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In Context: Measuring and Basics
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Foundational skills
Read a decimal from a number line
\[ \text{6th mark after 2.3} \to 2.36 \]
Read decimal values from a marked number line.
Identify place value in measurement contexts
\[ \text{In } 23.7°C, \text{ value of 7?} \]
Identify the place value of a digit in a decimal measurement.
Order three decimals in measurement context
\[ 2.15, 2.3, 2.8 \text{ in order} \]
Order three decimal measurements from smallest to largest.
Reading measurements from scales
Read length from a ruler
\[ \text{7th mark after 12 cm} \to 12.7 \]
Read a decimal length measurement from a ruler.
Read mass from kitchen scales
\[ \text{Halfway 1.2 to 1.3} \to 1.25 \]
Read a decimal mass from scales marked between two values.
Read capacity from measuring jug
\[ \text{3rd mark after 1L} \to 1.3 \]
Read decimal capacity from a marked measuring vessel.
Read temperature from thermometer
\[ \text{4th mark after 20°C} \to 20.8 \]
Read a decimal temperature from a marked thermometer.
Read race time from stopwatch
\[ \text{Display: } 12.34 \text{ s} \]
Read decimal time from a digital display.
Comparing and ordering
Which measurement is larger
\[ 2.45 \text{ m vs } 2.7 \text{ m?} \]
Compare two decimal measurements.
Find the difference between measurements
\[ 1.72 – 1.45 = 0.27 \text{ m} \]
Find the difference between two decimal measurements.
Find which is closest to target
\[ \text{Closest to } 2.5: 2.3, 2.6, 2.8 \]
Determine which measurement is closest to a target value.
Order four or more decimal measurements
\[ \text{Race times: fastest to slowest} \]
Order multiple decimal measurements.
Rounding in context
Round measurement to nearest whole unit
\[ 3.7 \text{ kg} \to 4 \text{ kg} \]
Round a decimal measurement to the nearest whole number.
Round measurement to 1 decimal place
\[ 15.73 \text{ s} \to 15.7 \text{ s} \]
Round a decimal measurement to 1 decimal place.
Round to appropriate precision for context
\[ 245.673 \text{ g} \to 246 \text{ g} \]
Round to appropriate precision based on practical context.
Round to nearest tenth
\[ 23.47°C \to 23.5°C \]
Round a decimal to nearest tenth (1 d.p.).
Adding decimals in context
Add two measurements with same decimal places
\[ 2.3 + 1.5 = 3.8 \text{ L} \]
Add two decimal measurements with the same number of decimal places.
Add two measurements with different decimal places
\[ 3.2 + 1.75 = 4.95 \text{ m} \]
Add two decimal measurements with different numbers of decimal places.
Add three or more decimal measurements
\[ 0.5 + 1.2 + 0.8 = 2.5 \text{ kg} \]
Add three or more decimal measurements.
Add measurements requiring conversion
\[ 1.5 \text{ L} + 300 \text{ ml} = 1.8 \text{ L} \]
Add measurements given in different units of the same type.
Find total time in decimal hours
\[ 2.5 + 1.75 = 4.25 \text{ hours} \]
Add decimal times expressed in hours.
Subtracting decimals in context
Subtract measurements with same decimal places
\[ 2.5 – 0.8 = 1.7 \text{ L} \]
Subtract decimal measurements with the same number of decimal places.
Subtract measurements with different decimal places
\[ 5.2 – 1.65 = 3.55 \text{ m} \]
Subtract decimal measurements with different numbers of decimal places.
Find how much more is needed
\[ \text{Need } 3, \text{ have } 1.6 \to 1.4 \]
Calculate the additional amount needed to reach a target.
Compare by finding difference
\[ 14.3 – 13.8 = 0.5 \text{ s faster} \]
Find time difference to determine ‘how much faster/slower’.
Temperature drop
\[ 18.5 – 12.3 = 6.2°C \text{ drop} \]
Calculate decrease in temperature (positive values only).
Basic multiplication
Multiply decimal by single-digit whole number
\[ 1.5 \times 4 = 6 \text{ L} \]
Multiply a decimal by a single-digit whole number.
Multiply decimal by two-digit whole number
\[ 2.5 \times 12 = 30 \text{ kg} \]
Multiply a decimal by a two-digit whole number.
Find total distance in stages
\[ 4 \text{ laps} \times 0.4 = 1.6 \text{ km} \]
Calculate total distance by multiplying lap distance by number of laps.
Scale a recipe up
\[ \text{2 people} \to \text{8 people} \]
Scale recipe quantities by multiplying.
Basic division
Divide whole number giving decimal remainder
\[ 7 \div 4 = 1.75 \text{ m} \]
Divide a whole number by whole number, express answer as decimal.
Share decimal amount equally
\[ 4.5 \div 3 = 1.5 \text{ L} \]
Divide a decimal amount by a whole number.
Find average of simple values
\[ (2.5 + 3.0 + 3.5) \div 3 = 3 \]
Calculate the mean of decimal measurements.
Two-step problems
Add then compare to target
\[ 0.8 + 0.6 = 1.4 \text{ (need 2)} \]
Add measurements then compare to a target value.
Subtract then compare
\[ 5 – 2.3 = 2.7 \text{ (need 3?)} \]
Subtract then compare remainder to a target.
Add three measurements then round
\[ 1.2 + 0.85 + 1.6 \approx 4 \text{ kg} \]
Add multiple measurements then round the result.
Calculate then order
\[ \text{Compare totals from products} \]
Calculate multiple products then order the results.
Find difference of sums
\[ \text{Team A vs Team B totals} \]
Calculate two sums and find their difference.
Special cases
Very small measurements
\[ 0.15 \text{ mm thick} \]
Work with very small decimal measurements.
Measurements with trailing zeros
\[ 2.50 = 2.5 \text{ ?} \]
Understand equivalence of decimals with trailing zeros.
Converting between decimal and fraction
\[ \tfrac{3}{4} \text{ kg} = 0.75 \text{ kg} \]
Express a common fraction as decimal in measurement context.
Measurements between decimal places
\[ \text{Between } 2.3 \text{ and } 2.4 \text{?} \]
Identify values between two given decimals.
Timer (Optional)
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