 plus 375.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  5. G5

    Convert 3 kg 20 g into g.

    Reveal explanation

    Answer: 3,020 g

    3 kg = 3,000 g; add 20 to make 3,020 g.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Independent · 8 questions

Independent practice

Work these without hints and explain the method used. Write answers on paper.

  1. I1

    Convert 7 kg 375 g into g.

    Reveal explanation

    Answer: 7,375 g

    7 kg = 7,000 g; add 375 to make 7,375 g.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  2. I2

    Express 7,650 g as kg and g.

    Reveal explanation

    Answer: 7 kg 650 g

    Partition 7,650 into 7 full groups of 1,000 plus 650.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. I3

    Convert 7 kg 65 g into g.

    Reveal explanation

    Answer: 7,065 g

    7 kg = 7,000 g; add 65 to make 7,065 g.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  4. I4

    Express 5,375 g as kg and g.

    Reveal explanation

    Answer: 5 kg 375 g

    Partition 5,375 into 5 full groups of 1,000 plus 375.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  5. I5

    Convert 7 kg 250 g into g.

    Reveal explanation

    Answer: 7,250 g

    7 kg = 7,000 g; add 250 to make 7,250 g.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  6. I6

    Express 3,055 g as kg and g.

    Reveal explanation

    Answer: 3 kg 55 g

    Partition 3,055 into 3 full groups of 1,000 plus 55.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  7. I7

    Convert 7 kg 875 g into g.

    Reveal explanation

    Answer: 7,875 g

    7 kg = 7,000 g; add 875 to make 7,875 g.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  8. I8

    Express 7,875 g as kg and g.

    Reveal explanation

    Answer: 7 kg 875 g

    Partition 7,875 into 7 full groups of 1,000 plus 875.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Challenge · 2 questions

Challenge and error analysis

Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.

  1. C1

    Explain why 6 kg 250 g equals 6,250 g.

    Reveal explanation

    Answer: 6,250 g

    Each kg is 1,000 g. Add the remaining 250 g.

  2. C2

    A measurement is 6,125 g. Explain why its mixed-unit form is 6 kg 125 g.

    Reveal explanation

    Answer: 6 kg 125 g

    There are 6 full groups of 1,000 g and 125 leftover g.

Exit · 3 questions

Exit check

Solve independently, then return on another day to check retention.

  1. E1

    Convert 7 kg 125 g into g.

    Reveal explanation

    Answer: 7,125 g

    7 kg = 7,000 g; add 125 to make 7,125 g.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  2. E2

    Convert 8 kg 650 g into g.

    Reveal explanation

    Answer: 8,650 g

    8 kg = 8,000 g; add 650 to make 8,650 g.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. E3

    Express 4,875 g as kg and g.

    Reveal explanation

    Answer: 4 kg 875 g

    Partition 4,875 into 4 full groups of 1,000 plus 875.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
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