Curriculum Map
Math
Grade 5

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Month	Unit	Benchmark	Grade Level Indicators	Assessment
Sept. – Oct. October October Nov. Nov. Dec/Jan Dec/Jan Dec/Jan February/ March February/ March April/ May April/ May April/ May	Mathematical Thinking & Building on Numbers You Know Picturing Polygons Picturing Polygons Algebra Algebra Name That Portion Name That Portion Between Never and Always Patterns of Change Patterns of Change Containers & Cubes	Numbers, Number Sense and Operations Standard F. Apply number system properties when performing computations. G. Demonstrate factorization and finding common factors and common multiples Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers. Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents. Fourth Grade Indicators: Number, Number Sense & Operations Model and use commutative and associative properties for addition and multiplication. Use relationships between operations, such as subtraction as the inverse of addition and division as the inverse of multiplication. Use a variety of methods and appropriate tools (mental math, paper and pencil, calculators) for computing with whole numbers. Measurement Standard A. Select appropriate units to measure angles Degrees C. Identify appropriate tools and apply appropriate techniques for measuring angles Geometry and Spatial Sense Standard A. Identify and label angle parts and the regions defined within the plane where the angle resides. Specify locations and plot ordered pairs on coordinate plane. Identify, describe and classify types of line pairs, angles and two dimension figures. Use proportions to express relationships among corresponding parts of similar figures. Describe and use the concepts of congruence, similarity and symmetry to solve problems. Describe and use properties of triangles to solve problems involving angle measures and side lengths of right triangles. Number, Number Sense and Operations Standard Represent and compare numbers less than 0 through familiar applications and extending the number line. Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results. Patterns, Functions and Algebra B. Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules. C. Use variables to create and solve equations and inequalities representing problem situations. F. Use representations such as physical models to solve problems. Number, Number Sense and Operations Standard F. Compare, order and convert among fractions, decimals and percents. Develop meaning for percents including percents greater than 100 and less than 1. Use models and pictures to relate concepts of ratio, proportion and percent. Apply number system properties when performing computations. Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers. Number, Number Sense and Operations Standard I. Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents. E. Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results. H. Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers. Data Analysis and Probability Standard A. Read, create, and use circle graphs. E. Collect, organize, display, and interpret data for a specific purpose or need. Patterns, Functions and Algebra F. Use representations such as physical models to solve problems. Measurement Standard Select appropriate units to measure angles, circumference, surface area, mass and volume, using: · U.S. customary units; e.g., degrees, square feet, pounds, and other units as appropriate. · Metric units; e.g., square meters, kilograms and other units as appropriate. Convert units of length, area, volume, mass and time within the same measurement system. Measure perimeter and area of rectangles, triangles and parallelograms and volume of rectangular prisms. Select a tool and measure accurately to a specified level of precision. and technology as needed to solve Use problem-solving techniques problems involving length, eight, perimeter, area, volume, time and temperature. Geometry and Spatial Sense Draw circles and identify and determine relationships among the radius, diameter, center and circumference. Identify and draw three-dimensional objects from different views (top, side, front and perspective). Measurement Standard Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed. Understand and demonstrate the independence of perimeter and area for two-dimensional shapes and of surface area and volume for three-dimensional shapes. Data Analysis & Probability A. Read, create and use line graphs, histograms, circle graphs, box-and-whisker plots, stem-and-leaf plots, and other representations when appropriate. C. Evaluate interpretations and conclusions as additional data are collected, modify conclusions and predictions, and justify new findings. H. Find all possible outcomes of simple experiments or problem situations, using methods such as lists, arrays and tree diagrams. I. Describe the probability of an event using ratios, including fractional notation. J. Compare experimental and theoretical results for a variety of simple experiments. K. Make and justify predictions based on experimental and theoretical probabilities. Patterns, Functions & Algebra A. Describe, extend and determine the rule for patterns and relationships occurring in numeric patterns, computation, geometry, graphs and other applications. L. Analyze functional relationships, and explain how a change in one quantity results in a change in the other. Data Analysis & Probability D. Compare increasingly complex displays of data, such as multiple sets of data on the same graph. F. Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data. E. Collect, organize, display and interpret data for a specific purpose or need. Measurement Standard F. Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are change. G. Understand and demonstrate the independence of perimeter and area for two-dimensional shapes and of surface area and volume for three-dimensional shapes.	Numbers, Number Sense and Operations Standard 7. Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations. 8. Identify and use relationships between operations to solve problems. 