Open Sentences and Finding Missing Values for Primary 1

Open Sentences (1)

Performance Objectives

By the end of the lesson, students should be able to:

1. find missing numbers/values in open sentence
2. use of symbols to find missing values
3. solve simple related open sentences

What is an Open Sentence?

An open sentence is a mathematical statement that has a missing number or value. It is like a puzzle where a part of the number sentence is hidden.

For example, if someone says, “I have 3 oranges, and I bought some more. Now I have 5 oranges,” the “some more” is the missing part. In mathematics, we use a special symbol or a box to show this missing part.

Identifying Symbols for Missing Values

In open sentences, we use different symbols to stand for the missing number. These symbols help us know where the puzzle piece is missing.

Common symbols used to represent missing values include:

1. A box, like $\square$
2. A circle, like $\bigcirc$
3. A triangle, like $\triangle$
4. A letter, like $x$ or $y$

These symbols are placeholders for the number that makes the sentence true.

Finding Missing Numbers in Open Sentences

To find a missing number in an open sentence, we need to think about what number makes the sentence correct. This is like solving a small puzzle.

We will look at open sentences that use addition and subtraction.

Missing Numbers in Addition Sentences

In addition, we combine numbers. If one of the numbers is missing, we can find it by thinking about what needs to be added to reach the total.

Example 1: Missing Second Number

Consider the open sentence:

$$ 3 + \square = 5 $$

This means “3 plus what number gives 5?”

To find the missing number, we can count up from 3 to 5:

1. Start at 3.
2. Count 4 (one finger up).
3. Count 5 (another finger up).

We counted 2 fingers. So, the missing number is 2.

$$ 3 + 2 = 5 $$

Example 2: Missing First Number

Consider the open sentence:

$$ \square + 4 = 7 $$

This means “What number plus 4 gives 7?”

To find the missing number, we can count up from 4 to 7:

1. Start at 4.
2. Count 5 (one finger up).
3. Count 6 (another finger up).
4. Count 7 (a third finger up).

We counted 3 fingers. So, the missing number is 3.

$$ 3 + 4 = 7 $$

Missing Numbers in Subtraction Sentences

In subtraction, we take away numbers. If one of the numbers is missing, we can find it by thinking about what was taken away or what was left.

Example 3: Missing Second Number (Number Taken Away)

Consider the open sentence:

$$ 6 – \square = 2 $$

This means “6 minus what number gives 2?”

To find the missing number, we can count back from 6 to 2:

1. Start at 6.
2. Count 5 (one finger down).
3. Count 4 (another finger down).
4. Count 3 (a third finger down).
5. Count 2 (a fourth finger down).

We counted 4 fingers down. So, the missing number is 4.

$$ 6 – 4 = 2 $$

Example 4: Missing First Number (Starting Number)

Consider the open sentence:

$$ \square – 3 = 5 $$

This means “What number minus 3 gives 5?”

To find the missing number, we can think of it as an addition problem. If we take 3 away from a number and get 5, then the starting number must be 5 plus 3.

$$ 5 + 3 = 8 $$

So, the missing number is 8.

$$ 8 – 3 = 5 $$

Solving Simple Related Open Sentences

We can use the same ideas to solve different open sentences, even when the symbols change.

Example 5: Using a Circle Symbol

Solve the open sentence:

$$ 7 + \bigcirc = 10 $$

This means “7 plus what number gives 10?”

Count up from 7 to 10:

1. Start at 7.
2. Count 8, 9, 10.

We counted 3 numbers. So, the missing number is 3.

$$ 7 + 3 = 10 $$

Example 6: Using a Triangle Symbol

Solve the open sentence:

$$ 9 – \triangle = 4 $$

This means “9 minus what number gives 4?”

Count back from 9 to 4:

1. Start at 9.
2. Count 8, 7, 6, 5, 4.

We counted 5 numbers. So, the missing number is 5.

$$ 9 – 5 = 4 $$

Example 7: Using a Letter Symbol

Solve the open sentence:

$$ x + 2 = 8 $$

This means “What number plus 2 gives 8?”

Count up from 2 to 8:

1. Start at 2.
2. Count 3, 4, 5, 6, 7, 8.

We counted 6 numbers. So, the missing number is 6.

$$ 6 + 2 = 8 $$

Drawing Boxes or Shapes to Represent Missing Values

Sometimes, you might be asked to draw a box or a shape to show a missing value in a number story.

Example 8: Drawing a Box for a Missing Value

A boy had 5 pencils. He bought some more pencils and now has 7 pencils. Write an open sentence for this story using a box.

The story starts with 5 pencils. He bought “some more,” which is the missing value. Then he has 7 pencils in total.

The open sentence is:

$$ 5 + \square = 7 $$

To find the missing value, we know that $5 + 2 = 7$. So, the boy bought 2 more pencils.

Example 9: Drawing a Circle for a Missing Value

There were 8 birds on a tree. Some birds flew away, and 3 birds were left. Write an open sentence for this story using a circle.

The story starts with 8 birds. “Some birds flew away” is the missing value. Then 3 birds were left.

The open sentence is:

$$ 8 – \bigcirc = 3 $$

To find the missing value, we know that $8 – 5 = 3$. So, 5 birds flew away.