## Description

- Overview:
- This lesson unit is intended to help assess how well students are able to interpret and use scale drawings to plan a garden layout. This involves using proportional reasoning and metric units.

- Level:
- Lower Primary, Upper Primary, Middle School, High School
- Grades:
- Kindergarten, Grade 1, Grade 2, Grade 3, Grade 4, Grade 5, Grade 6, Grade 7, Grade 8, Grade 9, Grade 10, Grade 11, Grade 12
- Material Type:
- Assessment, Lesson Plan
- Provider:
- Shell Center for Mathematical Education
- Provider Set:
- Mathematics Assessment Project (MAP)
- Date Added:
- 04/26/2013

- License:
- Creative Commons Attribution Non-Commercial No Derivatives
- Media Format:
- Downloadable docs, Text/HTML

# Comments

## Standards

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Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them.

Standard: 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.

Degree of Alignment: 3 Superior (6 users)

Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them.

Standard: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Degree of Alignment: 2 Strong (1 user)

Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them.

Standard: 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.

Degree of Alignment: 2 Strong (1 user)

Cluster: Use properties of operations to generate equivalent expressions

Standard: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

Degree of Alignment: 2 Strong (1 user)

Cluster: Use properties of operations to generate equivalent expressions

Standard: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Degree of Alignment: 2 Strong (1 user)

Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Standard: 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.

Degree of Alignment: 2 Strong (1 user)

Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Standard: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Degree of Alignment: 2 Strong (1 user)

Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Standard: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Degree of Alignment: 2 Strong (1 user)

Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Standard: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Degree of Alignment: 2 Strong (1 user)

Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Standard: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example, As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Degree of Alignment: 2 Strong (1 user)

Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Standard: 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.

Degree of Alignment: 2 Strong (1 user)

Standard: 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 as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Degree of Alignment: 2 Strong (1 user)

# Common Core State Standards Math

Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Standard: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Degree of Alignment: 2 Strong (1 user)

# Common Core State Standards Math

Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Standard: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Degree of Alignment: 2 Strong (1 user)

# Common Core State Standards Math

Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Standard: 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.

Degree of Alignment: 2 Strong (1 user)

# Common Core State Standards Math

Grade 7,Ratios and Proportional RelationshipsStandard: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Degree of Alignment: 2 Strong (1 user)

# Common Core State Standards Math

Grade 7,Ratios and Proportional RelationshipsStandard: 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.

Degree of Alignment: 2 Strong (1 user)

Cluster: Mathematical practices

Standard: Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Degree of Alignment: 2 Strong (1 user)

# Common Core State Standards Math

Grade 7,Ratios and Proportional RelationshipsStandard: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.

Degree of Alignment: 2 Strong (1 user)

Cluster: Mathematical practices

Standard: Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a 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 analyze 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.

Degree of Alignment: 2 Strong (1 user)

Cluster: Mathematical practices

Standard: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Degree of Alignment: 2 Strong (1 user)

# Common Core State Standards Math

Grade 7,Ratios and Proportional RelationshipsStandard: Recognize and represent proportional relationships between quantities.

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems

Indicator: Recognize and represent proportional relationships between quantities.

Degree of Alignment: 3 Superior (1 user)

Learning Domain: Geometry

Standard: Draw, construct, and describe geometrical figures and describe the relationships between them.

Indicator: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Expressions and Equations

Standard: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Indicator: 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 as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Expressions and Equations

Standard: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Indicator: 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.

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Geometry

Standard: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Indicator: 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.

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Geometry

Standard: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Indicator: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Geometry

Standard: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Indicator: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems

Indicator: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems

Indicator: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Expressions and Equations

Standard: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Indicator: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Expressions and Equations

Indicator: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example, As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Geometry

Standard: Draw, construct, and describe geometrical figures and describe the relationships between them.

Indicator: 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.

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Geometry

Standard: Draw, construct, and describe geometrical figures and describe the relationships between them.

Indicator: 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.

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Expressions and Equations

Standard: Use properties of operations to generate equivalent expressions

Indicator: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Degree of Alignment: 1 Limited (1 user)

Learning Domain: Expressions and Equations

Standard: Use properties of operations to generate equivalent expressions

Indicator: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%"ť is the same as "multiply by 1.05."ť

Degree of Alignment: 1 Limited (1 user)

Learning Domain: Ratios and Proportional Relationships

Indicator: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Indicator: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Indicator: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Indicator: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a 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 analyze 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize"Óto abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents"Óand the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Indicator: Solve multi-step real world and mathematical problems involving ratios and percentages.

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Ratios and Proportional Relationships

Standard:

Indicator: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Degree of Alignment: 2 Strong (1 user)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Indicator: Recognize and represent proportional relationships between quantities.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Indicator: Compute unit rates, including those involving complex fractions, with like or different units.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard:

Indicator: Decide whether two quantities in a table or graph are in a proportional relationship.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard:

Indicator: Represent proportional relationships with equations.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard:

Indicator: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Indicator: Draw geometric shapes with given conditions using a variety of tools (e.g., ruler and protractor, or technology). 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Indicator: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing.

Degree of Alignment: Not Rated (0 users)

## Evaluations

# Achieve OER

Average Score (3 Points Possible)Degree of Alignment | 2.1 (6 users) |

Quality of Explanation of the Subject Matter | 2.9 (7 users) |

Utility of Materials Designed to Support Teaching | 2.6 (7 users) |

Quality of Assessments | 2.2 (6 users) |

Quality of Technological Interactivity | 2.5 (2 users) |

Quality of Instructional and Practice Exercises | 2.3 (6 users) |

Opportunities for Deeper Learning | 2.5 (6 users) |

# Tags (14)

- Mathematics
- Algebra and Calculus
- Geometry and measures
- Algebra
- CCSS
- Common Core Math
- Common Core PD
- Equations
- Geometry
- Math Modeling
- ODE Learning
- Ratios and Proportions
- Scale Drawing
- Math Literacy Lessons

This is a lesson/assessment unit. It has many resources for the teacher. It includes student handouts, detailed teacher lessons, ppt to go with the lesson, and assessments. It also provides prompts teachers can use to guide students to make connections. It is addressing CCSS 7.G.1. Good lesson for scale drawing