5. Recognize and identify perfect squares and their roots. 13. Estimate the results of computations involving whole numbers. Fourth Grade Indicators: 7. Recognize that division may be used to solve different types of problem situations and interpret the meaning of remainders; e.g., situations involving measurement, money. 13. Use a variety of methods and appropriate tools for computing with whole numbers; e.g., mental math, paper and pencil, and calculator. Measurement Standard 1. Identify and select appropriate units to measure angles; i.e., degrees. 2. Identify paths between points on a grid or coordinate plane and compare the lengths of the paths; e.g., shortest path, paths of equal length. 7. Use benchmark angles (e.g., 45°, 90°, 120°) to estimate the measure of angles, and use a tool to measure and draw angles. Geometry and Spatial Sense Standard 2. Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular. 3. Label vertex, rays, interior and exterior for an angle. 4. Describe and use properties of congruent figures to solve problems. 5. Use physical models to determine the sum of the interior angles of triangles and quadrilaterals. 6. Extend understanding of coordinate system to include points whose x or y values may be negative numbers. 7. Understand that the measure of an angle is determined by the degree of rotation of an angle side rather than the length of either side. Number, Number Sense and Operations Standard 6. Represent and compare numbers less than 0 by extending the number line and using familiar applications; e.g., temperature, owing money. 9. Use order of operations, including use of parentheses, to simplify numerical expressions. Patterns, Functions and Algebra 3. Use variables as unknown quantities in general rules when describing patterns and other relationships 4. Create and interpret the meaning of equations and inequalities representing problem situations. 1. Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs. Number, Number Sense and Operations Standard 1. Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole. 2. Use various forms of “one” to demonstrate the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = ¾ x 6/6. 3. Identify and generate equivalent forms of fractions, decimals and percents. 10. Justify why fractions need common denominators to be added or subtracted. 11. Explain how place value is related to addition and subtraction of decimals; e.g., 0.2 + 0.14; the two tenths is added to the one tenth because they are both tenths. 12. Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. 13. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. Number, Number Sense and Operations Standard 4. Round decimals to a given place value and round fractions (including mixed numbers) to the nearest half. 12. Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. 13. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. Data Analysis and Probability Standard 1. Read, construct and interpret frequency tables, circle graphs and line graphs. 4. Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. Patterns, Functions and Algebra 1. Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs. 5. Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. Measurement Standard 4. Demonstrate understanding of the differences among linear units, square units and cubic units. 5. Make conversions within the same measurement system while performing computations. 4. Demonstrate understanding of the differences among linear units, square units and cubic units. 6. Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. 1. Draw circles and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximate π. 8. Predict what three-dimensional object will result from folding a two-dimensional net, then confirm the prediction by folding the net. Measurement Standard – 3 Dimensional 3. Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three-dimensional objects. 4. Demonstrate understanding of the differences among linear units, square units and cubic units. 6. Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. Data Analysis & Probability 1. Read, construct and interpret frequency tables, circle graphs and line graphs. 5. Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected. 7. List and explain all possible outcomes in a given situation. 8. Identify the probability of events within a simple experiment, such as three chances out of eight. 9. Use 0, 1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome. 10. Compare what should happen (theoretical/expected results) with what did happen (experimental/actual results) in a simple experiment. 11. Make predictions based on experimental and theoretical probabilities. Patterns, Functions & Algebra 2. Use calculators or computers to develop patterns and generalize them using tables and graphs. 6. Describe how the quantitative change I a variable affects the value of a related variable; e.g., describe how the rate of growth varies over time based upon data in a table or graph. Data Analysis & Probability 3. Read and interpret increasingly complex displays of data, such as double bar graphs. 6. Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. 2. Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data.	Task 1A, 1B Quiz #2 Quiz #2 Task 4 & 5B Quiz #1 Task 1,2, 3, 5 Quiz #2 Task 2, 6 Task 4, 5A, 5 B Quiz #2 Task 1A, 1B, 2, 3, 4, 5B, 6 Quiz #2 Task 3C, 2A, 2B? Quiz #3 Task 1A, 1B, 1C? Quiz #3 Task 3A, 3B, 3C? Quiz #3 Task 2A, 2B, 3A? Quiz #3 Work Samples Tasks 2A, 2B, 3B? Quiz #3 Task 3C? Quiz #3 Task 1A, 1B? Quiz #3 Task 3C? Quiz #3 Task 1A & 1B? Quiz #3 Quiz #4 Quiz #4 Quiz #4 Task 3B Quiz #3 Task 2A, 2B Quiz #5 Quiz #5 Quiz #5 Teacher Observation Task being developed Task 4A, 4B Quiz #5 Task being developed Quiz #5 Quiz #5 Quiz #5 Work Sample Teacher Observation Task 1A, 1B Quiz #5 Task 2A, 2B Quiz #5 Teacher Observation Quiz #6 Quiz #6 Task 1C Tasks 1B, 2A Quiz #6 Task 1C Quiz #6 Task 1A, 1D, 2B Quiz #6 Work Sample Task 2A, 2B Quiz 7 Task 1B Task 1B, 2A, 2B Task 1C Teacher observation Teacher Observation Observation Task 2A, 2B Quiz #8 Work Sample Quiz #8 Work Sample Task 1B

