Operations & Algebraic Thinking

Addition and Subtraction within 100: Word Problems and Arrays

Grade 2

✓By the end of this lesson students will be able to solve one- and two-step word problems involving addition and subtraction within 100.
✓By the end of this lesson students will be able to represent addition and subtraction word problems using drawings and equations with a symbol for the unknown number.
✓By the end of this lesson students will be able to use arrays to represent repeated addition.
✓By the end of this lesson students will be able to understand that arrays can be used to show equal groups, laying the foundation for multiplication.

Key concepts

Word Problems: Addition and Subtraction within 100

Word problems tell a math story. To solve them, we need to read carefully to understand what the problem is asking. We look for clues, often called keywords, to help us decide if we need to add (put together, find total) or subtract (take away, find the difference). We can use drawings, number lines, or place value strategies to solve these problems. It's important to write an equation to show our thinking and include the correct units in our answer.

Foundations of Multiplication: Arrays

An array is a way to arrange objects in rows and columns. Rows go across, and columns go up and down. In an array, every row has the same number of objects, and every column has the same number of objects. We can find the total number of objects in an array by using repeated addition. For example, if an array has 3 rows with 4 objects in each row, we can add 4 + 4 + 4 to find the total. This helps us understand what 'equal groups' means.

Key facts to remember

1Always read word problems carefully to understand the story and what is being asked.
2Look for keywords like 'in all,' 'total,' 'altogether' for addition, and 'left,' 'difference,' 'how many more' for subtraction.
3You can use drawings, number lines, or place value strategies (like base ten blocks) to solve addition and subtraction problems within 100.
4An array is an arrangement of objects in equal rows and equal columns.
5Rows go across, and columns go up and down.
6You can use repeated addition to find the total number of objects in an array.
7Arrays help us understand the concept of 'equal groups,' which is a foundation for multiplication.

Worked examples

Example 1

There are 47 red apples and 35 green apples in a basket. How many apples are there in all?

I1. Read the problem carefully: We need to find the total number of apples.

II2. Identify the numbers: 47 red apples, 35 green apples.

III3. Identify the operation: The phrase 'in all' tells us to add.

IV4. Write an equation: 47 + 35 = ?

V5. Solve using place value:

VI Add the ones: 7 ones + 5 ones = 12 ones. Regroup 12 ones as 1 ten and 2 ones.

VII Write down 2 in the ones place and carry over 1 ten to the tens place.

VIII Add the tens: 4 tens + 3 tens + 1 regrouped ten = 8 tens.

9 Write down 8 in the tens place.

106. State the answer with units.

Answer

There are 82 apples in all.

Drawing a picture of the apples or using base ten blocks can help visualize the addition and regrouping.

Example 2

A baker made 92 cookies. He sold 58 cookies. How many cookies does the baker have left?

I1. Read the problem carefully: We need to find how many cookies remain.

II2. Identify the numbers: 92 cookies made, 58 cookies sold.

III3. Identify the operation: The phrase 'have left' tells us to subtract.

IV4. Write an equation: 92 - 58 = ?

V5. Solve using place value:

VI Subtract the ones: We have 2 ones and need to subtract 8 ones. We cannot do this directly, so we need to regroup.

VII Regroup 1 ten from the 9 tens, leaving 8 tens. Add 10 ones to the 2 ones, making 12 ones.

VIII Now subtract the ones: 12 ones - 8 ones = 4 ones.

9 Write down 4 in the ones place.

10 Subtract the tens: 8 tens - 5 tens = 3 tens.

11 Write down 3 in the tens place.

126. State the answer with units.

Answer

The baker has 34 cookies left.

Using a number line to 'jump back' or drawing base ten blocks to 'take away' can be helpful strategies.

Example 3

Draw an array with 4 rows and 3 columns. Then, write a repeated addition equation to find the total number of objects.

I1. Understand the terms: 'Rows' go across, 'columns' go up and down.

II2. Draw the array: Draw 4 rows, with 3 objects (like stars or dots) in each row.

III * * *

IV * * *

V * * *

VI * * *

VII3. Identify the number of objects in each row: There are 3 objects in each row.

VIII4. Write the repeated addition equation: Since there are 4 rows and each has 3 objects, we add 3 four times.

9 3 + 3 + 3 + 3 = ?

105. Solve the repeated addition: 3 + 3 = 6; 6 + 3 = 9; 9 + 3 = 12.

Answer

The array has 12 objects. The repeated addition equation is 3 + 3 + 3 + 3 = 12.

You can also think of it as 3 columns with 4 objects in each column: 4 + 4 + 4 = 12. Both ways give the same total!

Common mistakes

✗Not reading the entire word problem before trying to solve it, leading to misunderstanding the question.
✗Choosing the wrong operation (addition instead of subtraction, or vice versa) for a word problem.
✗Making calculation errors, especially when regrouping (carrying over or borrowing) during addition or subtraction.
✗Confusing rows and columns when drawing or interpreting arrays.
✗Forgetting to include the correct units (e.g., 'apples,' 'cookies') in the final answer to a word problem.

Exam tips

★Underline or circle the important numbers and keywords in word problems to help you focus.
★Draw a picture or a model (like base ten blocks) to help visualize the word problem before solving.
★Show all your work, step by step, for addition and subtraction problems, especially when regrouping.
★Double-check your calculations by adding or subtracting in a different order, or by using the inverse operation (e.g., if you subtracted, add to check your answer).

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