Grade 3 · Mathematics
Quarter 3 · Week 2 · TEKS
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This lesson helps Grade 3 students understand how to describe multiplication expressions as comparisons, such as interpreting 3 x 24 as 3 times as much as 24. Students will also learn to determine unknown whole numbers in multiplication or division equations involving three whole numbers. The lesson aligns with TEKS standards and focuses on algebraic reasoning by analyzing and creating patterns and relationships through multiplication and division.
Students should understand basic multiplication and division facts and be familiar with multiplication as repeated addition.
Multiplication expressions can be understood as comparisons between quantities. For example, the expression 3 x 24 means '3 times as much as 24.' This means if you have 24 objects, and you have 3 groups of these 24 objects, you have 3 times as many objects as 24. This helps students see multiplication not just as repeated addition but as a way to compare amounts.
In a multiplication expression like 3 x 24, the numbers 3 and 24 are called factors, and the result is called the product. Understanding these parts helps students solve equations where one number is unknown. For example, in 3 x ? = 72, the unknown factor can be found by thinking about how many times 3 fits into 72.
Students learn to find the missing number in equations involving multiplication or division with three whole numbers. For example, if the equation is 3 x ? = 72, students can use division to find the unknown factor: 72 ÷ 3 = 24. Similarly, for division equations like ? ÷ 4 = 6, students can multiply 6 x 4 to find the unknown dividend, which is 24.
Using counters or objects to create groups helps students visualize multiplication as comparison. Drawing pictures or using strip diagrams can also show how one number is multiplied by another. These models support understanding of the relationship between factors and products and help solve for unknown numbers.
A common misconception is thinking multiplication always means 'times by' in a way that confuses the order of factors. Teachers should emphasize that multiplication is commutative (3 x 24 is the same as 24 x 3) but the comparison meaning focuses on one quantity being 'times as much' as another. Another misconception is confusing the unknown factor with the product; clear examples and practice help clarify this.
Explain what the multiplication expression 3 x 24 means as a comparison.
The expression 3 x 24 means that you have 3 times as much as 24. This means if you have 24 objects, and you have 3 groups of those objects, the total number of objects is 3 times 24, or 72.
3 x 24 means 3 times as much as 24, so the total is 72.
Find the unknown number in the equation 3 x ? = 72.
To find the unknown factor, divide the product 72 by the known factor 3. So, 72 ÷ 3 = 24. The unknown number is 24.
The unknown number is 24 because 3 times 24 equals 72.
Introduce the lesson by asking students if they have ever compared amounts, such as having 3 times as many apples as a friend. Write the expression 3 x 24 on the board and ask what it might mean in terms of comparison.
Discuss with a partner what 3 x 24 could mean. Share ideas with the class about how multiplication can show 'times as much' of a number.
This activity connects students' real-life experiences with the mathematical concept of multiplication as a comparison, setting the stage for deeper understanding.
Provide counters and ask students to make 3 groups of 24 counters each. Have them count the total and describe what they see.
Use counters to create 3 groups of 24. Count all counters and explain how this shows 3 times as much as 24.
Hands-on grouping helps students concretely see multiplication as repeated groups and understand the comparison meaning.
Demonstrate how to write multiplication expressions as comparisons on the board. Show that 3 x 24 means 3 times as much as 24. Introduce equations with unknown numbers and model how to find the unknown.
Practice writing multiplication expressions as comparisons. Solve simple equations with one unknown factor or product using drawings or equations.
This phase clarifies the meaning of multiplication expressions and teaches strategies to find unknown numbers in equations.
Present real-world problems involving multiplication comparisons and unknown numbers. Guide students to solve and explain their reasoning.
Solve problems such as 'If one box has 24 toys, how many toys are in 3 boxes?' or '3 times a number is 72, what is the number?' Explain how multiplication shows comparison and how to find unknowns.
Applying concepts to real-world problems deepens understanding and connects math to everyday life.
Ask students to write a multiplication expression as a comparison and solve an equation with an unknown number. Collect responses to assess understanding.
Write and explain a multiplication expression as a comparison. Solve an equation with a missing factor or product and explain the steps taken.
This assessment checks if students can describe multiplication as comparison and find unknown numbers in equations independently.
Use counters to create 3 groups of 24. Count all counters and explain how this shows 3 times as much as 24.
What does the multiplication expression 3 x 24 mean as a comparison?
It means 3 times as much as 24, or 3 groups of 24, which equals 72.
Find the unknown number in 3 x ? = 72.
The unknown number is 24 because 3 times 24 equals 72.
Write a multiplication expression to show 6 times as many pencils as 8 pencils.
6 x 8.
Explain how to find the unknown number in ? x 9 = 54.
Divide 54 by 9 to find the unknown number, which is 6.
If 7 times a number is 63, write the equation and find the number.
7 x ? = 63; the number is 9 because 7 times 9 equals 63.
Use manipulatives and visual models to support understanding of multiplication as comparison. Provide step-by-step guidance for solving equations with unknown numbers. Use simpler numbers for initial practice before progressing to larger numbers.
Use clear, simple language and visuals to explain multiplication as comparison. Provide sentence frames like '3 times as much as 24 means...'. Use gestures and drawings to support vocabulary understanding.
Challenge students to create their own multiplication comparison problems. Encourage explaining reasoning in writing with detailed comparisons. Introduce related division problems to deepen understanding of inverse operations.
Ask students to find examples at home where multiplication shows comparison, such as recipes or groups of items, and explain what the multiplication means in those contexts.
In this lesson, students learned that multiplication expressions can be described as comparisons, such as 3 x 24 meaning 3 times as much as 24. They practiced using manipulatives and drawings to visualize multiplication as repeated groups and comparisons. Students also learned to find unknown numbers in multiplication and division equations by using inverse operations. These skills help students understand multiplication more deeply and apply it to real-world problems.
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