Maths
Bar-model problem solver
Represent equal groups, parts and comparison problems with bars, then use matching number sentences to solve them. The worked example shows 4 × 24, subtracts 30 and checks the answer in context. Explain the diagram as you work.
Read the worked bar model, then use the four moves on a new problem.
Read the complete materialRead the material
Represent equal groups, parts and comparison problems with bars, then use matching number sentences to solve them. The worked example shows 4 × 24, subtracts 30 and checks the answer in context. Explain the diagram as you work.
Activity. Use the preview for diagrams and layout.
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NAME CLASS DATE LEARNING GOAL Use bar models to plan and solve one- step and multi-step word problems. SUCCESS CRITERIA I can find the key numbers and the question. I can draw a bar model with parts to scale. I can write number sentences from my bar. I can answer with units and check it. Watch the four moves Worked example PROBLEM A school buys 4 boxes of 24 pencils and gives 30 away. How many pencils are left? Read the bar: find each ? 2 points a 120 75 ? ? = b 36 ? ? ? Each ? = Bar-model frame 1 WATCH 2 SOLVE 3 ANSWERS MATHS AGES 9 TO 11 BAR MODELS Bar-model problem solver Four moves that crack any word problem. 1 Read Numbers, question 4 boxes 24 in each box 30 given away Find: pencils left 1 Draw Equal means equal 96 pencils Bought 24 24 24 24 After 30 given away ? = 66 left 4 equal parts, so 4 equal lengths. 30 is more than 24, so its part is longer than one box. 2 Write A sentence a step a 4 × 24 = b 96 − 30 = 3 96 66 Answer Units, then check There are 66 pencils left. Check: 66 + 30 = 96 4 2 Page 1 of 2
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FOUR MOVES 1 Read: underline numbers 2 Draw: equal means equal 3 Write 4 Answer with units Part and whole LEVEL 1 3 points MOVE 1: READ A library trolley holds 145 books. 68 are fiction and the rest are non-fiction. How many books are non-fiction? MOVE 2: DRAW THE BAR MOVE 3: NUMBER SENTENCE MOVE 4: ANSWER Compare two bars LEVEL 2 3 points MOVE 1: READ A blue ribbon is 18 cm long. A red ribbon is 4 times as long as the blue ribbon. How much longer is the red ribbon than the blue ribbon? MOVE 2: DRAW THE BAR Blue Red MOVE 3: NUMBER SENTENCES MOVE 4: ANSWER Two steps LEVEL 3 4 points MOVE 1: READ Ben and Ava share 84 marbles. Ava has 18 more marbles than Ben. How many marbles does Ben have? MOVE 2: DRAW THE BAR Your bar model, your way. MOVE 3: NUMBER SENTENCES MOVE 4: ANSWER BONUS ROUND Ava gives Ben some marbles so they both have the same number. How many does she give him? ANSWER Bar-model frame 1 WATCH 2 SOLVE 3 ANSWERS MATHS AGES 9 TO 11 WORD PROBLEMS Your turn: climb the levels 3 BOOKS 4 CM 5 MARBLES MARBLES Page 2 of 2
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Bar-model problem solver Teacher companion Mathematics | Pupils aged 9 to 11 Use with the exact 2-page original file. Keep pupil or staff activity pages separate from this teacher companion. When to use it Use the frame after pupils have met the operations involved and need to interpret a word problem before calculating. The worked example models multiplication and subtraction; follow it with one problem at a time and encourage diagrams that show the quantities accurately. Purpose Represent relationships in word problems with bar models, write linked number sentences and check a solution with units. Start here Read the pencil problem in the worked example, identify the question and underline the quantities before drawing the bar. A teaching sequence 1. Read for the quantities and question, then draw bars that show equal groups, parts or comparisons. 2. Label known amounts and the unknown. Ask whether the visual lengths represent equal amounts or a stated difference. 3. Write one number sentence for each step and calculate, including intermediate totals where needed. 4. State the answer with units and check by reversing the operation or using a related total. Ask, “How can you check the bar and calculation agree?” Reverse the operation or use a related total. Checking guidance Read the bar: a = 45; b = 12 for each of the three equal parts. Worked pencil example: 96 pencils bought, 66 left. Level 1: 145 - 68 = 77 non-fiction books. Level 2: the red ribbon is 4 x 18 = 72 cm, so it is 72 - 18 = 54 cm longer. Level 3: remove the extra 18 from 84, then halve: Ben has 33 marbles and Ava has 51. Ava gives Ben 9 marbles so both have 42. Use the printed point values with a marking approach agreed before the lesson. Check the relationship shown by the bars as well as the final number. Support Start with the worked example and give pupils counters or paper strips to build equal bars before drawing. Cover later steps until the first relationship is clear; provide number-sentence frames and keep units visible. Take it further Ask pupils to invent a word problem that matches a bar model, exchange it with a partner and check whether the model supports more than one calculation step. Require units and a reasonableness check. Things to keep in mind Use the worked example to model the routine before pupils try the other problems. Encourage them to check their own bars and calculations against each other. Bar-model problem solver Teacher companion | Page 1
A teaching sequence
Represent relationships in word problems with bar models, write linked number sentences and check a solution with units.
