Students will start today's lesson with a fluency assessment. This assessment is from Monitoring Basic Skills Progress Second Edition: Basic Math Computation by Lynn S. Fuchs, Carol L. Hamlett, and Douglas Fuchs.
This is an assessment I have my students do each week and then graph their results. It allows them to reflect on their learning of basic math facts, as well as using all four operations with whole numbers, and adding and subtracting unit fractions. (It also happens to be the quietest time in my math classroom all week!!)
This is what my classroom looks like as students work on this assessment.
Click hereto see an example of a typical fourth grade fluency decrease since students are completing the fourth grade fluency set that incorporates division, multiplication, addition, subtraction, and adding and subtracting fractions with like denominators. (At this point, students have not had many fraction lessons, thus very very students are able to complete the fraction problems)
I do not start my students with the fourth grade skills, but at this point in the year, all students are using the fourth grade set.. I chose to start them with the end of the third grade skills which covers addition, subtraction and multiplication and division of basic facts. I strongly believe in a balanced math approach, which is one reason why I also believe in common core standards. By having a balance of building conceptual understanding, application of problems, and computational fluency, students can experience rigorous mathematics. I want to make clear that this assessment ONLY measures basic math computation. It is only one piece of students' knowledge. The assessments in this book, for each grade level, do not change in difficulty over the course of the year. Therefore, a student's increase in score over the school year truly reflects improvement in the student's ability to work the math problems at that grade level.
Students continue solving problems today just as in yesterdays lesson using the 3 ÷ 1 worksheet. This is day 2 of a three day problem solving activity. Students continue using the Think Aloud Partner Problem Solving approach and talk through problems with their partner in order to solve all the problems on the page.
A major focus of the Standards for Mathematical Practice is on using problem solving to reinforce important concepts and skills to demonstrate mathematical understanding. In Improving Mathematical Problem Solving in Grades 4 Through 8, published in May 2012 under the aegis of the What Works Clearinghouse (NCEE 2012-4055, U.S. Department of Education, available online from the Institute of Education Sciences) reported and made some recommendations about problem solving in mathematics. This report provides educators with specific recommendations that address improving mathematical problem solving. The first recommendation was to Prepare problems and use them in whole-class instruction.
Students utilize Math Practice Standard 1 and 3 in this lesson along with content standard 4.NBT.6. CCSS MP1 states mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
One of the strengths in this lesson is directly related to the above bold text. The think aloud partner problem solving (TAPPS) instructional strategy allows and encourages students to share their thinking with peers and allows peers to help or guide checking work and reasonableness of answers. Student partners can continually check each other's work and ask each other if their answer makes sense. Often times, one student's strategy or method differs from their partners which creates an opportunity to see and hear other approaches and build students' abilities to think flexibly.
The goal for today's lesson is for partners to work on the problems presented on the problem set worksheet. I know that students will not finish this worksheet in the time allotted, but I encourage them to work wisely and efficiently so they are able to finish in tomorrow's lesson. As students work, I am constantly moving around the classroom to observe students thinking. As much as I can, I resist the urge to re-direct students thinking until I am certain they have talked with their learning partner about the problem. By doing this, students partners often help correct misunderstandings and errors.
In this video you can hear two students talking and thinking through a problem utilizing the TAPPS strategy.
This pair of students are thinking about a problem and trying to figure out what they will do with a remainder. They have some incorrect calculations happening. Listen and watch my questioning process as I help guide their thinking.
This is a sample student work paper for a partnership that finished all problems. Many students are very close to finishing.
You can see that this student had quite a few comments and a few questions. This student also listed all of the problem answers on the left hand side of the comments.
Students worked right up to the end of the class period. I collected their work and problem so they may finish tomorrow.