Grade 3 · Mathematics
Quarter 2 · Week 6 · TEKS
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This Grade 3 mathematics lesson focuses on helping students determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10. Students will represent multiplication facts using various approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting. The lesson also supports recall of multiplication facts up to 10 by 10 and their corresponding division facts, promoting efficiency and accuracy in whole number computations.
Students should understand the concept of equal groups and basic addition. They should be familiar with counting by ones and have some experience with simple multiplication as repeated addition.
Equal groups are collections where each group has the same number of objects. Arrays are arrangements of objects in rows and columns, forming a rectangular pattern. Both models help visualize multiplication as combining equal groups or counting objects arranged in rows and columns. For example, 3 groups of 4 objects each can be arranged as 3 rows with 4 objects in each row, making an array of 3 by 4.
Multiplication facts can be represented in multiple ways: - Repeated addition: Adding the same number multiple times (e.g., 4 + 4 + 4 = 12). - Equal-sized groups: Counting the total objects in groups of the same size. - Arrays: Visualizing objects arranged in rows and columns. - Area models: Using length and width to find total units (like an array). - Equal jumps on a number line: Moving forward equal steps repeatedly. - Skip counting: Counting by a number repeatedly (e.g., counting by 4s). These approaches help students understand the concept of multiplication deeply and connect it to addition and counting.
Automaticity in multiplication means recalling facts quickly without hesitation. For example, knowing that 6 × 7 = 42 immediately. Corresponding division facts relate multiplication and division, such as 42 ÷ 7 = 6 and 42 ÷ 6 = 7. Understanding this relationship helps students solve problems efficiently and check their work.
- Misconception: Multiplication always makes a bigger number. Address by showing examples like 1 × 5 = 5 or 0 × 7 = 0. - Misconception: Arrays must be square. Clarify that arrays can be rectangular, such as 3 by 4 or 2 by 5. - Misconception: Skip counting is just counting by ones. Emphasize that skip counting jumps by equal intervals, like counting by 2s or 5s.
Use concrete materials like counters to build equal groups and arrays. Draw arrays on grid paper to visualize rows and columns. Use number lines to demonstrate equal jumps and skip counting. Encourage students to explain their reasoning and compare different strategies. Connect multiplication facts to real-life contexts, such as arranging chairs in rows or packaging items.
You have 4 groups of 5 counters each. How many counters do you have in total? Show your answer using repeated addition and an array.
Each group has 5 counters, and there are 4 groups. Repeated addition adds 5 four times: 5 + 5 + 5 + 5 = 20. An array can be drawn with 4 rows and 5 columns, showing 20 counters in total.
Total counters = 5 + 5 + 5 + 5 = 20. The array has 4 rows and 5 columns, so 4 × 5 = 20 counters.
Draw an array for 3 groups of 7 objects. Write the multiplication fact and the corresponding division facts.
The array has 3 rows (groups) and 7 columns (objects per group). The multiplication fact is 3 × 7 = 21. The corresponding division facts are 21 ÷ 7 = 3 and 21 ÷ 3 = 7.
Array: 3 rows and 7 columns. Multiplication fact: 3 × 7 = 21. Division facts: 21 ÷ 7 = 3 and 21 ÷ 3 = 7.
Show students a collection of objects arranged in equal groups and ask them how they would find the total number of objects quickly.
Observe the objects and share ideas on how to count the total without counting each object one by one.
This activity activates prior knowledge about grouping and counting, setting the stage for learning multiplication as repeated addition and arrays.
Provide students with counters and ask them to create equal groups and arrays up to 10 by 10. Have them count the total objects and record their findings.
Use counters to make equal groups and arrays, count the total objects, and write multiplication expressions to represent them.
Hands-on exploration helps students connect concrete objects to multiplication expressions and understand the structure of arrays and equal groups.
Demonstrate representing multiplication facts using repeated addition, arrays, area models, number lines, and skip counting. Explain the relationship between multiplication and division facts.
Watch demonstrations and practice representing multiplication facts using different methods. Discuss how multiplication and division facts relate.
Explicit teaching clarifies multiple ways to represent multiplication and reinforces the connection to division facts for efficient problem solving.
Present real-world problems involving equal groups and arrays, such as seating arrangements or packaging items. Guide students to solve using multiplication strategies learned.
Solve real-world multiplication problems using arrays, repeated addition, or skip counting. Explain their reasoning to peers.
Applying skills to real-world contexts deepens understanding and shows the usefulness of multiplication strategies.
Ask students to demonstrate how to find the total number of objects in equal groups or arrays and represent the multiplication facts using at least two different methods.
Show understanding by solving problems, representing multiplication facts in multiple ways, and recalling multiplication and division facts.
Assessment confirms students' mastery of determining totals in equal groups and arrays and their ability to represent and recall multiplication facts.
Use counters to make equal groups and arrays, count the total objects, and write multiplication expressions to represent them.
If you have 4 groups of 6 objects, how many objects are there in total?
4 groups × 6 objects = 24 objects in total.
Show how to represent 5 × 3 using repeated addition.
5 × 3 is 3 added 5 times: 3 + 3 + 3 + 3 + 3 = 15.
What multiplication fact does an array with 7 rows and 2 columns represent?
7 × 2 = 14.
What are the division facts related to 8 × 5 = 40?
40 ÷ 8 = 5 and 40 ÷ 5 = 8.
Explain why skip counting is useful for multiplication.
Skip counting helps find the total by counting equal jumps, making multiplication faster and easier to understand.
Use counters and visual aids for students needing concrete examples. Provide step-by-step guidance for forming arrays and writing multiplication expressions.
Use pictures and gestures to explain equal groups and arrays. Provide vocabulary cards with key terms and definitions.
Challenge students to create and solve word problems involving arrays up to 10 by 10. Encourage students to explain the relationship between multiplication and division facts in their own words.
Encourage students to find examples of equal groups or arrays at home, such as rows of chairs or sets of utensils, and write multiplication facts to represent them.
Students learned to determine the total number of objects in equally-sized groups and arrays up to 10 by 10. They explored multiple ways to represent multiplication facts, including repeated addition, arrays, area models, number lines, and skip counting. The lesson emphasized recalling multiplication facts up to 10 by 10 and understanding their relationship to division facts, supporting efficient and accurate problem solving.
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