Lesson 30: Analyzing Sets
Lesson Objectives
- Use objects, pictures, drawings, and number lines to understand multiplication
- See multiplication as repeated addition
- Apply skip counting and the TouchMath approach for finding products
- Apply understanding in making comparisons of pairs of factors
- Skip count up and down by 5’s using concrete objects and pictures
- Use arrays as a strategy for skip counting
Materials
- Extend Workbook (Page 30)
- Counters or manipulatives
- Graph paper
- Highlighters, markers, or crayons
Step 1: Warm Up (5 min)
Draw a few multiplication arrays with multiples of 2 (2×1, 2×2, 2×3, 2×4), using stars, dots, or another symbol (e.g. 2 dots in one row, 2 dots in two rots, 2 dots in three rows). Draw boxes around each group of 2 in the array drawings. Within each array, write the multiplication sentence next to each group of 2. You can break down each group to simplify things or show the skip counting sequence on one side of the box (2, 4, 6). Play around with different ways to visually illustrate arrays using multiples of 2 to start.
Step 2: Vocab Review (5 min)
Review prior vocabulary: repeated addition and skip counting. Skip counting is a tool that will help us find pairs of equal addends. It is also the foundation of multiplication. Tell students that they will be learning a process that will make it very easy for them to learn how to multiply. Introduce new vocabulary: arrays (an arrangement of a set of numbers or objects in rows and columns) and products of multiplication problems.
Step 3: Model (5 min)
Once students have grasped multiplication arrays, use real-life connections to help build stronger connections to the concept, using multiples of 5: Ask students how much it would cost if each member of their family went out to dinner and had $5 each to spend; Ask the class, how many total problems would be done if each student were assigned 5 problems (can ask a group of students if class is large); or, another relevant example. Model making arrays wit multiples of 5’s. Review skip counting by 5’s song for further support.
Step 4: Guided Practice (5 min)
Distribute a 100s chart, and start on 5. Ask students to skip count by 5’s forward to 50. Have them circle each number with a red marker. Ask students to write down multiples of 5 from their 100s Chart up to 50 on a separate sheet of paper. In groups, ask students to draw 1-2 arrays with multiples of 5 (5×2, 5×3, 5×4, etc.). Have students circle each group of 5. Ask them, “how many groups of dots/stars did you circle? How many dots/stars are in each group?” Then have them write down their multiplication sentences/problems next to their arrays (e.g. “We circled 3 groups of dots and there are 5 dots in each group. Therefore, my multiplication sentence is 5×3=15 OR 3×5=15. There are 15 total dots altogether. This means the product of 5×3 is 15.”). Ask what the repeated addition statements would look like (e.g. 3+3+3+3+3 OR 5+5+5).
Step 5: Student Practice (5 min)
Go to Student Workbook Page (30). Read the directions at the top of the page. Tell students they will be practicing working with arrays to understand groups of items. Remind students that they can use any supports from today or previous lessons. Have students draw 15 dots with some space between them. Tell them they already have their product (15 dots) and now they are working to build their multiplication problems. Then, go through each question, reminding them to box their groups of dots based on the questions.
Step 6: Wrap Up (5 min)
To wrap up the lesson, review the learning objectives and core vocabulary words again and ask your students about their experience.
