Halving and doubling

Halving and doubling

Auto-markingPencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about halving and doubling numbers.

Question 2Change answer

a)  Halve the following numbers:
     i)     half of 4 equals 
     ii)    half of 16 equals 
     iii)   half of 100 equals 
     iv)   half of 80 equals 
     v)    half of 50 equals 

Question 2Change answer

b)  Double the following numbers:
     i)    double 5 equals 
     ii)   double 7 equals 
     iii)  double 20 equals 
     iv)  double 15 equals 
     v)   double 75 equals 
 
Task administration: 
This task can be completed with pencil and paper or online (with auto marking displayed to students).
Levels:
2, 3
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
halving, doubling, basic facts, multiplication
Description of task: 
Students halve and double a range of numbers.
Curriculum Links: 
This resource can help to identify students' ability to use strategies  and basic facts for multiplication tasks.
 
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Multiplicative thinking, sets 3-4
Multiplicative thinking, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y4 (11/2005)
a) i)
ii)
iii)
iv)
v)		 2
8
50
40
25		 moderate
(for all correct)

easy
(4 correct)
b) i)
ii)
iii)
iv)
v)		 10
14
40
30
150
NOTE: Overall, students found doubling easier than halving.		 moderate
(for all correct)

easy
(3-4 correct)
Based on a representative sample of 183 Y4 students in November 2005.
Teaching and learning: 
This resource explores doubling and halving and some base ten understanding.
Diagnostic and formative information: 
  Common error Likely misconception
a) v) 20 or 30 Place value misconception: renaming the 10 to two 5's
Halving 50 requires the understanding of halving a 5 (in the tens), and breaking a ten and redistributing the two 5's.
b) v) 145 or 140 Place value misconception: renaming two 5's to one 10
Doubling 75 is the reverse of halving 50, and involves how to include the ten (result of doubling the 5).  Students either added the 5 on after doubling the 70, or ignored it completely.
Next steps: 

Students who had difficulty halving 50 or doubling 75 could look at how to double 15 / halve 30 and work to transfer whatever strategy they used to the larger numbers.  Interestingly, students very successfully doubled 15 to 30.  This could be because the number was still in the number range the students are working with at these early stages of the Numeracy framework. 
The relationship of the 5 being doubled and the ten being halved could be explored – the carrying for the doubling may well lead to some discussion about place value and the need for making the adjustment (carrying /borrowing) from the ones to the tens (and vice versa).

Links to the Numeracy framework
Halving and doubling is considered to be an aspect of the Basic facts operational domain at Stage 3: Counting from one (numbers to 10) and Stage 4: Advanced counting (for numbers to 20).