Month

Unit

Benchmark

Grade Level Indicators

Assessment

Sept. – Oct.

October

Nov.

Dec/Jan

February/

March

February/

March

April/ May

April/

May

April/

May

Mathematical Thinking & Building on Numbers You Know

Picturing Polygons

Algebra

Name That Portion

Between Never and Always

Patterns of Change

Containers & Cubes

Numbers, Number Sense and Operations Standard

F. Apply number system properties when performing computations.

G. Demonstrate factorization and finding common factors and common multiples

Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers.

Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents.

Fourth Grade Indicators:

Number, Number Sense & Operations

Model and use commutative and associative properties for addition and multiplication.

Use relationships between operations, such as subtraction as the inverse of addition and division as the inverse of multiplication.

Use a variety of methods and appropriate tools (mental math, paper and pencil, calculators) for computing with whole numbers.

Measurement Standard

A. Select appropriate units to measure angles

Degrees

C. Identify appropriate tools and apply appropriate techniques for measuring angles

Geometry and Spatial Sense Standard

A. Identify and label angle parts and the regions defined within the plane where the angle resides.

Specify locations and plot ordered pairs on coordinate plane.

Identify, describe and classify types of line pairs, angles and two dimension figures.

Use proportions to express relationships among corresponding parts of similar figures.

Describe and use the concepts of congruence, similarity and symmetry to solve problems.

Describe and use properties of triangles to solve problems involving angle measures and side lengths of right triangles.

Number, Number Sense and Operations Standard

Represent and compare numbers less than 0 through familiar applications and extending the number line.

Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results.

Patterns, Functions and Algebra

B. Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules.

C. Use variables to create and solve equations and inequalities representing problem situations.

F. Use representations such as physical models to solve problems.

Number, Number Sense and Operations Standard

F. Compare, order and convert among fractions, decimals and percents.

Develop meaning for percents including percents greater than 100 and less than 1.

Use models and pictures to relate concepts of ratio, proportion and percent.

Apply number system properties when performing computations.

Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers.

Number, Number Sense and Operations Standard

I. Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents.

E. Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results.

H. Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers.

Data Analysis and Probability Standard

A. Read, create, and use circle graphs.

E. Collect, organize, display, and interpret data for a specific purpose or need.

Patterns, Functions and Algebra

F. Use representations such as physical models to solve problems.

Measurement Standard

Select appropriate units to measure angles, circumference, surface area, mass and volume, using:

· U.S. customary units; e.g., degrees, square feet, pounds, and other units as appropriate.

· Metric units; e.g., square meters, kilograms and other units as appropriate.

Convert units of length, area, volume, mass and time within the same measurement system.

Measure perimeter and area of rectangles, triangles and parallelograms and volume of rectangular prisms.

Select a tool and measure accurately to a specified level of precision.

and technology as needed to solve Use problem-solving techniques problems involving length, eight, perimeter, area, volume, time and temperature.

Geometry and Spatial Sense

Draw circles and identify and determine relationships among the radius, diameter, center and circumference.

Identify and draw three-dimensional objects from different views (top, side, front and perspective).

Measurement Standard

Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed.

Understand and demonstrate the independence of perimeter and area for two-dimensional shapes and of surface area and volume for three-dimensional shapes.

Data Analysis & Probability

A. Read, create and use line graphs, histograms, circle graphs, box-and-whisker plots, stem-and-leaf plots, and other representations when appropriate.

C. Evaluate interpretations and conclusions as additional data are collected, modify conclusions and predictions, and justify new findings.

H. Find all possible outcomes of simple experiments or problem situations, using methods such as lists, arrays and tree diagrams.

I. Describe the probability of an event using ratios, including fractional notation.

J. Compare experimental and theoretical results for a variety of simple experiments.

K. Make and justify predictions based on experimental and theoretical probabilities.

Patterns, Functions & Algebra

A. Describe, extend and determine the rule for patterns and relationships occurring in numeric patterns, computation, geometry, graphs and other applications.

L. Analyze functional relationships, and explain how a change in one quantity results in a change in the other.

Data Analysis & Probability

D. Compare increasingly complex displays of data, such as multiple sets of data on the same graph.

F. Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data.

E. Collect, organize, display and interpret data for a specific purpose or need.

Measurement Standard

F. Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are change.

G. Understand and demonstrate the independence of perimeter and area for two-dimensional shapes and of surface area and volume for three-dimensional shapes.

Numbers, Number Sense and Operations Standard

7. Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations.

8. Identify and use relationships between operations to solve problems.

5. Recognize and identify perfect squares and their roots.

13. Estimate the results of computations involving whole numbers.

Fourth Grade Indicators:

7. Recognize that division may be used to solve different types of problem situations and interpret the meaning of remainders; e.g., situations involving measurement, money.

13. Use a variety of methods and appropriate tools for computing with whole numbers; e.g., mental math, paper and pencil, and calculator.

Measurement Standard

1. Identify and select appropriate units to measure angles; i.e., degrees.

2. Identify paths between points on a grid or coordinate plane and compare the lengths of the paths; e.g., shortest path, paths of equal length.

7. Use benchmark angles (e.g., 45°, 90°, 120°) to estimate the measure of angles, and use a tool to measure and draw angles.

Geometry and Spatial Sense Standard

2. Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular.

3. Label vertex, rays, interior and exterior for an angle.

4. Describe and use properties of congruent figures to solve problems.

5. Use physical models to determine the sum of the interior angles of triangles and quadrilaterals.

6. Extend understanding of coordinate system to include points whose x or y values may be negative numbers.

7. Understand that the measure of an angle is determined by the degree of rotation of an angle side rather than the length of either side.

Number, Number Sense and Operations Standard

6. Represent and compare numbers less than 0 by extending the number line and using familiar applications; e.g., temperature, owing money.

