Grade 3: Unit 4 Multiplication Facts and Strategies
- Distributive Property with Ten-Frames
Recommended comprehension strategies for problem solving:
- A line at a time
- Making a mathematical sketch (look at pg. 2 – 3)
- What is the question? (Problem Posing)
- Rework a problem (by changing the numbers)
- What do the numbers mean?
- Match the Mathematical Sketch or Model
- Worked examples (Math Playground, Thinking Blocks)
- Dr. X’s Multiplication Contraption
- Math Learning Center App
- K-5 Math Teaching Resources
- Dr. Nicki’s Pintrest: Multiplication
- Skip counting by 3s, 4s,
- Multiplication facts for 3s, 4s using strategy such as using 3 x 5 to figure out 3 x 6
- Skip counting by 2s, 5s and 10s
- Multiplication facts for 2s, 5s, 10s
- Lesson 4.1: Model in many ways using concrete objects, math models of equal groups, using words, using repeated addition. Use “Advanced Learners” Activity for lesson, but adapt so that 2 is a constant factor. Students would model the expressions created and write in many ways. Students would then double the representation and record the new equation. For example, 2 x 4 doubled becomes (2 x 4) + (2 x 4) or 4 x 4. “Enrich” is good for a center later on the chapter or for a daily puzzler. Have students create their own. Use the “Unlock the Problem” as a “What is the question?” situation and show only the situation, “Ms. Peterson’s class sold tickets for the class play.” and the graph. Ask the students to tell us what the questions might be. Have students brainstorm in small-groups, then we will make a list of questions with the entire class. In the “Practice and HW” question #7 needs to be acted out. We cannot assume that students understand the term “double”. This is leading towards multiplicative comparison, but students do not have the prior knowledge at this time to support this. Adaptation #1: Need center that allows students to build and then double the representation. This structure can be used in subsequent lessons. Adaptation #2: Build on knowledge by helping students see that if they know 2 x 1, and 2 x 2 and 2 x 3 and 2 x 4 and 2 x 5, then they can figure out 2 x 8 by combining (2 x 4) + (2 x 4). Make this a center to build the mental prep work for the Distributive Property. Do this activity on index cards.
- Lesson 4.2: POD? Have they done a line plot recently or ever? This activity would be better done in a small-group with guidance or as a whole group, but with actual student names to represent the “Xs”. Look at “Unlock the Problem” and repeat structure from Lesson 4.1 for #32. Repeat bolded italicized structure from Lesson 4.1. Have students build group cards using five frames and ten-frames. For questions #28 and 29 you will need to model using concrete materials. Also, consider problem posing. For example, #28 could be turned into: Marcel played 5 songs on the banjo. Each song lasted 8 minutes. Now have the student visualize, symbolize with Unifix cubes and create a bar/tape diagram model for the situation.
- Lesson 4.3: The “Enrich” connects back to Adaptation #2 from Lesson 4.1.Repeat bolded italicized structure from Lesson 4.1, but extend that understanding by incorporating a new model (arrays). In a guided math group address the idea of using our knowledge of the 5 times tables as an anchor for figuring out multiplication facts involving factors of 5 or greater. Use a ten-frame to model this work. Can also have students build with arrays…using 2 different colored square tiles. This needs to be scaffolded, as this chapter jumps into the representations with arrays.
- It is very important to have students constantly says 3 x 4 is 3 groups of 4 things or 4 three times.
- Lesson 4.4: Model concretely and use concrete tool like a pencil to separate the groups. Adaptation: Have students work in groups to build, but each person has a responsibility in terms of how to represent. Once again, students may not know what the parenthesis mean. Build the idea that it means that this expression is a group or is another way of saying a particular expression. Would use pattern blocks to visualize ideas. Turn this idea into a Number Talk and ask, “How do you see this?”
- Lesson 4.5, 4.8, 4.9 need to follow the structures outlined in previous lessons. Build it and interpret what it means. Student need many opportunities to make sense of these ideas. Naked number equations should be given a context. Adaptation: Center idea for creating arrays. Find My Match by writing a multiplication equation on one side of an index card, then having other index cards that have the same value, but written using the Distributive or Associative Properties of Multiplication.
- Lesson 4.6 needs to happen in 2-parts. Part 1 is about understanding the property and why it works. Part 2 is about using the Associative Property of Multiplication. Need to ensure that the Commutative Property is solidified before this lesson. Adaptation #1: Build rectangular prisms with Unifix cubes to concretely show how we can get to the product. “Advanced Learners” idea on pg. 224 can be made into a center or posted for the week for all to figure out. Adaptation #2: Would use “Enrich” on pg. 223 as an Quiz, Quiz, Trade activity. Could also adapt lesson to do a Back to Back Face to Face or Give One, Get One activity. Look at page 225, #26: Turn this idea into a Number Talk and ask, “How do you see this?”
- Lesson 4.7: Teaching kids how to read the multiplication grid and how to look for patterns. Focus on focusing attention, but not telling. The vital outcome of this lesson is about getting to see and understand the patterns when multiplying by odd or even factors. Doing #17 on pg. 232 could be very useful. It is about setting up the structure so that students can make generalizations about the patterns.
- Tools: counters, base-ten blocks, ten-frames, grid paper
- Models: equal groups, arrays/area model, open number line, number bonds, sticks, ratio table
- Strategies: Properties of Operations for Multiplication (Commutative, Associative, Distributive),
- Exam question #12 should be done as a performance task. Provide additional paper to have kids show their thinking. For #16 the possible answer is correct, but not appropriate for the grade level due to the use of the parenthesis. Do not expect students to show answers this way. Provide additional paper for kids to show work.