Weber State University



Video / Practice Discussion

PLC Guide 1

|Pre-Session |

|View video “Use Appropriate Tools Strategically “ |

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|This lesson is designed to demonstrate the use of mathematical tools to solve problems involving fractions. This lesson is a part of the 7th grade |

|common core. This lesson is used as an introduction to our unit on adding and subtraction rational numbers. The students have prior knowledge of |

|fractions, but it is helpful to review what they know, and then to take their knowledge a step beyond by using the mathematical tools. |

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|Students are asked to solve problems using addition, subtraction, multiplication and division of fractions. To assist each student, they create |

|different fractions using a 360 degree compass. This is an additional tool created, along with their existing tools of calculator, ruler, paper and |

|pencil. Students are asked to measure, manipulate, make a hypothesis, and do the handwritten calculations to prove their hypothesis. |

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|Using these mathematical tools should help the student visualize the appropriate answer while solving the problem using the fraction rules. The student |

|can then prove their answers using paper and pencil. These fraction pieces are a tool to make conjectures, to prove, and to check their mathematical |

|calculations. |

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|Mathematical Practice Overview #5 |

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|Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete|

|models, ruler, protractor, calculator, spreadsheet, computer algebra system, statistical package, or dynamic geometry software. Proficient students are |

|sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, |

|recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students interpret graphs of |

|functions and solutions generated using a graphing calculator. |

|They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that |

|technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically |

|proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, |

|and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. |

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|My Fraction Circle Lab |

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|[pic] |

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|Use the above template to produce cardstock copies for each student in the class. The students will need 10 different colors which will represent the |

|fractions 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12, 1/16, and 1 whole. By following the video instructor, students are asked to measure and cut the |

|different circles into the fraction amounts. The worksheet which was provided to the students is printed below. |

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|For this lab, it is better to put students in groups so that they can help each other. But groups can sometimes get off task! It is a good idea for the|

|teacher to walk around the room. (I used the excuse that I was collecting their trash) I walked around and checked on the different groups the entire |

|class period, to keep students on task and to answer questions. |

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|This lesson was taught during an 80 minute class period. |

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|Name:______________________________ Period:____________ |

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|Fraction Lab with Fraction Circles |

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|Use the left side of the paper to draw the problem using your fraction circles, and use the right side of the paper to do your math calculations. |

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|Addition: |

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|1/2 + 1/4 = |

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|1/4 + 1/8 +1/2 = |

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|1/10 + 1/12 + 1/2 = 1/3 (yes or no?) |

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|1/5 + 1/6 + 1/8 = 1/2 (yes or no?) |

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|Use the left side of the paper to draw the problem using your fraction circles, and use the right side of the paper to do your math calculations. |

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|Subtraction: |

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|2/5 – 3/10 |

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|5/6 – 2/6 |

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|1/3 – 1/6 |

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|11/12 – 1/3 |

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|Use the left side of the paper to draw the problem using your fraction circles, and use the right side of the paper to do your math calculations. |

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|Multiplication: |

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|1/2 x 4 |

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|1/4 x 5 |

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|1/6 x 10/5 |

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|5/16 x 2/5 |

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|Use the left side of the paper to draw the problem using your fraction circles, and use the right side of the paper to do your math calculations. |

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|Division: |

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|1/6 ÷ 2 |

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|1/2 ÷ 8 |

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|1/2 ÷ 1/4 |

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|2/3 ÷ 1/3 |

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|Extra Credit Problem: |

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|Make your own quiz problem: Make up an Addition, Subtraction, Multiplication or Division problem which can be used on an upcoming quiz. Provide the |

|problem, the solution, and show the steps in solving the problem. If your problem is used on the quiz, you will receive 10 extra credit points! |

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|Brain Teaser Problem: |

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|1/2 + 1/3 + 1/4 +1/5 +1/6 +1/8 + 1/10 + 1/12 + 1/16 = |

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|Introductory Activity – Video discussion |

|Discussion |Why is it sometimes easier to solve fractions problems using fraction circles instead of paper and pencil? |

|Questions |How can using these tools help students to make appropriate estimations? |

| |When is it best to use the fraction circles as a math tool instead of paper and pencil? |

| |How does adding the fraction circles as a mathematical tool deepen students’ understanding of manipulating fractions? |

| |Where and when will students have to use and manipulate fractions in real life situations? |

|Discussion – What does this mean in my classroom? |

|Discussion |Do you think that using these mathematical tools will help students learn concepts better than using tradition paper and pencil? |

|Questions |How? When? |

| |What deeper understanding can students gain by using these fraction tools? |

| |How can students use these tools to analyze, predict and discover more about the rules of fractions than they already know? |

|Application – Create a lesson plan implementing the practice |

| |Choose a concept that typically students do not remember or have had difficulty understanding from their previous year in |

| |mathematics. Choose a manipulative, tool, or have students make a tool that will help students to best review this concept. |

| |Sometimes students do not understand the algorithms for concepts, but can use tools to gain better understanding. This is when you |

| |hear a student say “Oh, now I get it!” An example of this would be using integer chips to teach and review adding and subtracting of|

| |positive and negative integers. |

|Reflections – Write in Journal |

|Did this tool accomplish the desire learning, and how do I know that it did? |

|Where did this lesson go well? |

|What parts of this lesson did not go well and should be changed? |

|Did watching the video give a better understanding of this mathematical practice? |

|Were there other important teaching strategies that I saw when I watched this video? |

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|Additional thoughts: |

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