For this warm up I give my students a review word problem. The problem reviews multiplication and place value concepts. You can see the problem below and one student's strategies.
In this video, watch and listen as a student catches his errors through my questioning about his strategy.
In this video you can see two girls struggle with making sense of the problem. This was surprising to me, but also a good reminder about using more real world review type problems and their importance in my classroom to ensure students' skills stay strong and that they continue to make sense of problems.
For this warm up, I chose a word problem to review place value concepts and problem solving. Often, students get into a mindset that a teacher only gives problems that have to do with the operations or concepts of a current unit. I did have several students comment that there no fractions on the page. Some of my students asked right away, "do I divide, multiply, add or what?" While that comment makes the hair on my neck stand up, it is important for me to hear so I can remind my students that mathematicians make sense of problems and then solve them.
For this lesson, students work in their table teams to play a Jeopardy review game. I purposely chose to have this be a somewhat non-competitive game by allowing each team to receive points for correct answers. This helps to keep all students engaged to acquire as many points as possible.
I ask the groups to decide which person will be the recorder and the holder. This person is responsible for holding up a whiteboard that will display the TEAMS answer, not necessarily their individual answer. Each individual on the team also has a whiteboard to allow for all team members to calculate and compute answers. On my signal, which is a chime sound, the "holder and recorder" must hold up the team's answer. Each team receives the points per question if they answer correctly.
This is the link to the game: jeopardyfractions.ppt
When using the game on a smart board, after students have answered, touch anywhere on the screen and the answer will be displayed at the top of the screen. Then I touch the home key at the bottom of the page to go back to the category page. When using a smart board, I mark off each question on the board as we play the game.
In this video, you can see students playing the Jeopardy game.
This lesson builds students procedural fluency with fraction skills and computation. As stated in the CCSS, procedural fluency refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently.
Procedural fluency can involve memorizing multiplication tables and other facts, but it also involves thinking. Students must know when, as opposed to just how, to use a procedure. They must not only be able to perform procedures accurately, but also flexibly and efficiently.
One reason students don't always choose the most efficient method for various skills, is that they don't really choose any method. From past experiences and teachers, they may just apply an algorithm without thinking. Students know how to use procedures but not always when to use them. They perform procedures accurately but not always flexibly or efficiently. In other words, they lack procedural fluency.
The CCSS challenges educators to help students develop procedural fluency AND conceptual understanding.
Much of my beliefs and ideas about procedural fluency come from countless articles, books, and research by Jo Boaler. You can read an article about math timings here. Timed Tests and the Development of Math Anxiety -
I do timed tests in my classroom each week and have students track their progress throughout the year. You can see an example of how I use math timings by checking out this warm up in this lesson.
Note: I adapted this PowerPoint from another teacher. There is a simplifying fraction category, which is not applicable to common core standards for fourth grade. I explain to my students that we are finding equivalent fractions. I tell students that sometimes we would "simplify" a fraction to lowest terms by finding an equivalent fraction in which the numerator and denominator are as small as possible. I tell students that this means that there is no number, except 1, that can be divided evenly into both the numerator and the denominator. I tell students that they often do this without thinking about it when they talk about the fraction 1/2. I remind students that many of them would automatically "simplify" 12/24 as 1/2 when talking about that fraction in a real world context, like boys compared to girls in our classroom.