Rates and compound measures (speed, density, and best buys)

Calculate and compare rates and compound measures (speed, density, and unit price/best buys) using the product relationship top = left x right, and interpret distance-time and speed-time graphs.

 Worksheet Builder All resources ☕ Shout us a flat white Download All

Te reo Māori terms

click each term to open in Te Aka

Related resources in Measurement

Open notes PDF
Open terms PDF
Open worksheet PDF Open solutions PDF
Open tasks PDF Open solutions PDF
Open tasks PDF Open solutions PDF
Open tasks PDF Open solutions PDF

Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA5-4
  • NA6-8
New NZC (2026)
  • NZC26-P4-NUM-FIN-K-Y10-01
  • NZC26-P4-NUM-FIN-P-Y10-02
  • NZC26-P4-NUM-NSO-P-Y10-11
  • NZC26-P4-NUM-FIN-K-Y9-07
  • NZC26-P4-MEA-MEA-K-Y9-05
  • NZC26-P4-MEA-MEA-P-Y9-10
  • NZC26-P4-MEA-MEA-P-Y10-11
  • NZC26-P4-MEA-MEA-P-Y9-09
  • NZC26-P4-MEA-MEA-K-Y9-10

Resources

Terminology

  • Rate
  • Compound measure
  • Derived unit
  • Speed
  • Distance
  • Density
  • Unit rate
  • Best buy

Task goals

  • Calculate speed given distance and time, using speed = distance / time.
  • Rearrange the same relationship to find distance (= speed x time) or time (= distance / speed).
  • Apply the same product-relationship structure to density (mass, volume) and unit price (cost, quantity) to compare best buys.
  • Compare two or more unit rates to decide which option is better value.
  • Interpret a distance-time or speed-time graph: read off values, identify stationary/constant-speed sections, and find the speed represented by a section's gradient.

Where this fits

What leads into this objective, and where it goes next.

Before

Ratios and Rates: Simplifying, Dividing and Comparing

Ratios and Rates: Simplifying, Dividing and Comparing

Simplifying Fractions

Simplifying Fractions

Ratios: Simplifying, Equivalent Ratios, and Sharing a Quantity

Ratios: Simplifying, Equivalent Ratios, and Sharing a Quantity

You are here

Rates and compound measures (speed, density, and best buys)

Rates and compound measures (speed, density, and best buys)

Know

A rate proportionally compares two quantities that have different units of measure; when working with rates, 'per' means 'for every' in day-to-day contexts.

Statement▸
Year 9 · Number · Financial mathematics
NZC26-P4-NUM-FIN-K-Y9-07
Know

Derived units (e.g. cm^2, km/h) reflect a relationship—a product or quotient—between two different measurements.

Statement▸
Year 9 · Measurement · Measuring
NZC26-P4-MEA-MEA-K-Y9-05

Next

Converting currency using an exchange rate, and working with ratios

Converting currency using an exchange rate, and working with ratios

Ratios and Rates: Simplifying, Dividing and Comparing

Ratios and Rates: Simplifying, Dividing and Comparing

Estimating Measurements and Rounding to Significant Figures

Estimating Measurements and Rounding to Significant Figures

Also under NA5-4:

Also under NA6-8:

Explore the whole sequence →

For teachers

Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.