Teaching unit · Grade 2 (ages 7 to 8)

Addition and subtraction word problems within 100

Part-whole and comparison bar models for putting together, taking from, and comparing, with the unknown in any position

About three to four lessons of 40 to 55 minutes

Start here · hook

The maths is hiding inside the story

The class is baking for the school fair. There are 28 chocolate-chip cookies cooling on one tray and 34 oatmeal cookies on another. How many cookies are there altogether? Later, 28 of them are sold in the first hour. How many are left to sell? And your friend Maya has 45 stickers on her cookie boxes while Ben has 27 on his, so how many more did Maya use?

Every one of these is a story with a sum hidden inside it. The hard part is not the adding or the subtracting, it is working out which sum to do. Today you will learn to draw the story as a bar, a simple picture that shows the whole and its parts, or two amounts side by side. Once the bar is drawn, the picture tells you whether to add or subtract, even when the missing number is hiding at the start, the middle, or the end.

28 choc-chip and 34 oatmealput the two parts together: 28 + 34 = 62 cookies
62 cookies, 28 soldtake a part from the whole: 62 - 28 = 34 left
Maya 45 stickers, Ben 27compare the two: 45 - 27 = 18 more
34 tickets, 28 more, then 15 given awaytwo steps: 34 + 28 = 62, then 62 - 15 = 47

Learning objective

What students will be able to do

Students will solve one- and two-step addition and subtraction word problems within 100 by drawing a part-whole bar or a comparison bar to reveal the structure of the problem, deciding on the operation from the picture rather than from keywords, carrying out the calculation by working with tens and ones, and answering with a labelled number that makes sense in the story.

Success criteria

I can read a word problem and say what it is asking before I touch the numbers.
I can draw a part-whole bar for a putting-together or taking-from problem.
I can draw a comparison bar for a 'how many more' or 'how many fewer' problem.
I can find a missing part or a missing whole, wherever the unknown is hiding.
I can solve a two-step problem and check that my answer fits the story.

Curriculum anchor

Standards this unit teaches

2.OA.A.1Common Core (US)
Add and subtract word problems within 100
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using drawings and equations with a symbol for the unknown number to represent the problem.
2.NBT.B.5Common Core (US)
Add and subtract within 100 (the calculation)
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. This is the calculation the word problems ask students to set up and then carry out.
AC9M2N05Australian Curriculum v9 (ACARA)
Model everyday adding and taking-away problems (Year 2)
Model and solve everyday adding and taking-away problems, including simple money situations, using diagrams, materials and number sentences. The cookie and sticker stories in this unit are exactly this kind of modelling.
AC9M2N01Australian Curriculum v9 (ACARA)
Partition into tens and ones (Year 2)
Partition, rearrange and regroup two-digit numbers using their place value, including splitting a two-digit number into tens and ones. This is the strategy students use to actually work out each sum a bar model sets up.

Before you start

Prior knowledge

This unit builds on skills students should already have met. Revisit any that are shaky first.

Key vocabulary

Words to teach and display

Whole: the total amount, made when the parts are joined
Part: one piece of the whole, joined with the other parts to make it
Sum: the total you get when you add the parts
Difference: how many more one amount is than another, found by subtracting
Compare: line two amounts up to see how much bigger one is than the other
Unknown: the number the problem is asking for, shown as a gap or a box in the bar

Teaching sequence

Teach it: concrete, pictorial, abstract

The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.

1. Act out the story with a part-whole bar

Concrete

Read the whole cookie story out loud before touching a single number. There are 28 chocolate-chip cookies and 34 oatmeal cookies, and we want the total. Build it: 28 counters in one pile, 34 in another, then push them together into one bar. The two piles are the parts and the joined bar is the whole. A putting-together story is a part-whole picture, and joining the parts means adding.

Say the structure in plain words the class repeats: two parts join to make a whole, so we add. Nothing about the picture depends on the exact numbers, which is why the bar works for every putting-together problem.

Draw the bar as one long strip split into two pieces, one labelled 28 and one labelled 34, with a brace over the top for the whole we are looking for. The gap over the top is the unknown.

The two parts, 28 and 34, join to make the whole. The whole is the unknown, so we add: 28 + 34 = 62 cookies.