9. Use order of operations, including use of parentheses, to simplify numerical expressions.

Patterns, Functions and Algebra

3. Use variables as unknown quantities in general rules when describing patterns and other relationships

4. Create and interpret the meaning of equations and inequalities representing problem situations.

1. Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs.

Number, Number Sense and Operations Standard

1. Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole.

2. Use various forms of “one” to demonstrate the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = ¾ x 6/6.

3. Identify and generate equivalent forms of fractions, decimals and percents.

10. Justify why fractions need common denominators to be added or subtracted.

11. Explain how place value is related to addition and subtraction of decimals; e.g., 0.2 + 0.14; the two tenths is added to the one tenth because they are both tenths.

12. Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals.

13. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.

Number, Number Sense and Operations Standard

4. Round decimals to a given place value and round fractions (including mixed numbers) to the nearest half.

12. Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals.

13. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.

Data Analysis and Probability Standard

1. Read, construct and interpret frequency tables, circle graphs and line graphs.

4. Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings.

Patterns, Functions and Algebra

1. Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs.

5. Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions.

Measurement Standard

4. Demonstrate understanding of the differences among linear units, square units and cubic units.

5. Make conversions within the same measurement system while performing computations.

4. Demonstrate understanding of the differences among linear units, square units and cubic units.

6. Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms.

1. Draw circles and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximate π.

8. Predict what three-dimensional object will result from folding a two-dimensional net, then confirm the prediction by folding the net.

Measurement Standard – 3 Dimensional

3. Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three-dimensional objects.

4. Demonstrate understanding of the differences among linear units, square units and cubic units.

6. Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms.

Data Analysis & Probability

1. Read, construct and interpret frequency tables, circle graphs and line graphs.

5. Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected.

7. List and explain all possible outcomes in a given situation.

8. Identify the probability of events within a simple experiment, such as three chances out of eight.

9. Use 0, 1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome.

10. Compare what should happen (theoretical/expected results) with what did happen (experimental/actual results) in a simple experiment.

11. Make predictions based on experimental and theoretical probabilities.

Patterns, Functions & Algebra

2. Use calculators or computers to develop patterns and generalize them using tables and graphs.

6. Describe how the quantitative change I a variable affects the value of a related variable; e.g., describe how the rate of growth varies over time based upon data in a table or graph.

Data Analysis & Probability

3. Read and interpret increasingly complex displays of data, such as double bar graphs.

6. Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data.

2. Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data.

Task 1A, 1B

Quiz #2

Task 4 & 5B

Quiz #1

Task 1,2, 3, 5

Quiz #2

Task 2, 6

Task 4, 5A, 5 B

Quiz #2

Task 1A, 1B, 2, 3, 4, 5B, 6

Quiz #2

Task 3C, 2A, 2B?

Quiz #3

Task 1A, 1B, 1C?

Quiz #3

Task 3A, 3B, 3C?

Quiz #3

Task 2A, 2B, 3A?

Quiz #3

Work Samples

Tasks 2A, 2B, 3B?

Quiz #3

Task 3C?

Quiz #3

Task 1A, 1B?

Quiz #3

Task 3C?

Quiz #3

Task 1A & 1B?

Quiz #3

Quiz #4

Task 3B

Quiz #3

Task 2A, 2B

Quiz #5

Teacher Observation

*Task being developed

Task 4A, 4B

Quiz #5

*Task being developed

Quiz #5

Work Sample

Teacher Observation

Task 1A, 1B

Quiz #5

Task 2A, 2B

Quiz #5

Teacher Observation

Quiz #6

Task 1C

Tasks 1B, 2A

Quiz #6

Task 1C

Quiz #6

Task 1A, 1D, 2B

Quiz #6

Work Sample

Task 2A, 2B

Quiz 7

Task 1B

Task 1B, 2A, 2B

Task 1C

Teacher observation

Teacher Observation

Observation

Task 2A, 2B

Quiz #8

Work Sample

Quiz #8

Work Sample

Task 1B