Early Algebra, Early Arithmetic
Lesson 2: Comparisons
The Mason School
2 — COMPARISON SYMBOLS: COMPARING NUMBERS ............................... 2
Summary.................................................................................................................................................... 2
Introduction ............................................................................................................................................... 2
Activities ........................................................................................................................................................ 3
Activity 1: Comparison Symbols [whole class] .................................................................................... 3
Activity 2: Comparison Symbols [small group work] .......................................................................... 3
Activity 3: Comparing Different Attributes & Ambiguity [whole class] .............................................. 3
Activity 4: Introduce the Homework .................................................................................................... 3
Overheads & Printouts ................................................................................................................................ 4
Equality and Inequality .............................................................................................................................. 4
Overhead 1: Equals (an obvious case) .................................................................................................. 4
Overhead 2: Does the circle matter? ..................................................................................................... 5
Overhead 3: Inequality .......................................................................................................................... 6
Overhead 4: What Counts? ................................................................................................................... 7
Overhead 5: “How many” could be what matters ................................................................................. 8
Overhead 6: What does the symbol > mean? ........................................................................................ 9
Overhead 7: What does the symbol < mean? .......................................................................................10
Overhead 8: Comparing Numbers .......................................................................................................11
Overhead 10: Comparing Number Expressions ...................................................................................13
Overhead 11: Other expressions to compare........................................................................................14
Overhead 12: Comparing Sets Again ...................................................................................................15
Overhead 13: Comparing Blocks .........................................................................................................16
Overhead 14: Comparing Liquids ........................................................................................................17
Overhead 15: Comparing Lengths .......................................................................................................18
Class Handout ...........................................................................................................................................19
Overhead 16: Using comparison symbols ............................................................................................19
Ambiguous Comparisons ..........................................................................................................................20
Overhead 17: A Difficult Comparison: What could be compared? .....................................................20
Overhead 18: Another Hard Comparison ............................................................................................21
Overhead 19: What could be compared? .............................................................................................22
Overhead 20: A Tricky Money Comparison ........................................................................................23
3 cents + 4 cents + 2 cents + 40 cents
2 dollars ...................................................................23
Homework, page 1 ....................................................................................................................................24
Overhead 21: Comparing Sets, Number Expressions, and Amounts ...................................................24
Homework, page 2 ....................................................................................................................................26
Overhead 22: Comparing Sets, Number Expressions, and Amounts ...................................................26
Reflections ....................................................................................................................................................28
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Early Algebra, Early Arithmetic
Lesson 2: Comparisons
The Mason School
2 — Comparison Symbols:
Comparing Numbers
Summary
Activity
Comparisons and comparison operators: =, ≠, <, >.
Goals
Learn conventions for comparing numbers and number
expressions; realizing that some comparisons require making
decisions about which attributes to focus on.
Materials
Overheads.
Terms
Greater than, less than, equal to, different from.
Introduction
In this class we will explore: mathematical symbols for greater than (>), less
than (<), equals to (=) and is not equal to (≠); comparative terms (more
than, less than, longer than, shorter than, bigger than, smaller than). We
will also focus on ambiguous situations where the choice of the attribute to
be compared determines the comparison symbol to be used.
To top
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Early Algebra, Early Arithmetic
Lesson 2: Comparisons
The Mason School
Activities
Activity 1: Comparison Symbols [whole class]
= and ≠ : Show pairs of amounts of objects (Overheads 1-5) and ask the
children to suggest what comparison symbol should be inserted in each case.
> and < : Show Overheads 6 and 7 and ask the children to try to find out
what each symbol means.
Show Overheads 8 to 15, discuss them with the children, guiding them to the
correct use of the comparison symbols.
Activity 2: Comparison Symbols [small group work]
Children work in pairs. They will be asked to fill out Handout 1 (Overhead
16) with the appropriate comparative term.
Activity 3: Comparing Different Attributes &
Ambiguity [whole class]
Briefly discuss children’s answers to the handout questions.
Show Overheads 17 to 20 and discuss the cases where, for the same
problem, different symbols could be used, depending upon the different
attributes one is comparing.
Activity 4: Introduce the Homework
The homework requires students to pay attention to the attribute being
compared. Sometimes the attribute is explicitly given (the number of
candies). Sometimes the student must determine the attribute.
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Lesson 2: Comparisons
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Overheads & Printouts
Equality and Inequality
Overhead 1: Equals (an obvious case)
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Overhead 2: Does the circle matter?
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Overhead 3: Inequality
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Lesson 2: Comparisons
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Overhead 4: What Counts?
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Lesson 2: Comparisons
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Overhead 5: “How many” could be what matters.
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Lesson 2: Comparisons
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Overhead 6: What does the symbol > mean?
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Lesson 2: Comparisons
Overhead 7: What does the symbol
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<
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mean?
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Lesson 2: Comparisons
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Overhead 8: Comparing Numbers
Find a symbol that could go between the
numbers:
Can you find another one?
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Overhead 9: The Same Numbers, in Reverse Order
Find a symbol that could go between the
numbers:
Can you find another one?
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Lesson 2: Comparisons
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Overhead 10: Comparing Number Expressions
A student wrote this.
Do you think what she wrote is right or
wrong?
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Lesson 2: Comparisons
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Overhead 11: Other expressions to compare
A student wrote this.
Do you think what she wrote is right or
wrong?
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Lesson 2: Comparisons
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Overhead 12: Comparing Sets Again
Find a symbol that could go between the
two sets.
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Lesson 2: Comparisons
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Overhead 13: Comparing Blocks
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Lesson 2: Comparisons
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Overhead 14: Comparing Liquids
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Overhead 15: Comparing Lengths
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Lesson 2: Comparisons
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Class Handout
Overhead 16: Using comparison symbols
Name: ______________________________________________Date:_______________
For each pair of objects, insert the correct comparison
symbol: =, > or <









50 cents
____
2 dollars
________
_________________________________________________________
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Lesson 2: Comparisons
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Ambiguous Comparisons
Overhead 17: A Difficult Comparison: What could be
compared?
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Lesson 2: Comparisons
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Overhead 18: Another Hard Comparison
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Lesson 2: Comparisons
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Overhead 19: What could be compared?
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Lesson 2: Comparisons
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Overhead 20: A Tricky Money Comparison
3 cents + 4 cents + 2 cents + 40 cents
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2 dollars
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Early Algebra, Early Arithmetic
Lesson 2: Comparisons
The Mason School
Homework, page 1
Overhead 21: Comparing Sets, Number Expressions,
and Amounts
Name: ______________________________________ Date:_______________
>
<
=
What I Compared


6 + 3
boxes
5 + 4


The amount of water

The size of the
glasses

1+2+3+4
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The Mason School
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Early Algebra, Early Arithmetic
Lesson 2: Comparisons
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Homework, page 2
Overhead 22: Comparing Sets, Number Expressions,
and Amounts
Name: ______________________________________ Date:_______________
The number of
stars
=
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=
+
-
The amount of
money
>
+
-
The amount of
money
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Lesson 2: Comparisons
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Line length
<
[Be careful!]
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Early Algebra, Early Arithmetic
Lesson 2: Comparisons
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Reflections
The comparison symbols actually take on different meanings in different
contexts and depending upon what is being compared.
Greater can mean:

Has more elements…

Is longer than…

Is worth more than…

Contains more liquid than…
Equal to can mean:

Has the same number of elements…

Is the same length as…

Is worth the same as…

Contains the same amount of liquid as…
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