Check for understanding, ask

What are the two parts in this story, and what is the whole?
Do we add or subtract to find the whole? How does the bar tell you?

2. Putting together and taking from

Pictorial

Now use the same bar without the counters. For 28 + 34, the parts are known and the whole is missing, so we add. Work the sum with tens and ones: 20 and 30 is 50, 8 and 4 is 12, and 50 and 12 is 62. So there are 62 cookies. A taking-from story uses the very same bar read the other way: if there are 62 cookies and 28 are sold, the whole and one part are known and the other part is missing, so we subtract.

The single bar holds both stories. Read it as parts-to-whole and it says 28 + 34 = 62. Cover a part and read it as whole-minus-part and it says 62 - 28 = 34. Same three numbers, one picture.

This is why the bar is worth drawing every time: it turns 'is this an adding problem or a taking-away problem?' into something you can see instead of guess.

Worked example

There are 28 chocolate-chip cookies and 34 oatmeal cookies. How many cookies are there altogether?

Read for the question: how many cookies in all. The two amounts are the parts.
Draw the bar: parts 28 and 34, whole unknown over the top.
Parts join to a whole, so add. Ones: 8 + 4 = 12. Tens: 20 + 30 = 50.
Combine: 50 + 12 = 62.

Parts 28 and 34, whole 62. The bar shows 28 + 34 = 62.

Answer: There are 62 cookies altogether.

Check for understanding, ask

In '62 cookies, 28 are sold, how many left?', which numbers are the whole and the part?
Why does the same bar work for both the adding story and the taking-away story?

3. Taking from: a part is missing

Pictorial

Take the taking-from story on its own. There are 62 cookies and 28 are sold in the first hour, and we want the number left. The whole is 62 and one part is 28, so the missing part is found by subtracting: 62 - 28. Take the tens then the ones: 62 take 20 is 42, then 42 take 8 is 34. So 34 cookies are left. The bar shows the whole 62 split into the 28 that went and the piece we are looking for.

Check it with the inverse: the two parts should rebuild the whole. 28 sold and 34 left is 28 + 34 = 62, which matches the number we started with, so the answer is sound.

Notice the unknown has moved. In section 2 the whole was missing, here a part is missing. The bar looks almost the same, but where the gap sits tells you whether to add or subtract.

Worked example

There are 62 cookies. In the first hour 28 are sold. How many cookies are left?

The whole is 62 and one part is 28. The other part is missing.
Whole minus a known part gives the missing part, so subtract: 62 - 28.
Take the tens: 62 - 20 = 42. Take the ones: 42 - 8 = 34.
Check: 28 + 34 = 62, back to the whole.

Whole 62, known part 28 sold, missing part 34 left. 62 - 28 = 34.

Answer: There are 34 cookies left.

Check for understanding, ask

Is the missing number a part or the whole here?
How can adding the two parts check a subtraction answer?

4. Comparing: how many more

Pictorial

Some stories do not put amounts together at all, they line them up. Maya used 45 stickers and Ben used 27, and we want to know how many more Maya used. Draw the two amounts as two bars on the same baseline, one above the other, so their lengths can be compared. Maya's bar is longer. The extra bit that sticks out past Ben's bar is the difference, and you find it by subtracting: 45 - 27 = 18.

Comparing is still subtraction, but the picture is different: not one whole split into parts, but two separate bars measured against each other. The question 'how many more' or 'how many fewer' is the signal to draw a comparison, not a keyword to trust blindly.

Work the subtraction with tens and ones: 45 take 20 is 25, then 25 take 7 is 18. So Maya used 18 more stickers than Ben.

Maya's 45 and Ben's 27 on the same scale. The gap between the bar ends is the difference: 45 - 27 = 18.

Worked example

Maya used 45 stickers and Ben used 27 stickers. How many more stickers did Maya use?

Draw two bars on the same line: Maya 45, Ben 27.
'How many more' asks for the gap between them, so subtract the smaller from the larger.
45 - 27: take 20 to get 25, take 7 to get 18.

The difference between the two bars is 18.

Answer: Maya used 18 more stickers than Ben.

Check for understanding, ask

Which of Maya and Ben has the longer bar, and how do you know from the numbers?
What does the part that sticks out past the shorter bar stand for?