Read the worked bar model, then use the four moves on a new problem.
Read the complete materialRead and draw the quantities
Read for the quantities and question, then draw bars that show equal groups, parts or comparisons.
Which quantities are equal groups, and which show a comparison?
Read the worked bar model, then use the four moves on a new problem.
Read the complete materialLabel known and unknown parts
Label known amounts and the unknown. Ask whether the visual lengths represent equal amounts or a stated difference.
Do equal bar lengths stand for equal amounts?
Calculate one step at a time
Write one number sentence for each step and calculate, including intermediate totals where needed.
What intermediate total do you need before the next calculation?
Check the answer and units
State the answer with units and check by reversing the operation or using a related total.
How can you check that the bar and calculation agree?
Before you teach
Look for the thinking behind an answer, choose the support your class needs and leave room for an independent response.
What to look for
Read the bar: a = 45; b = 12 for each of the three equal parts. Worked pencil example: 96 pencils bought, 66 left. Level 1: 145 - 68 = 77 non-fiction books. Level 2: the red ribbon is 4 x 18 = 72 cm, so it is 72 - 18 = 54 cm longer. Level 3: remove the extra 18 from 84, then halve: Ben has 33 marbles and Ava has 51. Ava gives Ben 9 marbles so both have 42. Use the printed point values with a marking approach agreed before the lesson. Check the relationship shown by the bars as well as the final number.
Give a little support
Start with the worked example and give pupils counters or paper strips to build equal bars before drawing. Cover later steps until the first relationship is clear; provide number-sentence frames and keep units visible.
Take the idea further
Ask pupils to invent a word problem that matches a bar model, exchange it with a partner and check whether the model supports more than one calculation step. Require units and a reasonableness check.
Things to keep in mind
Use the worked example to model the routine before pupils try the other problems. Encourage them to check their own bars and calculations against each other.
Keep the idea. Make it yours.
Bring your topic, learning goal and class context to PLAI™, then review what you create.
Ideas to try with your class
Sample teaching perspectives on what to try, what to adapt and what to watch for.
Meet The Creators
Meet a creator whose teaching interests connect with this template.
Notes Between Bells
The worked example shows four boxes of 24 pencils, 30 given away and a final total of 66, with the bar matching each calculation. Later levels move to a part-whole problem, a four-times comparison and a two-step sharing problem.
Gentle Reminder
The four moves (read, draw, write and answer with units) are repeated across the levels. In the example, the bar makes the equal groups and subtraction visible before the arithmetic is checked by adding the 30 pencils back.
The Curious Pencil
Start with the completed pencil example and let pupils label the known quantities before drawing. A ruler or equal-length bar segments can support proportional representation, while verbalising the question helps separate the whole from the unknown part.
Kindly Red Pen
The examples vary in structure, so success on the four-box multiplication problem does not show that a pupil can solve the later comparison or two-step question. Review the bar and number sentence together for each new problem type.