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Grade: 6Lesson Title: Relating Fractions, Decimals, and Percents in Floor PlanDate: Jan.22 2015Curriculum Expectations OE - Read, represent, compare, and order whole numbers to 1 000 000, decimals numbers to thousandths, proper and improper fractions, and mixed numbersSE – determine and explain, through investigation using concrete materials, drawings, and calculators, the relationships among fractions, decimal numbers, and percents (e.g. use a 10 x 10 grid to show that ? = 0.25 or 25%)What do students need to know and be able to do? Students need to be comfortable with looking at fractions as part of hundredths (i.e. 20/100) represented visuallyStudents should be able to represent parts of a visual by using a decimal (i.e. 0.2)Students may be comfortable using benchmark percents (although this has not been covered yet)Learning GoalsContent: Students will represent different parts of whole using decimals, fractions and percents with a visual aid of their creation.Process: We will be looking at representing parts of a whole in different ways, communicating proof of meeting particular criteria, and we will also be asking student to make estimations during the planning phase of solving a particular problem to assess if their answers are realistic.Lesson ComponentsAnticipated Student Responses and Teacher Prompts / QuestionsAction! Create your own floor plan for your condo using 100 square units (all units must be used in the floor plan).Design and draw the floor plan using the following criteria:2 bedroomsKitchen and dining roomBathroomLiving roomLaundry room*The living room should be the largest space.*One room needs to be L-shaped.*You can include hallways if you wish. Represent each part of the floor plan, in as many ways possible, as parts of the whole. You need to communicate how you know that the living room is the largest room in your floor plan, using pictures, numbers and words. Feel free to use your tool kit with scissors, additional grid paper, calculator, colour pencils, and chart of fractions/percents/decimals. Anticipated Student Responses and Possible MisconceptionsStudents might not be able to convert simple fractions/unit fractions to decimals or percents.Students might confuse numbers such as 2 tenths and 2 hundredths when they are writing these numbers.Sample Scaffolding Questions How else can you represent this?How are these ___the same or different?If I do ____, what will happen?How can you prove your answer or verify your estimate?How do you know?Have you found all the possibilities? How could you arrive at the same answer in a different way?Minds-On AFL(Based on Page 312 in Grade 6 Math Makes Sense)Here is a floor plan of a daycare centre. How can you describe each part of the floor plan (room) compared to the whole?You will have 2 minutes to make an estimate (you can use terms like about, less than half, less than a quarter, greater than half, etc.)You now need to describe exactly how much of the floor plan each room makes up of the whole in as many ways as possible. What are we listening and looking for from the student conversation and responses?We are listening to see if students are familiar with converting between fractions, decimals and percents.We are listening to see if any of them can simplify fractions into lowest form.We are listening to see if they are communicating, with appropriate proof to the starred criteria. Lesson ComponentAfter / Consolidation / Reflecting and ConnectingConsolidation Highlights and Summary(Uncover Learning Goal, Success Criteria)Modified gallery walk (students come to the front and display their work under the ELMO) with one representative from each group. (2-4 depending on time)Start with students that might only represent with one or two out of the three main methods (fractions, decimals and percents). Continue to students who are showing all three main methods.Continue with students who may have simplified fractions or used lowest terms to represent the fraction. Continue with students who clearly explained how they met the starred criteria (i.e. My living room took up 25 out of the 100 squares in the grid – 25%, and the next biggest room only took up 20 squares in the grid) (i.e. One bedroom takes up 15/100 and the other bedroom takes up 0.12, which I know is 12/100, which is smaller than 15/100) (i.e. One bedroom is 1/5 of the whole floor plan and the other bedroom 1/10. I know that 1/10 is 0.10 and 1/5 is 0.20, and if the number in the tenths column (because there is no number in the ones) is larger like it is for 0.20, than it is larger than 0.1.) Use the Twizzlers book, to introduce the concept of percents, compared to fractions and decimals. In our decimals unit, you got comfortable representing 0.1 and 0.01. You know that 10 squares can be represented as 1 tenth, 0.1, 1/10 and some of you might of realized that it can also be represented as 10%. Percents are fractions out of 100, where you only represent the numerator. 80 = 80%100Percents are often used in the real world to give statistics (i.e. 60% chance of rain), marks (i.e. 92% on your math test), and information in the media (i.e. 15% of Canadians get their water from a well). Because people are comfortable with 100, percents is a great representation of fractions and decimals because they are usually represented in whole numbers. Some decimals are not easy to represent. If I had asked you to do a floor plan with 60 squares, some of the floor plan, such as a room that takes up 6 squares could easily be represented as a fraction 6/60 or 1/10, or as a decimal 0.1 and then to 10/100 which is 10%. But other numbers such as 5/60 or 1/12 do not lend themselves nicely to writing them as something out of 100, and therefore not easy to calculate as a percent. When you have a fraction like 1/12, and need to convert to a percent, you take the numerator and divide it by the denominator. You will get a decimal number, _______, then you can round this number to the nearest hundredths. The number written in hundredths can be written as a percent. Independent Practice:Exit CardReflectionHomeworkStudent Next Steps (Large Group/Small Group/Individual)Draw a floor plan of your bedroom using a maximum of 25 units. You need to draw in your furniture or other features into your floor plan. (i.e. bed, dresser, desk, chair, bookshelf, rug, etc.)Make sure you include at least 4 pieces of furniture.State the number of units that each piece of furniture represents as part of the whole in as many different ways as possible.State the amount of space not covered by furniture or other features. Explain how you came up with this answer. Look at different unit fractions that are easily converted into percents to establish benchmark percentages with a variety of equivalent fractions (i.e ? = 25/100 = 0.25 = 25%)Look at unit fractions that are repeating decimals and teach students to convert to decimal and round to the nearest hundredth(i.e 1/3 = 0.3333333 = 0.33 = 33%)- Give students examples of fractions that do not nicely lend themselves to percents and get students to write them in simplest form or calculate numerator divided by denominator.- Chart where they have different decimals, fractions and percents in different columns and they have to fill in the blanks.Create your own floor plan for your condo using 100 square units. All parts of the grid must be included in your floor plan. Design and draw the floor plan using the following criteria:Must include:2 bedroomsKitchen and dining roomBathroomLiving roomLaundry room*The living room should be the largest space.*One room must be L-shaped.*You can include hallways if you wish. Represent each part of the floor plan, in as many ways possible, as parts of the whole. You need to communicate how you know that the living room is the largest room in your floor plan, using pictures, numbers and words. FractionDecimal PercentOtherLiving RoomLaundry RoomBathroomKitchen and Dining RoomBedroom One Bedroom Two Hallways (if applicable)Here is a floor plan of a daycare centre. How can you describe each part of the floor plan (room)?You will have 2 minutes to make an estimate (you can use terms like about, less than half, less than a quarter, greater than half, etc.)Play room – Quiet room – Kitchen – Bathroom - You now need to describe exactly how much of the floor plan each room makes as parts of the whole in as many ways as possible. Play room – Quiet room – Kitchen – Bathroom – You need to communicate how you know that the living room is the largest room in your floor plan, using pictures, numbers and words. ................
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