5. The unknown can hide anywhere, and two-step stories

Abstract

Sometimes the story starts with a mystery. Ben had some stickers, used 18 more, and ended with 53. How many did he start with? Here the whole is 53 and one part is 18, so the missing start is a missing part: 53 - 18 = 35. The bar makes the subtraction obvious even though the story sounds like adding. Then some stories take two steps: you had 34 tickets, sold 28 more, then gave 15 away.

The lesson of the whole unit lives here: do not choose the operation from a keyword like 'more' or 'left'. Draw the bar, see where the gap is, and let the picture decide. 'Got 18 more' sounds like adding, but because the total is known and the start is not, it is really a subtraction.

For a two-step story, solve one step, write the in-between answer, then use it in the next step. 34 tickets and 28 more is 62 (an adding step), then 62 give away 15 is 47 (a taking-away step). Keep the two bars stacked so the 62 flows from the first into the second.

Worked example

There were 34 raffle tickets. 28 more were printed, then 15 were given away. How many tickets are there now?

Step 1, adding: 34 + 28. Ones 4 + 8 = 12, tens 30 + 20 = 50, so 62.
Step 2, taking away: use the 62. 62 - 15. Take 10 to get 52, take 5 to get 47.
Check the answer is sensible: we printed more then gave a few away, so an answer near 62 but a bit less fits.

Step 1 as a part-whole bar: 34 + 28 = 62. Step 2 then takes 15 from this 62 to reach 47.

Answer: There are 47 tickets now.

Check for understanding, ask

In 'had some, got 18 more, now 53', is the missing number a part or the whole?
In a two-step problem, why do we write the answer to step one before doing step two?

Watch for

Common misconceptions and how to address them

MisconceptionPick the operation from a keyword: 'altogether' always means add, 'left' always means subtract.

Why it happens: Keyword rules work on easy problems, so students lean on them, but they break the moment a problem is worded to trick them, such as a start-unknown story that says 'more' but needs subtraction.

How to address it: Teach the bar instead of the keyword. Draw the story, find where the gap is, and choose the operation from the picture. Show a 'more' problem that is really a subtraction to prove the keyword can lie.

'Got 18 more, now 53' sounds like adding, but the start is a missing part: 53 - 18 = 35. The bar overrules the keyword.

MisconceptionGrab the two numbers and do a sum without reading the whole problem.

Why it happens: Students see numbers and rush to calculate, skipping the comprehension that is half the task.

How to address it: Insist on reading the whole story once for meaning before any number is written. Ask 'what is the question?' and have students underline it, then draw the bar, and only then calculate.

MisconceptionFor 'how many more', add the two amounts instead of finding the gap.

Why it happens: Comparison stories mention two numbers, and students default to adding whenever they see two numbers.

How to address it: Draw the two bars side by side so the difference is a visible gap, not a total. 'How many more' measures the gap, which is subtraction, not the combined length.

Comparing is not combining. The answer is the gap, 45 - 27 = 18, not the total 72.

MisconceptionAnswer with a bare number and no label, like writing 34 with no idea of 34 what.

Why it happens: Once the calculation is done, students stop, forgetting the number has to answer the actual question.

How to address it: Require a full-sentence answer that names the thing: '34 cookies are left', not '34'. Reread the question and check the answer replies to it.

MisconceptionA two-step problem is one sum, so add or subtract all the numbers at once.

Why it happens: Students treat every number in the story as belonging to a single calculation.

How to address it: Split the story into two bars and solve one step at a time, writing the in-between total. Make the answer to step one visibly feed into step two.

Do it together

Guided practice (with answers)

1. There are 35 red apples and 24 green apples. How many apples altogether?
Parts 35 and 24, whole 59.
Answer: 59 apples. Two parts join to a whole, so add: 35 + 24 = 59.
2. A jar holds 52 marbles. 27 are taken out. How many are left?
Answer: 25 marbles. Whole 52, part 27 gone, so subtract: 52 - 27 = 25.
3. Ella read 46 pages and Sam read 38 pages. How many more pages did Ella read?
The gap between the bars is 8.
Answer: 8 pages. Compare the two: 46 - 38 = 8.
4. Tom had some stickers, was given 19 more, and now has 44. How many did he start with?
Answer: 25 stickers. The whole 44 and a part 19 are known, so the missing start is 44 - 19 = 25.
5. A shop has 63 balloons. It sells 28 in the morning and 15 in the afternoon. How many are left?
Answer: 20 balloons. Step 1: 28 + 15 = 43 sold. Step 2: 63 - 43 = 20 left.
6. There are 47 blue counters and 47 red counters. How many counters in all?
Answer: 94 counters. Two equal parts join: 47 + 47 = 94.

