Measurement of Length and Motion · Answer guide

Lesson 1 · Use units that everyone can compare

Choose and convert common length units without changing the measured object.

1. Which record is a complete length measurement?

   Answer: 18 cm. 18 cm gives both the number and the unit. A number alone does not tell the scale.

2. A strip is 4 cm long. What is its length in millimetres?

   Answer: 40 mm. Each centimetre contains 10 millimetres, so 4 × 10 = 40 mm.

3. Why can two learners count different hand spans for the same desk?

   Answer: Their hand spans may be different sizes. Hand spans vary between people; the desk can stay exactly the same length.

Discuss: Find two labelled lengths at home. Rewrite each in a second suitable unit and explain why both records describe the same length.

Teaching note: A larger unit does not mean a larger object: 2 m and 200 cm describe the same length. Open responses need discussion; they are not automatically marked.

Lesson 2 · Measure carefully and check the starting mark

Read a ruler and calculate a length from two endpoints.

1. A pencil runs from 2 cm to 8 cm on a ruler. Its length is…

   Answer: 6 cm. The measured interval is 8 − 2 = 6 cm.

2. Where should your eye be when reading the endpoint?

   Answer: Directly above the mark. Looking directly above the mark reduces apparent shifting of the endpoint.

3. How can a flexible thread help measure a curved drawing?

   Answer: Lay it along the curve, then measure its marked length. The marked thread follows the curve and can then be straightened for measurement without stretching.

Discuss: Draw a curved path on paper. Estimate its length, measure it with a non-stretchy thread, and record how you kept the thread on the path.

Teaching note: A ruler reading of 9 cm is not always the object’s length. If the object begins at 2 cm, its length is 7 cm. Open responses need discussion; they are not automatically marked.

Lesson 3 · Describe motion using a reference

Explain motion relative to a named reference and recognise different paths.

1. A passenger sits still in a moving bus. Relative to the seat, the passenger is…

   Answer: at rest. The passenger’s position relative to the seat stays the same. Relative to the road, the description differs.

2. Which observation best identifies motion relative to a tree?

   Answer: Its position relative to the tree changes over time. Motion relative to the tree is established by changing position over time.

3. The tip of a clock’s rotating second hand follows which path?

   Answer: A circular path around the clock centre. The tip stays the same distance from the clock centre while travelling around it.

Discuss: Observe a clock’s second-hand tip or a safe toy. Name your reference and describe the path. Do not step onto roads or moving vehicles to make observations.

Teaching note: A passenger can be still relative to a seat while moving relative to the road. These two descriptions do not contradict each other. Open responses need discussion; they are not automatically marked.

Final check · Set 1

Try one set after the lessons. Use the other set after reviewing any errors.

1. Convert 3 m to centimetres.

   300 cm. Each metre has 100 centimetres, so 3 m = 300 cm.

2. Which unit is suitable for a distance between towns?

   km. Kilometres describe long travel distances conveniently.

3. A strip starts at 4 cm and ends at 13 cm. How long is it?

   9 cm. The interval is 13 − 4 = 9 cm.

4. Which method best measures a curved pencil line?

   Place thread along the curve and measure it without stretching. The thread follows the path; the straight gap misses the curve’s length.

5. A seated passenger is moving relative to…

   a tree beside the road as the bus passes. The passenger changes position relative to the roadside tree.

6. A playground swing moves back and forth. This is…

   oscillatory motion. The repeated back-and-forth movement about a central position is oscillatory.

Final check · Set 2

Try one set after the lessons. Use the other set after reviewing any errors.

1. Convert 70 mm to centimetres.

   7 cm. Ten millimetres make one centimetre, so 70 ÷ 10 = 7 cm.

2. Two students get different counts using their feet. What improves comparison?

   Use the same standard unit. Using an agreed standard unit avoids differences in foot size.

3. A card lies from 1.5 cm to 6.5 cm. Its length is…

   5 cm. 6.5 − 1.5 = 5 cm.

4. The zero edge of a ruler is broken. A valid method is…

   Start at a clear mark and subtract that reading. A length is the interval between two known marks.

5. What must change to show motion relative to a bench?

   Position relative to the bench over time. Changing relative position over time gives evidence of motion.

6. The tip of a fan blade turning about a fixed centre traces…

   a circular path. A blade tip rotates around the centre at a fixed distance.