Lesson plan - Study Island



763270-133350Math Lesson: Ratios and ProportionsGrade Level: 7Lesson Summary:The teacher engages students in a review of ratios by determining the ratio of girls to boys in the class. Next, the teacher models the concept of proportion by drawing rectangles in proportion, having students calculate equivalent ratios, and graphing them on a coordinate grid. Students then draw proportional rectangles on a coordinate grid, make a chart of the measurements, graph those measurements, and write the proportion equation that represents the different rectangles. Finally, they measure an object and draw it in proportion on a coordinate grid, recording the equivalent ratios and proportion equation. Advanced students have the opportunity to create a scale drawing of a room and a drawing with a rearrangement of the objects in the room. Struggling students calculate proportions needed to mat a picture.Lesson Objectives:The students will know…that proportional relationships can be expressed by an equation, table, or graph.equivalent ratios are proportional relationships.the difference between a ratio and a proportion. The students will be able to…analyze proportional relationships and use them to solve real-world and mathematical problems.decide whether two quantities are in a proportional relationship by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.represent proportional relationships by equations.Learning Styles Targeted: FORMCHECKBOX Visual FORMCHECKBOX Auditory FORMCHECKBOX Kinesthetic/TactilePre-Assessment:Use this quick assessment to determine if students can calculate equivalent fractions, which is a prerequisite to finding equivalent ratios and proportions.Give students one minute to list as many fractions as they can that are equivalent to 13. 26, 39, 412, etc.Quickly check student answers. Note any students who were unable to calculate equivalent fractions.Whole-Class InstructionMaterials Needed: Coordinate Grid*, tape measures or rulersProcedure: PresentationReview ratios by asking students to find the ratio of girls to boys present in the class. If possible, have them simplify the ratio. Review that a ratio is a comparison of two quantities. Ask students to give examples of other types of ratios [if a team wins 4 out of 5 games the ratio of wins to total games is 45; if a candidate wins 3 out of 5 votes, the ratio of votes for that candidate to total votes is 35].Ask what ways, other than a fraction, the ratio 35 can be expressed. [3:5; as a percent, 60%; as a decimal, 0.6]Ask students to calculate fractions equivalent to 35 610, 915, 1220, etc.. Explain that equivalent ratios represent a proportional relationship. Then, draw a 4 in × 6 in rectangle, a common size for photographs, on the board. Ask students to calculate the dimensions of the photographs if it is enlarged to twice its original size [8 in × 12 in] or if it is reduced to half its original size [2 in × 3 in].Make a table of the proportional measurements with width in one column and length in the other column. Graph the ordered pairs on the Coordinate Grid. Then, draw a line through the points. Ask students to identify other points that would be in the same proportion as the 4 in × 6 in picture. Ask if 10 in × 14 in would be in the same proportion. [no]Discuss the difference between a ratio and a proportion. [A ratio is a comparison of two quantities; a proportion is two equivalent ratios.] Confirm that ratios and proportions can be expressed using fractions.Review how to find equivalent ratios and explain that this is the same process used for solving proportions. For example, ask students if 1 inch on a map represented 10 miles, how many miles would 4 inches represent? [40 miles]Guided PracticeHave students draw four rectangles in proportion on a Coordinate Grid. Have them start by drawing one rectangle. Then draw another rectangle that is twice as big, another that is 2.5 times as big, and one that is one-half the size of the original rectangle.Then have them record the length and width of each rectangle by counting the spaces on the grid and build a table of the proportional relationships.Next, have them plot the ordered pairs from their chart on the grid and draw a line through the coordinates to prove that they are proportional because they are in a straight line. Then write the proportions as an equation.Independent PracticeExplain that to create realistic art, you need to get proportions correct. You must measure the size of one object to show it in proportion.Have students choose an object to draw. It could be a pencil, a chair, a desk, or a self-portrait. Have them measure the object and then calculate the proportional measurements using equivalent ratios. Have them show the actual measurement and at least three equivalent ratios in a chart and graph the coordinates to prove that the measurements are in proportion.Then have them use the Coordinate Grid to draw their objects in proportion and write each proportion as an equation that represents the equivalent ratios [for example: 34=1.52]Closing ActivityReview student drawings and comment on whether the drawing is in proportion to the real object or not.Discuss how students calculated the proportions and their challenges and effective strategies.Advanced LearnerScale DrawingMaterials Needed: Coordinate Grid*Procedure: Have students choose a space to redesign. It could be a room at home or at school. Then have them record approximate measurements of the size of the room and the objects in the room. Next, have them create two scale drawings of the room on a Coordinate Grid, one that shows the arrangement of the room as it is and one as they envision it to pare drawings and confirm that the proportions are correct.Struggling LearnerMat a PictureMaterials Needed: cardboard, scissors, 8 in × 10 in pictureProcedure:Give students ten minutes to calculate acceptable sizes to cut a sheet of 18 in × 18 in mat board to mat an 8 in × 10 in picture. They need to consider the overlap of the edges of the picture and cutting the outside and the inside of the mat proportionally.Have students compare their results and then experiment by using their measurements to cut a mat for an 8 in × 10 in picture.*see supplemental resources ................
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