We are currently focusing on MA Frameworks Standard 4.MBT.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. "
Students will be able to solve division problems involving whole numbers, using strategies such as drawing out the problem, breaking the problem into parts, or using the traditional long-division algorithm. Here is an example:
QUESTION: Our school is planning a field trip for 117 students. We will be taking buses, which can hold 8 students each. How many buses will we need for the field trip?
ANSWER: 15 buses (115/8 = 14 with a remainder of 5, but we will need one more bus for the 5 students left over)
Strands of Mathematical Proficiency:
a breakdown of your child's knowledge of division
1. Conceptual Understanding
(comprehension of mathematical concepts, operations, and relations)
With a mastered concept of division, students will understand that division is when one large group of objects is broken down into smaller groups. This can mean that they are trying to find either the number of groups, or the number of objects in each group. For example, 48 / 6 = 8 can either represent "We have 48 cookies and 6 jars. How many cookies are in each jar?" (8 cookies) or "We have 48 cookies, and we want to put 6 cookies in each jar. How many jars do we need?" (8 jars). Also, students will recognize the relationship between multiplication and division. For example, since 48 / 6 = 8, 6 x 8 = 48. In other words, students will have a firm grasp on the "big idea" of division.
2. Procedural Fluency
(skill in carrying out procedures fluently, accurately, efficiently, and appropriately)
Students will be able to solve division problems correctly, using any number of strategies that we have learned and practiced in class. This process involved not only understanding what the problem means, but being able to find an accurate answer in a timely manner. For example, if the question asks, "We have 48 cookies, and we want to put 6 cookies in each jar. How many jars do we need?" and the student answers "5 jars with 6 cookies in each jar," (which is not correct), they are lacking in procedural fluency.
3. Strategic Competence
(ability to formulate, represent, and solve mathematical problems)
Students will be able to demonstrate that they understand division by drawing out the problem, arranging blocks or other manipulatives, or explaining using their words. Students are encouraged to represent a problem in another way so they can visualize what the question is really asking them to do. Also, by the end of our units students should be able to write division problems of their own, either just with numbers or in a story context. Either way, students should be able to explain what they problem is asking, as well as be able to solve it. For example, a student might write "We have 40 kittens and 5 boxes. How many kitten go in each box?" They might draw: (Where "O" represents 1 kitten and [ ] is a box),
[OOOOOOOO] [OOOOOOOO] [OOOOOOOO] [OOOOOOOO]
and explain "If there are 40 kittens and you put 1 into each of the 5 boxes until you run out, there are 8 kittens in each box."
4. Adaptive Reasoning
(capacity for logical thought, reflection, explanation, and justification)
With a mastered concept of division, students will be able to explain their reasoning after solving a problem. This skill is extremely important because it allows students to check their answer. They should ask themselves questions like, "Does this solution make sense? What are my units? Did I answer the question?" The best learning experiences are often when a student can realize for themselves that they made a mistake, and why, and be able to go back and rethink their strategy or solution. Students should not onlu understand that their strategy works, but WHY it works.
5. Productive Disposition
(habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with the belief in diligence and one's own efficiency)
A student's attitude towards math can have a huge impact on their success. If a student believes that with practice and determination, they can master a skill, then they have the capacity to continue to grow in their understanding. However, if a students has no confidence in their own ability, or in the value of what they are learning, it is going to be very challenging for them to become invested and learn new material. I believe that any and all of the students in our class is capable of having a successful and productive year in math, and I will be making it a point to praise and support their progress every day.