CENTRE FOR EDUCATIONAL DEVELOPMENT Teaching students to solve algebra word problems BOPMA 28 Novembe

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CENTRE FOR EDUCATIONAL DEVELOPMENTTeaching
students to solve algebra word problems
BOPMA 28 November 2008
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A BIG question

• What can teachers do to help their students
  tackle algebra word problems more successfully?

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Outline of this session

• Background
• Word problems and algebra
• Solving word problems
• Informal strategies
• Expert model
• Teaching strategies

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Teacher to Adviser

• Team Leader, Numeracy and MathematicsCentre for
  Educational DevelopmentMassey University College
  of EducationPalmerston North
• New Zealand
• a.lawrence_at_massey.ac.nz

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The problem

• Peter has more than twice as many CDs as Mary.
  Altogether they have 97 CDs.
• Find the least number of CDs that Peter could
  have.

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Merit level question for NCEA level 1
Achievement Standard 90147

• Peter has more than twice as many CDs as Mary.
  Altogether they have 97 CDs. Write a relevant
  equation, and use it to
• find the least number of CDs that Peter could
  have.

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Requirements for the standard

• use algebraic strategies to investigate and
  solve problems Problems will involve modelling
  by forming and solving appropriate equations, and
  interpretation in context
• must form equationsat least one equation
  (assessment schedule, NZQA, 2005b, p. 2).

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I hate algebra
because its too hard. I dont get it cos the
letters confuse me. I can do things with numbers
but the letters confuse me. I see some letters
with numbers and it doesnt look right... I just
dont get it. Just in general I just dont like
it. I hate doing equations and stuff but words
are ok. I just avoid algebra as much as possible.
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Teachers talk about word problems

Word problems are something that we have taken
for granted for quite a long time and we havent
really looked explicitly at how to deal with them
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What can we do?

• What can teachers do to help more students
  tackle algebra word problems with more success
• ?

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Students need to

• understand the problem-solving cycle
• practise each of the steps of the problem-solving
  cycle
• generate meaningful word problems
• focus on the whole problem
• practise translating between different
  representations.

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The problem-solving cycle

(Adapted from Ellerton, N. Clements, K., 1996
MacGregor, M. Stacey, K., 1993)
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Matching activity

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Translating into English

• Write an English phrase for each of these
  expressions in Algebra
• n 4
• 10 I
• n 7
• 5n
• n²

6. 4n 6 7. n² 2n 8. 3 (n 7) 9. 15 3n 10.
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Translating into Algebra

• Write algebraic expressions for these
• Eleven more than a number.
• A number decreased by five.
• Twelve divided by a number.
• Three less than four times a number.
• The product of a number and six.
• The sum of a number and 7 and the result
  multiplied by 4.
• The product of a number and two more than the
  number.
• Double the number less than the square of the
  number.
• Triple the number divided by four less than the
  number.
• The difference between the number and eight and
  the result multiplied by four more than the
  number.

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A Year 12 student says

I liked how we learnt from both views - putting
it into word problems and taking a word problem
and putting it into algebraic. I understand it a
bit better - and starting with simple ones then
more complicated to see how they work rather than
doing the complicated ones straight away.
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Translating equations into words

• Example
• 2n 12 5
• could be written
• Twelve less than twice a number is five.
• What is the number?
• Or
• When I double a number and take away twelve,
  the answer is five. What is the number?

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Try these translations

• Write the following equations in words
• 5n 7 6
• n² - 3 5
• 7
• n 7 3n 8

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Students respond

Translating into words was really helpful before
we had to solve the equations. It made it easier
to solve them and it made it make more sense.
I understood what I was doing because I had
translated it into words first.
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Pass the paper

• Pairs Person A and Person B
• Complete the middle column
• Fold the paper so the first column is hidden
• Pass the paper to partner
• Partner completes the last column
• Pairs check first and last columns and discuss

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Students rated this highly

It was good - the fact that you had to write
every detail out cos you werent going to be
doing it yourself you got to see other peoples
cos sometimes what makes sense to you doesnt
make sense to other people and it was good to see
that.
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Students rated this highly

Because different people see it in different ways
so like with the sheets - different peoples
interpretations of how to do it can be quite
enlightening- different perspectives. Some were
ambiguous and so it was interesting to see what
words you could use and have it totally not
ambiguous.
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The four-step method

• Person 1 Assign the variable Let x
• Person 2 Write the equation
• Person 3 Solve the equation
• Person 4 Check the solution fits the
  problem
• Kushnir, D. (2001). Cooperative learning and
  mathematics grade 8-12 High school activities.
  San Clemente, CA Kagan Publishing.

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An algebra word problem?

• Amy is eight years older than John.
• In six years, Amy will be twice as old as John
  will be then.
• How old are they now?

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Using the four steps to solve the problem

• Amy is eight years older than John. In six
  years, Amy will be twice as old as John will be
  then. How old are they now?
• Person 1 Assign the variable Let x
• Person 2 Write the equation
• Person 3 Solve the equation
• Person 4 Check the solution fits the
  problem

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The four steps helped

Some of them were quite challenging like you had
to bring in other parts of maths so that was
really good.
The Four-steps was really good... Those steps
were really helpful. I hadnt done anything like
that before. Before youd think Oh maths no,
but this was stuff that I get so I felt lots
better about it.
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Increased awareness of the issues

Knowing what to let the variable be is critical
and initially it seemed like it didnt matter
I feel a bit more confident with writing algebra
now.
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Teachers can make a difference

• Quality tasks which press for algebra
• Matching activities
• Translation focus
• Explore translation both ways
• Develop translation AND manipulation skills
• Flexible approaches
• Explore different routes to a solution