Musical Math

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Objective

SWBAT subtract fractions and mixed numbers that require borrowing through a game of musical math.

Big Idea

Students review borrowing when subtracting fractions through an adapted musical chairs game.

Do Now

15 minutes

Students enter silently and find a do now on their desk. It instructs students to have their pencils ready for a speed test. This Do Now includes 6 spiral problems with skills on adding, subtracting and converting fractions/decimals. Students are instructed to click their answers for a graded Do Now assignment.

At the end of 5 – 6 minutes, assessments are stopped and two most common incorrect answers are reviewed.  Some students may be missing the right answer due to overall organization and neatness of work shown. 

Check HW

The answers to the HW from the previous night are provided. The answer document is usually a sample of student work that shows work neatly and solutions are easy to follow on paper. Students are directed to review these answers with their neighbors and use them to check their own answers in the homework. All directions are displayed on the board with a power point presentation.

Last night’s homework required students to convert fractions to decimals and vice versa. It also included two word problems which asked students to write a fact as a fraction and a decimal. The aim with this homework assignment is to get students to continue practicing the conversion skill and to see it applied in a word problem. At the end of the homework check I ask students to share their preferred strategy for turning fractions in to decimals (i.e. using equivalent fractions with powers of ten, or dividing).

 

Class Notes - Intro to Lesson

15 minutes

Students are provided with a print out of their “Cornell Notes” for the day. Two facts about fractions and borrowing are reviewed as students fill in the blanks at the beginning of this introduction. The facts, along with the words needed to fill in the blanks are also displayed on the power point. For fact 1 (Fractions are parts of a whole. They can represent smaller subsets of a group), I will need to provide an example such as “Two fifths of the class are girls”. The fraction 2/5 is a part of the whole group or class. The “girls” would be called a subset of a group.  Students must understand that fractions are not only pieces of pies or one unit of anything split into smaller pieces. Sometimes you can have large group of units (i.e. gallons of milk, populations of people, and bags with items inside) and split them into fractional pieces to find out how many pieces belong in each subset. I introduce this fact early on to prepare for multiplication of fractions by whole numbers.

We then complete examples to review the concept of borrowing. We begin with whole numbers. In the example on the power point, to subtract 2408 – 196 we will need to borrow from the hundreds place to complete the subtraction step at the tens place. I can ask students “what are you borrowing? How many of what are you borrowing?” What I have often found with these examples is that students remember the process for multiplying but many don’t understand the “why” behind it. To stimulate student thought I show the borrowing step as “borrowing from 24” instead of simply borrowing from the 4 alone. This warm up example will hopefully get students thinking about how many of a given place value we are borrowing.

In the next example I give students a mixed number subtraction problem where the denominators are the same. The problem (5 5/12 – 4 11/12) requires us to borrow one whole for our initial fraction. I ask students to explain why I cannot just write a 1 next to the 5 like we do with whole numbers. Why is that NOT like borrowing 1 whole?

Students are given two additional examples to complete with neighbors that will require finding LCDs. At the end of 5 minutes we review answers together. Students are then asked to clear their desks of everything except for a pencil and get ready for the game. 

 

 

Task

20 minutes

While students are getting ready for the game I display a picture of the TV show “Oh Sit!”, a game where people move around an obstacle course while music plays and rush to a limited amount of chairs in the middle of the course when the music stops. When all students are ready, I ask if they know which show is being displayed on the board. Once the game is identified and we review how it is played, as well as the connection to musical chairs, I let them know that we will be playing musical chairs today.

In this game, students will not be competing against each other for limited seats; they will be working as a class to compete against limited time. The musical and “round-and-around” aspect will take place in the form of their work. The first row will receive a worksheet where they are to subtract fractions that require borrowing, but the denominators are all equivalent (i.e. 5 ¼ – 1 ¾). The second row will receive a similar worksheet, where subtraction will require borrowing, but denominators will not be equivalent. These first two worksheets were created from a site that includes a worksheet generator. The third row will receive a sheet from a workbook also available online that includes 6 word problems about subtracting mixed numbers. 

Students race against time to complete 1 or more problems on their sheet as possible. Music will be playing in the background to track time. Once I change the song, the papers on students’ desks will be passed on to the next neighbor. I will need to stand between the third and first rows to aid in the passing of papers. The image inserted in this section displays the organization of my room and the movement of the papers. Students will earn achievement points as a class depending on the number of correctly answered problems on all worksheets.

Closing

10 minutes

When there are 10 minutes left in class, students are given the homework and are asked to pack everything up except for the sheets we used for the game. Each student is provided a marker to check the answers on the game worksheets. Each student is provided an answer sheet with correct answers and work for the check. Students are asked to mark correct answers with a check mark and to circle incorrect answers. All worksheets are turned in at the door on their way out. I will find the sum of all correct answers for the class and divide the achievement points evenly amongst the entire class (remainders will be dropped).