Grade 5: Unit 2 Dividing Whole Numbers
- Division C-R-A (See pg. 85E, 85G of TE)
- Vocabulary Game
- Interpreting the quotient in context
- Traditional Algorithm – What does it all mean?
- Division Strategies from Schultz Center: Partial Quotients, Ratio Table
- ITPs: Division Grid
- Dr. Nicki’s Pintrest: Division
- Article , Article w/ Video
- A Kids Maths Dictionary
Stage 3: Flexible, Effective Strategies
Stage 4: Automaticity (with conceptual understanding)
- Decomposing a number is a variety of ways based upon place value, i.e. 6,423 is 6,000 + 400 + 20 + 3 or 64 hundred + 23 ones or 642 tens + 3 ones
- Lesson 2.1: Use the second example to address the misconception of what to do when the first digit in the dividend is not divisible by the divisor. Students with say, “Well 4 can’t go into 3.” Would not teach the traditional algorithm, but start with a concrete model with smaller numbers and use an “Equal Groupings” strategy. Would use money where possible. “Advanced Learners” conversation could be a useful conversation to have in a Guided Math group. Adaptation Idea #1: Have specific problems at each table and have students use concrete materials and equal groups to solve. Use the word problems #9, 10 for student to place the naked number equations in context. Interpret the quotient. So if the problem is 275/8=34 r3 it means that I can make 34 groups with 8 things in each, but 3 will not be shared equally or (34 x 8) + 3 = 275. Question to ask: What does it tell me about the relationship between the divisor and dividend, if we do not get a remainder? Place each of the stories in a context. While the EQ of this lesson is appropriate to address conceptual understanding, the outline of the lesson it self does not support student achieving that end…they are simply expected to divide using the traditional algorithm. Adaptation Idea #2: Have a series of division equations and ask students to tell and explain if the quotient is going to be a triple, double or single-digit number or write the division situation as a calculation, but indicate place value in the set-up of the problem. Have students mark where the first digit will be and explain why using place value language.
- Lesson 2.2: Would not do this lesson. Would weave in the idea of275/8=34 r3 can be written as(34 x 8) + 3 = 275. Questions #16 – 18 on page 95 and #5 – 7 on page 97 support this idea. This can be made into a routine or Do Now. This helps get the relationship between multiplication and division. Would save “Advanced Learners” for later math centers.
- Lesson 2.3: Do the “Enrich” as a check after doing the “Advanced Learners” with concrete materials, then sketch and finally interpret. It is vital that students understand that the area model indicates that we are building on the idea of finding a missing factor (or side of a rectangle). Have multiplication mat. See sample. (Sample #2 for Go Math Lesson) Have student anticipate the quotient using place value. For example, 216/18 when can say, “If I had 18 groups, I could not give 100 to every group, because I only have 2 hundreds. So I would have to regroup my 2 hundreds to the tens place and I would have 21 tens, which I can share with 18 groups. The quotient has to be a double digit number or begins in the tens place. Save problem #9 for a problem solving exploration. Use the Social Studies Connection, but rework the problem by using numbers from “Share and Show” section. Can use #5 and 6 on page 103. Adaptation Idea: Do a Quiz, Quiz Trade with equation and visual (Side B). On the other side (Side A) student should have just the equation. So when they are walking around they should show Side A first. The person has to say using place value if the quotient is going to be a triple, double or single digit answer, then they go to Side B and they interpret the sketch. When interpreting the sketch, they note the divisor and how it is decomposed. They note the amount that every group has. By doing this they can say if every group received a hundred, ten or a one. To push the understanding and be more precise, you can have student regroup when needed. This model is limited to dividends less than 1,000 for concrete models.
- Lesson 2.4: Connect the partial quotients to equal groups and use of concrete objects in equal groups or pictorial representation. Adaptation Idea: Have students work in teams of 3 to solve different problems in 2 or 3 ways. They must be able to explain how each way works and how it relates to the other using place value language. Do #19 and 20 “Problem Solving Application” but the focus should be on having students figure out why this is a division situation. Make a table to show relationships. Have students make visualize, act out and sketch out #21.
- Lesson 2.5: Would not do. Would work on the Stage 4 fluency of dividing by tens and also recognizing when the dividend is a multiple of the divisor, thus being to use the basic facts. Would focus on explaining these patterns using concrete objects. Would focus on proportional reasoning and equivalence. For example, on page 113 in the “Unlock the Problem” we have 12/6 = 2 and 120/60 = 2. It is important to note that (12 x 10)/(6 x 10) = 2.
- Lesson 2.6: Would not do. We use this time to solidify understanding of partial quotients, open array/area model and equal groups. Fluency Builder on page 2.6 is useful to do with understanding.
- Combine Lessons 2.7 – 2.9: Focus on strategies to use and what the quotient means in relationship to the context.
- Recommendation: Allow students to select the strategy that they want to use on the final exam and give extra credit if they also use the one requested.
- Tools: base-ten blocks, money, place value chart
- Math Models: open array/area model diagram, number line, equal groupings
- Strategies: partial quotients, subtracting equal groups, expanded notation,