problems. Examples: discount, percent increase and decrease. SMP.1 Make sense of problems and persevere in solving them. SMP.2 Reason abstractly and quantitatively. SMP.3 Construct viable arguments and critique the reasoning of others. SMP.4 Model with Mathematics. SMP.6 Attend to precision. Massachusetts Curriculum Framework for English Language Arts and Literacy, 2011: 6-8.WHST.1 Write arguments focused on discipline-specific content 6-8.WHST.2.D Use precise language and domain-specific vocabulary to inform about or explain the topic. 6-8.WHST.2.F Provide a concluding statement or section that follows from and supports the information or explanation presented. of proportionality, origin (x, y plot), scale factor, complex fraction. Proportional relationship may exist between variables in an equation (e.g., d/r=t) A variety of ways to represent a proportion (e.g., in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships). Plotting a set of points and interpreting the points (0, 0) and (1, r) where r is the unit rate. Solving problems (discounts, percent increase, percent decrease, percent of error) Writing and sharing word problems involving proportions. Constructing viable arguments and critiquing others when proportions/proportional reasoning would or would not solve a problem Scaling a rate, or fraction up or down with the same relative characteristics as the original. (e.g., enlarge a photo) Evidence Curriculum Embedded Performance Assessment PERFORMANCE TASK(S):
Assumptions about what students know and are able to do coming into this lesson (including language needs): Students know what a is and that percent means out of 100. Students know how to simplify fractions, how to change percents to fractions and to decimals and how to multiply by fractions and decimals Outcome(s) By the end of this lesson students will know and be able to: Recognize that proportional reasoning involves comparisons of the relationships among ratios Compute unit rate. Solve problems (discounts, tax, percent decrease) Instructional Resources/Tools Sunday circulars or, alternatively, store circulars can be accessed on the web For example: On Line Shopper Chart paper, graph paper, journals Anticipated Student Preconceptions/Misconceptions 5% = .5 Discount = price Assessment Pre-assessment/ Formative (This could be assigned as homework. Choose some or all from the following.) Summative (optional) 1. Represent 17% as a fraction. 2. Using 17%, write a statement: ____ out ___ people prefer Crest Toothpaste. 3. Convert several percents to fractions and decimals. For example: ¾ = = _______ as a decimal _______ as a fraction = 67% = _________ as a decimal ________ as a fraction = __________ as a percent = 0.05 4. ½ x ¼ = __________ 5. 1.02 x 0.07 = _________ 6. Does percent off (discount) mean the person pays less or more than the original price? 7. Sneakers are on sale at 15% off. If the original price is $150, what is the discount and what will you pay for the sneakers? iPad Apps are on sale at 15% off. If the original price is $1.99 what is the discount and what will you pay for the App, including Mass tax (6 ¼)? Specific notes to teacher: Teacher circulates and observes students responding. Reinforce vocabulary Discount Convert Apps
Analysis Analysis for when gas prices become unreasonable is accurately analyzed with full consideration of all scenario parameters. Analysis for when gas prices become unreasonable is accurately analyzed with evidence of consideration of all scenario parameters. Analysis for when gas prices become unreasonable shows evidence of some inaccuracies mathematical reasoning. Analysis for when gas prices become unreasonable shows evidence of numerous inaccuracies in mathematical reasoning. Mathematical Concepts Work shows evidence of in-depth understanding of proportions and proportional relationships Work shows evidence of full understanding of proportions and proportional relationships Work shows evidence of partial understanding of proportions and proportional relationships Work shows evidence of limited understanding of proportions and proportional relationships Precision of Mathematical Language Complex mathematical language is accurately used, e.g. proportions, ratio, etc.(refer to stage 1 for additional vocabulary) throughout the presentation to communicate about mathematical reasoning Appropriate mathematical language is accurately used, e.g. proportions, ratio, etc.(refer to stage 1 for additional vocabulary) in much of the presentation to communicate mathematical reasoning Some mathematical language, e.g. proportions, ratio, etc.(refer to stage 1 for additional vocabulary) accurately used to communicate mathematical reasoning Limited or no mathematical language is accurately used to communicate mathematical reasoning Mathematical Accuracy All work is shown and contains little or no errors in calculations, equations, graphs, and tables. All work is and mostly accurate, containing a limited number of mathematical errors in calculations, equations, graphs, and tables. Most work is shown but contains a number of inaccuracies in calculations, equations, graphs, and tables. Work is limited, missing and/or contains numerous mathematical errors in calculations, equations, graphs, and tables. Argument Reasoning for when gas prices become unreasonable is included in the presentation and is convincing, thoughtful, and backed up with extensive evidence. Reasoning for when gas prices become unreasonable is included in the presentation, and is convincing and backed up with appropriate evidence. Some reasoning for when gas prices become unreasonable is included in the presentation. Reasoning is somewhat convincing and backed up with some evidence. Reasoning for when gas prices become unreasonable may or may not be included in the presentation. The reasoning is not convincing and may be backed up with little or no evidence.