On their own

Independent practice worksheets

Set the matching ChalkBee worksheets for independent work. The answer keys are computed in code, so they are never wrong. Start with the word-problem sets, then use the plain addition and subtraction sets for students who need to firm up the calculation the bar sets up.

Grade 2 word problems worksheet (set A)mixed adding and taking-away stories within 100 Grade 2 word problems worksheet (set B)more stories, including comparison Grade 2 addition worksheet (set A)the adding step on its own Grade 2 subtraction worksheet (set A)the taking-away step on its own All Grade 2 word problem worksheetsthe full set for extra practice

Reach every student

Differentiation

Support

Keep counters on desks so a stuck student can build both parts and physically push them together or take a part away.
Give a pre-drawn blank bar with a brace so students only have to label the parts and the whole, not draw the structure.
Start with result-unknown problems (the whole or a part missing at the end) before moving to start-unknown ones.
Read the problem aloud with the student and pause after each sentence to ask what is now known.

Extension

Write a matching story of your own for a given bar, so the same picture can be a putting-together and a comparison story.
Solve start-unknown comparison problems, such as 'Ana has 18 fewer than Beth, who has 52, how many has Ana?'.
Make up a two-step problem whose answer is exactly 50, and swap with a partner.
Explain why a comparison problem and a taking-from problem can use the same subtraction even though the pictures look different.

Check it stuck

Assessment: exit ticket

A three-question exit ticket for the last five minutes. It samples a putting-together, a comparison, and a start-unknown problem, the three shapes that trip students up.

1. There are 26 ducks and 37 geese on the pond. How many birds altogether?
Answer: 63 birds. Add the two parts: 26 + 37 = 63.
2. Priya scored 54 points and Leo scored 39. How many more did Priya score?
Answer: 15 points. Compare: 54 - 39 = 15.
3. A tank had some fish, 16 were added, and now there are 41. How many at the start?
Answer: 25 fish. The start is a missing part: 41 - 16 = 25.

For the teacher

Teacher notes and timings

Rough timing across three to four lessons: Lesson 1 acting out and part-whole bars for putting-together (sections 1 to 2), Lesson 2 taking-from with a missing part (section 3), Lesson 3 comparison bars (section 4), Lesson 4 unknown-anywhere and two-step problems plus the exit ticket (section 5 and assessment).
The whole unit is a campaign against keyword-spotting. Keep saying: draw the bar, find the gap, then choose the operation. A student who can draw the structure will beat a student who memorised that 'left means subtract'.
Two bar shapes cover everything at this level: the part-whole bar (one whole split into parts) for putting-together and taking-from, and the comparison bar (two lengths side by side) for how-many-more and how-many-fewer.
The calculations themselves are the Grade 2 within-100 methods (2.NBT.B.5): work tens and ones, and some of these deliberately need regrouping (28 + 34, 62 - 28) so students apply the bar to real, non-trivial sums. If regrouping is not yet secure, teach or revisit the Grade 2 add-and-subtract-within-100 unit first.
Insist on a labelled, full-sentence answer every time. '34 cookies are left' shows the child knows what the number means, a bare '34' does not.
US and AU alignment: the US names one- and two-step word problems with the unknown in all positions at Grade 2 (2.OA.A.1), with the calculations drawn from 2.NBT.B.5. ACARA reaches the same modelling at Year 2 through everyday adding and taking-away problems (AC9M2N05), using the place-value partitioning of AC9M2N01 to compute. The bar-model method here matches the diagrams both frameworks ask students to use.
Present mode and print both work: use the Print button for a clean teacher copy or a student handout, and project the page to draw the bars with the class straight from the diagrams.

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