Grade 4 – Unit 2: Multiplying by 1-Digit Numbers
- Originals and Copies – using physical bodies and/or Unifix cubes to represent relationships concretely and discretely.
- Fluency Carousel to build Stage 4 Fluencies
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)
Stage 3: Flexible, Effective Strategies
- Use of tape diagram, open arrays, open number line
- Use of partial products and Distributive Property of Multiplication
- Making a table to show and organize thinking as related to word problems
- Solving multiplicative comparison word problems
- Distinguishing by modeling additive vs. multiplicative situations
- Solving multi-digit by single-digit multiplication equations
Stage 4: Automaticity (with conceptual understanding)
- Multiplying by multiples of 10, 100, and 1000
- Single-digit multiplication facts
- Writing whole numbers in expanded for by place value (prerequisite)
- ITPs: Multiplication Grid
- Illustrative Mathematics for 4.OA
- EngageNY Math Studio
- Dr. Nicki’s Pintrest: Bar Diagramming
- Interactive Sites for Education
- Students need many opportunities to visualize word problem situations concretely, using pictorial representations and using math models. Students need to reflect on, compare and refine models.
- Lesson is needed to bridge student understanding of multiplicative comparison where students see “times as many” as copies of an original. Recognizing visually the number of parts to make the whole is important.
- Need to present problems where multiplicative and additive situations are presented and have student visualize and act out/model the situation. Discussions about how the problems are different is key.
- Lesson 2.1: “Advanced Learners” on pg. 64 needs to be made in to a center or whole-group activity which is used throughout this unit of study and the rest of the year. The “Enrich” for Lesson 2.1 could be used to replace the lesson given. The “Reteach” for Lesson 2.1 is where the lesson should begin. Use the problems in this lesson as ways to teacher comprehension strategies for word problems. Problems to use: Unlock pg. 63, #1 pg. 64, #9 pg. 65. Problem #9 is good for an exploration and using comprehension strategies. Use the equations to get students modeling and using multiplicative comparison language. For example, 9 x 2 = 18 can be seen as: 18 is 9 times as many as 2, 9 times as many 2 is 18 (simply stated: 9 times as many groups of twos is 18).
- Create a plan for addressing the multiplicative comparison problem types situation: Product Unknown, Group Size Unknown (“How many in each group?” Division), Number of Groups Unknown (“How many groups?” Division). Develop a plan for moving towards multi-step problems situations.
- Lesson 2.2: “Unlock the Problem” and “Share and Show” are similar, #2, 4, 5, 7 on p. 71 and #9 and 11 on pg. 72 are similar. Great opportunity to JigSaw and have student model and explain ideas to each other.
- Lessons 2.3 to 2.8 focus on models and strategies for multiplication. All calculations should be placed in a context, context is visualized, then skill is shown, followed by revisiting the context.
- Do Number Strings with “Reteach” and in the “Other Ways B” in Lesson 2.3 and visualize each time. Visualize using as proportionally accurate models as possible. For example, “Other Ways A” on pg. 76 is a model, but it is not proportionally accurate. Use the Associate Property of Multiplication as discussed in the “Advance Learners” on pg. 76.
- Use estimation through out as a way to connect to finding a reasonable product. Also use estimation to help students build their readiness for compensation strategies such as 49 x 5 is 50 x 5 without one group of 5. For Lesson 2.4, would make into routine and/center after middle of chapter. Would use the “Advanced Learners” on pg. 82 as a center. For Lesson 2.4, use problems on pg. 83 as conversations and opportunities for discussion.
- For Lesson 2.5 begin by modeling using concrete models with base-ten blocks, then move to the pictorial, then move to the open array. All the while connect the Distributive Property of Multiplication. Some students may be ready for or need the single-digit fact decomposed also. “Advanced Learners” of pg. 88, 94, 108 are a good ideas for a center. Use the “Reteach” and “Enrich” opposed to lesson. Use lesson as a guide, but have kids model on graph paper. Use the naked number problems in lesson as opportunities to have students build concretely and/or make pictorial representations.
- Weave in problems from Lesson2 2.9 and 2.12 after the middle of the chapter.
- Lesson 2.7: Ensure that students explain and show by writing the associated equation, where each of the partial products come from. Connect the open array, the Distributive Property and Partial Products.
- Do not teach Lessons 2.10 and 2.11 as prescribed. It is the traditional algorithm in disguise. Focus on student understanding of the tools, models and strategies previously outlined. This can be revised towards the end of Grade 4. It is vital that students understand what is happening, before they rush to an algorithm.
- Tools: base-ten blocks, Unifix cubes, grid/graph paper,
- Models: tape/bar diagram, open array, number line, table/chart, equal groups
- Strategies: partial products, Distributive Property, Associative Property, Commutative Property, decomposing factors, using basic fact and then multiplying by a power of 10, 100 or 1000, identify and use a pattern, use the unit number, e.g. 3,400 x 2 can be seen as 34 hundreds times 2 or 68 hundreds or 6,800 (See pg. 79),
- See pgs. 87A and 93A
- Ensure that students are given sufficient space to work out problems. For example, look at the mid-chapter review an ask, “Would this provide enough room for my students to use to strategies and models that we have been using?”
- Open Array Cards – create open arrays (Side A), grid paper (Side B)
- Multiplicative Comparison Center – Using Unfix cube have student create and record multiplicative comparison stories. (Lesson 2.1, pg. 64 Advanced Learners)
- Match the Math Model – Have student match the stories with the math models and explain why (Lesson 2.1, pg. 63 Enrich). Can have students create their own and use with small-groups.