Stretching and Shrinking

Standard / Notes / Also Covered in / Unit Test / State question
A / M / T
7.RP.2 / Recognize and represent proportional relationships between quantities / All will be covered again in comparing and scaling (but not with geometric figures). Student must what proportional relationships arise from similar figures. / Comparing and Scaling Inv. 1,2,3 / 3
4
7b
7.RP.2a / Decide whether two quantities are in a proportional relationship, e.g., 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. / Comparing and Scaling Inv. 2,3 / 5b / 6
7.RP.2b / Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. / Comparing and Scaling Inv. 2
Moving Straight ahead Inv. 1 / 1,2, / 7c
7.RP.3 / Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. / Comparing and Scaling Inv. 1,2,3
What do you expect? Inv. 3,4,5 / 8 / 10
7.EE.3 / Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies / Moving straight ahead Inv. 1,2
7.EE.4 / Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities / Setting stage for future work / Shapes and designs Inv. 2,3
Moving straight ahead. Inv. 1,2,4
7.G.1 / Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. / Focus area / 7a / 9 / Sampler 11
7.G.2 (Post) / Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. / Some work – not a focus even though there are a lot of activities in this unit / Shapes and designs. Inv. 1,2,3 / 5a
7.G.6 (Post) / Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. / Focus on how area is affected / Filling and wrapping: Inv. 1,2

Unit Notes:

Focus on the Geometric comparisons: how scaling affects angle, sides, area, and perimeter. Also focus on finding missing sides of geometric figures. Only an intro to formal written ratios. More formal numeric work will be done in Comparing and Scaling.

Transformations in not a 7th grade standards but this unit lays a foundation for 8th grade standards around similarity and transformations. Covered in Butterflies, Pinwheels, and Wallpaper

Inv. 1 – Needed (possibly skip rubber band activity) – focus on properties of similarity - descriptions – how it affects angles, sides, etc.

Inv. 2 – Good practice for graphing points, introduction to transformation but do not focus there. Main area of focus should be similarity descriptions, again how it effects angles, area etc… (Focus on Precision)

Inv. 3 – Rep-tile – good visual for seeing how area is affected. But could skip 3.1 and 3.2 if adequate time is spent focusing on area in previous activities.

Focus more time on 3.3 and 3.4. 3.3 challenging area problems and begins the process of finding missing side. 3.4 introduces the idea of nested triangles which can often be a difficult visual for students but is often used on state exams.

Inv. 4 – Shift to comparing ratio’s within figures. Introduces ratios as fractions. Spend time on real world applications (shadow type problems). Review many ideas from throughout rest of unit.