Greater than, less than, or equal number sentences

Greater than, less than, or equal number sentences

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Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources

Question 1Change answer

Add <  ,  > , or  =  to complete the following number sentences.
     i) 4 + 3 <=> 6 + 2
 
     ii) 2 × 5 <=> 19 – 11
 
     iii) 18 – 9 <=> 17 – 8
 
     iv) 3 × 3 <=> 14 – 6
 
     v) 2 × 3 <=> 12 – 5
 
     vi) 18 ÷ 3 <=> 12 ÷ 2

Question 1Change answer

Select from the following numbers 3, 5, 6, 9 to complete the number sentences.
For example    ×  5  <  4  ×  4
     i)   6   ×   4     >   5    ×    9653
     ii)   2    ×    9653    >    3    ×    4
     iii)  7    +    15    >    7    ×    9653
     iv)  13    -    9653    =    4    ×    2
     v)  9653    ÷    3    <    8    ÷    4
Task administration: 
This task can be completed with pencil and paper or online (with auto marking displayed to students).
Level:
2
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Keywords: 
greater than, less than, equal to, equality
Description of task: 
Students select the correct symbol or the correct number to make number sentences true.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Using symbols and expressions to think mathematically, set 3
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y4 (11/05)
a)

i)
ii)
iii)
iv)
v)
vi)

<
>
=
>
<
=

moderate
moderate
moderate
moderate
moderate
moderate
b)
 		 i)
ii)
iii)
iv)
v)		 T
F
F
T
F

moderate
difficult
difficult
difficult
difficult
Based on a representative sample of 183 students.
Teaching and learning: 
  • This resource can be used as part of an exploration of the concept of equality.  Many students believe that the equals sign means "and the answer comes next".
  • Examining the problems in this resource can be the beginning of looking at the idea of equality as meaning quantitative sameness – the expression on the left-hand side of the equals sign represents the same quantity as the expression on the right-hand side of the equals sign.
  • The equals sign means "is the same as", whereas the > and < symbols mean "is not the same as".
  • This resource also provides the opportunity for students to be introduced to the concept of "not equals" and the ≠ sign which would replace the < and > signs.
Diagnostic and formative information: 
  Common error Likely misconception
a) i)-vi) Incorrect use of < and >. Students are confused which way around the symbols go.  Most errors for question a) arose from confusion between the < and > symbols.
a) i)-vi) Students write the answer for both number sentences. Students solve the first part of the problem, but do not compare the results.
Next steps: 

Students who confused the < and > symbols may need a strategy for remembering which way around the open "mouth" goes, and more practice with using the symbols in order to consolidate their understanding.    Resources Greater than, less than, or equal number sentences, Older or younger? and Bear's picnic explore the concepts of greater than and less than by comparing numbers rather than expressions. 

For students who are able to correctly use the symbols <, >, and =, resources Emma's lollies and Matching equations provide further ways to compare expressions.  Another way to extend students is to have them create their own number sentences –using either single or double digit numbers or expressions.

Students are used to seeing sentences in the form a + b = c.  The number sentences in this resource allow students to see that there are other ways to write number sentences.  Cuisenaire number sentences is a practical activity that can be used to reinforce the ideas of equality and represent number sentences in alternative forms.

To further improve understanding about the concept of equality, use resource What is equal? to generate discussion about the meaning of the equals sign.  The idea of equality meaning balance can be introduced using simple balance pans and blocks, which can lead on to solving simple problems presented as open number sentences.  See Balance pans for balance pan ideas and Equal number sentences for open number sentences.

Further information about the concept of equality can be found in the Algebraic Thinking Concept Map.
 
Figure it Out:
Balance (Algebra, L3, p.19),
Crunch Machine? (Algebra, L2-3, p. 17 Activity 2),
What Goes Where? (Algebra, L2-3, p. 20 Activity 1),
Good as Gold (Algebraic Thinking and Number Sense, L2-3, Book 2, pages 12-13),
Finding a Balance (Algebraic Thinking and Number Sense, L2-3, Book 2, p. 17).