Lesson overview – Why does this learning matter?
In many mathematics problems students encounter, a “key words” approach does not work. Words such as “more” or “altogether” suggest addition and students who depend on key words are likely to use the wrong mathematical process to solve the problems (see
Problem 1, Resource 1). What we want students to think about is how the numbers in a problem relate to each other. To achieve this focus on the relationship we often encourage students to draw a diagram. Tape diagrams can be used to provide a common framework in using diagrams as thinking tools.
In this lesson we aim to teach a new diagram (strategy for solving a word problem) with a familiar mathematics concept. The mathematics in the word problems used in this lesson should not prove difficult for Stage 4 students. Once students become familiar with tape diagrams then the empty section of a tape diagram could be used to introduce the notion of a variable in Stage 4.
Students should:
1. Use Newman’s prompts to assist with solving word problems
2. Understand how to draw a tape diagram to represent a word problem that uses familiar arithmetic
3. Work co-operatively in pairs
Outcomes
NS4.1
Recognises the properties of special groups of whole numbers and applies a range of strategies to aid computation.
WMS4.2
Analyses a mathematical or reallife situation, solving problems using technology where appropriate.
Grouping
Step 1: Individual (prior to lesson assessment for learning)
Step 2: Whole class joint construction
Step 3: Students work in pairs
Step 4 Students work in pairs or small groups
Step 5 Whole class lesson closure
Materials

Word problems assessment for learning task (Resource 1)

Coloured card tapes of varying lengths

Tape diagram problems (Resource 2)

Working with tape diagrams (Resource 3)

Problem task cards (Resource 4)

Large paper, textas
Step 1 Assessment for learning

Prior to the lesson, students complete individually the word problems task
(Resource 1)
Discussion / questioning

Teacher assesses where students are according to their responses to the word problems. This information may be useful for grouping students for the tape diagram lesson to follow.
Mathematics Unit, Curriculum K –12 Directorate Introducing tape diagrams lesson plan
NSW Department of Education and Training
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Step 2 Introducing tape diagrams
(modelling)

Introduce the key idea of the lesson by asking Kurt Reusser’s question he asked 97 first and second grade students
“There are 26 sheep and 10 goats on a ship. How old is the captain?”
Seventy six of the 97 students solved the problem, providing a numerical answer by adding 26 and 10.
Explain why today’s learning matters - students often solve problems without really understanding them.

Outline the lesson briefly

Start with problem 1 on Tape diagram problems (Resource 2) written on the board
 Use Newman’s prompts:
1. Choose a student to read the question to the class
2. What is the question asking us to do?
3. How are we going to find the answer?
4. Show me what to do to get the answer?
5. Write down the answer to the question

Repeat the previous process with problem 2 on Tape diagram problems
(Resource 2)
Compare and contrast
Discussion / questioning
 Put Reusser’s question on the board
Ask students the question
Manage responses

We are learning about a new strategy to help us understand word problems – how the words of the problem relate to the mathematics. We will be working with familiar mathematics until we get used to
using the new strategy.

Use coloured cardboard tape and blutack on blackboard to illustrate the tape diagram

Introduce idea of a tape diagram

Model making the diagram using the coloured cardboard tapes – label the tape diagram, referring back to the words used in the problem regularly

State the number sentence modelled by the diagram and then the answer to the question

Draw the tape on the board for this question – don’t use the cardboard tape.
Go with student responses and seek refinements from other students where needed.
Mathematics Unit, Curriculum K –12 Directorate Introducing tape diagrams lesson plan
NSW Department of Education and Training
Page 2 of 3





Compare and contrast the tape diagrams for problem 1 and problem 2
Step 3 Pair task (Guided)
Students complete diagrams
Working with tape
(Resource 3) in pairs
Give students approximately 10 minutes for this activity
Check student responses to the four questions if clarification needed
Step 4 Problem task cards
(Independent)

Students work in pairs or small groups to complete a word problem using a tape diagram (15 mins)

Choose two or three groups to report back to whole class by discussing how they constructed their tape diagram

How are the tape diagrams similar?
How are the tape diagrams different?
Why? (Focus here on the language of the problem and how the numbers relate to each other)
Discussion / questioning

Teacher explains that students work in pairs
– one student completes the odd questions (Q1) while the other student coaches and then they swap. The other student completes the even questions while the other student coaches.

Teacher monitors student progress on the four word problems
Discussion / questioning

Students work together, discuss the problem using Newman’s prompts and draw a tape diagram to represent the problem on a large sheet of paper using textas

Compare the tape diagrams of the solutions reported. What do you notice about the diagrams?
Step 5 Closing

Close the lesson by referring back to
Reusser’s introductory problem

Reinforce the learning that occurred throughout the lesson
Discussion / questioning
References
Kurt Reusser, “Problem Solving beyond the Logic of Things: Contextual Effects on
Understanding and Solving Word Problems,” Instructional Science 17 (4): 309-38 (1988)
Mathematics Unit, Curriculum K –12 Directorate Introducing tape diagrams lesson plan
NSW Department of Education and Training
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