Diagnostic questions
- Three friends each have 1.5 litres of juice. How many litres do they have altogether?
Answer: 4.5 litres - If an eel weighs 0.6 kg, how much would 3 eels weigh?
Answer: 1.8 kg
What to notice in the student’s response
Can the student combine halves to create new wholes?
Do they see 3 x 1.5 as (3 x 1) + (3 x 0.5) or know that 1.5 + 1.5 = 3 and another 1.5 makes 4.5?
Does the student use a known fact such as 3 x 6 = 18 but get an incorrect answer such as 0.18?
Deliberate acts of teaching
Materials
- Decimats (Material master 7-3) (PDF, 82KB)
- Dice labelled with x 2 and x 0.5
Learning how to halve or double a decimal number will help students to avoid overgeneralising whole number strategies to decimals.
These activities will challenge the common misconception that “multiplication makes things bigger”.
Double or Half the Loot
The context for this activity is a group of pirates dividing up gold bars.
Make a set of cards with decimal amounts on them, using only even numbers initially. Create yellow decimats to represent gold bars. Label a dice so that three sides have “x 2” (double) and three sides have “x 0.5” (half). Take turns drawing a card, modelling the amount on the decimat, and then rolling the dice. Discuss how to double or halve the amount. Record the result as a running total.
Read aloud the total as whole bars and fractional amounts, for example, “3 whole bars and 2 tenths of a bar and 5 hundredths of a bar”.
Increase the difficulty by using odd numbers and by changing the operations on the dice, for example, x 4, x 0.1, + 0.5 …
What to do next if the student is stuck
Spend several lessons exploring decimat representations. Simplify the operations dice by using + 0.1 or – 0.1.
Initiating home-based activities
Encourage parents to use games to help the student practise working with decimals. One example is “How much more to make 1?” The student takes a playing card and uses the number to represent a decimal, for example, 8 becomes 0.8. The student states which decimal is required to make 1 (0.2).
Next teaching steps back in the classroom
Decimal Cards (www.nzmaths.co.nz)
Most level 3–4 maths activities involve working with decimal amounts.
Measurement and statistics are common applications.
Encourage the student to use their understanding of decimals to make estimates when solving problems in order to check whether their final answers are reasonable.
