Challenge: Turn 50% of the lessons in this chapter into a game!
Thoughts on Lessons:
- Tools: Base ten blocks, money, place value mats
- Models: Number Bonds, Pictorial base 10, Open Number Line Diagram
- Strategies: Counting backwards by 1s or 10s from the minuend,Counting forward by 1s or 10s from the subtrahend, Constant difference, Partial differences, Inverse relationships, Stacking by place value
- Stage 3 Fluencies:
- Selecting a strategy to use that is efficient given the situation
- Stage 4 Fluencies:
- Recognizing when regrouping is going to be involved
- Regrouping 3-digit number in multiples ways, e.g. 45 = 30 + 15 = 20 + 25 = 10 + 35
- Focus on understanding what is going on based upon place value. Focus on students explaining their thinking using precise language. Focus on student selection of a strategy to use and having a reason as to why they chose that strategy.
- Show What You Know: Adjust this formative assessment piece by including only 2 problems on addition and 2 problems on subtraction (one with regrouping for each different operation). Also provide students with additional paper to show additional strategies. As the page is set up, it only allows for the traditional algorithm.
- TG, pg. 387 I in the Perquisite Skills and pg. 390 and 390 A for Games – these are good ideas for centers and/or quick routines.
- Lesson 6.1: POD on pg. 391 B is not worth your time to do in this way. These are Stage 4 fluencies so students need to be asked verbally. Also the questions could be a re-adjusted to so that a pattern develops and could be discussed. Also, I would use teen numbers plus a single-digit number. For example, 17 + 4 = , 17 + 3 =, 17 – 2 =, etc. Adjust lesson: Your students have been making pictorial base tens for a while now. The way that this lesson is introduced in not going to be much of a cognitive challenge for them. Jump to the “Problem Solving”, pg. 394 and make this an exploration. Explain to the students that you would like then to use pictorial base-tens as a strategy to help solve this, but it should not be the only strategy to show their work and thinking. This is an opportunity for discussion and use of precise math vocabulary. Rework the problem and allow for regrouping. The examples in this lesson do not involve regrouping situations, so adjust as needed. Game Opportunity: Make the “Advanced Learner” into a game, where students have to work with a partner to make “quick sketches” and then add the amounts. Have the students write the 3-digit numbers. Later use this game to have students find the differences. Allow for regrouping.
- Lesson 6.2: So this lesson focuses on the use of partial sums. This strategy is vital, but students need to see this strategy concretely, so use base-ten blocks on a place value chart. Use place value chips on a place value chart. Use an alternative representation, such as an open number line to show the amounts. Have students identify when regrouping is going to be involved. Use the “Think Smarter” problem on pg. 399, but take off the question and have students come up with their own questions that could be answered given the situation. This could be a small-group guided activity. Game Opportunity: Instead of doing the problems a presented, how about providing students with cards to make 3-digit numbers that they then have to write in expanded form and use partial products to add. Students can work in partnership and the partnership with the greatest (or smallest) sum wins.
- Combine Lesson 6.3/6.4/6.5: By combining, I mean, include some problems from lesson 6.3 and 6.4 on day 1 and then on day 2. Focus on having students identify if and in what place value they have to regroup. Use the strategies used previously. Instructional strategy idea: Group students into triads and have them work on one problem, but have each student use a different strategy and then explain their work to each other. It is important that you provide an alternative space to work out problems, as the book does not allow room to make quick sketches and write addends in expanded form. Instead of writing the amounts as the traditional algorithm, I would use partial sums to show the regrouping. For example, instead of a “1” in the ten place, I would write 1 ten or 10. If I write a ten, then I would re-label my place value mat so that it does not say, Hundreds, Tens, One, but rather Value in the Hundreds Place, etc. Game Opportunity: “Advanced Learners” on pg. 404 is a great way to increase the cognitive demand, while having fun. You can have students make the riddles for others to figure out. The ones created by other students can be given as HW.
- Make Centers: Take a day to revisit ideas and strategies from Chapters 4 to 6. Do small-groups on subtraction to gather formative assessment data for upcoming lessons. Have a problem solving center.
- Lesson 6.6: This lesson focuses on subtraction with regrouping using word problems. Context is very important. Look at the problems carefully and ensure that they are appropriate to use with your students. Also look at the problem types. For example, the first problem on pg. 424 is a “Start Unknown/Take From” Problem, but all the other problems presented at “Result Unknown/Take From” problems. This is an issue and if you use the problem just mentioned, then you must scaffold appropriately for it. Use strategies and concrete models use previously. Use an open number line to as a strategy to help solve the problems.
- Combine Lesson 6.7/6.8/6.9: Apply strategies and ideas used previously. Use concrete materials! Adjust lessons: Do not focus on the traditional algorithm. Use a combination of partial differences and regrouping in expanded form. Use an open number line. For example, look at pg. 442 at the first problem. This can be shown on a number line. Spend 4 – 5 days on these batch of lessons. Combine the ideas. Ensure that students can identify when regrouping is needed. Have routines and games where students have to regroup. Look at the “Advanced Learners” for game ideas. Provide additional space to solve!
- Lesson 6.10: This lesson is a great opportunity for a rich discussion. The only method show id the standard algorithm. What about partial differences, combined with expanded form, what about constant differences, what about counting backwards, etc. As mentioned previously, include C-R-A (concrete-representational-abstract)…use tools, models and strategies previously used.
- End-of-Unit Exam: Use #10 for formative assessment data only. Knowing the standard algorithm in a 4th grade standard.