Common Core Standard: CCSS.MATH.CONTENT.4.NBT.B.6
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Placement in the year: This comes after the unit on division with a two-digit dividend and how to interpret the remainder in a division problem. Students will need these skills before they get to measuring angles because they need to be able divide the number 360 when looking at degrees in a circle. Students exceeding the standards will use these skills in the measurement conversion unit.
Overall plan:
Each day the students will learn a different method to solve division problems with one digit divisors.
Objective:
Students will be able to solve division problems with one digit divisors and three or four digit dividends using various methods.
Formative Assessment:
Students will be given an exit slip after learning each method to check for understanding as the unit progresses. I will also monitor understanding on IXL.
Summative Assessment:
Students will be given a test in which they will have to explain the thinking behind a particular method and then will solve some division problems using a method of their choice. Mastery is demonstrated by getting 70% of the problems correct. Questions will also allow for trouble spots with particular strategies to be detected and worked on.
Reteach Loop:
Students who do not demonstrate mastery will have a reteach lesson and reinforcement activities during math workshop in the next unit. I will pull them in a small group. They will retake the assessment after intervention.
Changes from last year:
I have added the box method, which is not a strategy mentioned in our book. A common problem in long division is that students are able to get through the steps once, but then they either have difficulty repeating the steps or they start to write crooked and they get confused about where they are in the problem. The box method alleviates this problem by keeping the numbers of the dividend in their own box.
Lessons:
Each day, we learn one strategy:
- Division as repeated subtraction: I can model division as subtracting the divisor from the dividend.
- Can be done on a concrete level with counters or moved to a concrete abstract stage/abstract stage.
- Division using the distributive property: I can use the distributive property to model division
- Can also be done on a concrete level with counters or concrete abstract level by drawing area models
- Partial products division: I can solve division problems using the partial products method.
- Modeling division using base-10 blocks: I can solve division problems using base ten blocks.
- Division will be done concretely using base-10 blocks.
- The box method: I can solve division problems using the box method.
- Students who struggle can still use base-10 blocks to model the problems and record their answers in the box.
- The algorithm: I can solve division problems using regrouping.
Next 4-5 days after this instruction: Students ready for assessment can take the test, and they move on to enrichment activities. Students who need more practice can take the test at any point over the next four days. If they pass, they move on to enrichment activities. If they do not pass, they continue to work during class time and retake the test.
Model for class time (each strategy will take 1 to 2 class periods):
- Opening activity-Introduce/practice game or number talk
- Whole class lesson on daily strategy
- Group work on the strategy to allow for peer modeling
- Individual practice on IXL, exit slip, or meet with teacher if additional help is needed