NECAP Standards Cycle of Review and Revision K8 Curriculum Alignment YHS Syllabi Curriculum Brochures Curriculum Maps YHS Program of Studies Maine Learning Results
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Grade Five Math Scope and Sequence Students will follow the Everyday Mathematics Project Program. Everyday Mathematics offers children a broad background in mathematics. The approaches used in this program may differ from those you learned as a child.
Following are some program highlights of Everyday Mathematics:
 Partner and smallgroup activities that promote cooperative learning, discussion, and communicating mathematically;
 Explorations of patterns in numbers and extensions of mathematical concepts;
 A handson approach often using physical and pictorial models to represent mathematical concepts;
 A problemsolving approach that uses everyday situations;
 Concepts and skills introduced and reviewed throughout the school year, not only promoting retention but allowing for a variety of exposures;
 Opportunities for home involvement;
 Frequent practice using games.
 K4 Everyday Mathematics emphasizes the following contents:
 Numeration and Order: saying, reading, and writing numbers; place value of whole numbers.
 Operations: number facts; fact families and simple addition and subtraction problems.
 Data and Chance: collecting, organizing, and interpreting data using tables, charts and graphs.
 Geometry and Spatial Sense: exploring 2 and 3dimensional shapes and classifying polygons.
 Measures and Measurement: using tools to measure length, weight, capacity, and volume; exchanging money amounts; using money as a tool for place value and decimal concepts.
 ·Reference Frames: activities involving clocks, calendars, thermometers, and number lines.
 Patterns, Functions and Sequences: functions, relations, attributes, patterns, and sequences.
 Algebra and Uses of Variables: missing numbers; properties of operations; “What’s My Rule?” puzzles.
SUBJECT AREA: MATHEMATICS GRADE: 5 Content Standards
 Performance Indicators
 Instructional Practice
 Assessment Tools
 Reporting Tools
 A. NUMBER: Students use numbers in everyday and mathematical contexts to quantify or describe phenomena, develop concepts of operations with different types of numbers, use the structure and properties of numbers with operations to solve problems, and perform mathematical computations. Students develop number sense related to magnitude, estimation, and the effects of mathematical operations on different types of numbers. It is expected that students use numbers flexibly, using forms of numbers that best match a situation. Students compute efficiently and accurately. Estimation should always be used when computing with numbers or solving problem  WHOLE NUMBER




 A.1. Students understand and use number notation to 10 million in numerals and words.
 a. Read and write numbers to 10 million in numerals.
 Numbers and Numeration Goal 1: Read and write whole numbers and decimals; identify places in such numbers and the values of the digits in those places; use expanded notation to represent whole numbers and decimals. Lessons: 1.1, 2.2, 2.4, 2.5, 2.7, 2.10, 3.2, 5.6, 5.7, 5.8, 7.2, 7.3, 9.2   classroom tests
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 b. Round numbers to the place value appropriate for given contexts.
 Operations and Computation Goal 6: Make reasonable estimates for whole number and decimal addition, subtraction, multiplication, and division problems and fraction and mixed number addition and subtraction problems; explain how the estimates were obtained. Lessons: 2.2, 2.3, 2.4, 2.7, 2.8, 2.9, 2.10, 3.2, 4.3, 4.5, 4.6, 4.7, 5.5, 5.9, 5.10, 9.7, 12.6   classroom tests
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  report cards
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 power school
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 c. Compare and order up to 10 million.
 Number and Numeration Goal 6 Compare and order rational numbers; use area models, benchmark fractions and analyses of numerators and denominators to compare and order fractions and mixed numbers; describe strategies used to compare fractions and mixed numbers. Lessons: 2.10, 5.2, 5.3, 5.5, 5.6, 5.7, 6.8, 7.1, 7.7, 8.1, 8.4, 12.3, 12.4   classroom tests
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  report cards
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 A.2. Students multiply and divide numbers up to four digits by numbers up to two digits, and by tens, hundreds, and thousands and interpret any remainders.

 Operations and Computation Goal 2: Demonstrate automaticity with multiplication facts and proficiency with division facts and fact extensions. Lessons: 1.3, 1.4, 1.5, 1.6, 4.1, 4.4, 7.8, 7.9, 7.11, 12.1 Goal 3: Use mental arithmetic, paperandpencil algorithms and calculators to solve problems involving the multiplication of whole numbers and decimals and the division of multi digit whole numbers and decimals by whole numbers; express remainders as whole numbers and fractions as appropriate; describe the strategies used and explain how they work. Lessons: 1.5, 2.7, 2.8, 2.9, 4.1, 4.2, 4.4, 4.5, 4.6, 10.1, 10.2, 12.8 Goal 5: Use area models, mental arithmetic, paperandpencil algorithms and calculators to solve problems involving the multiplication of fractions and mixed numbers; use diagrams, a commondenominator method and calculators to solve problems involving the division of fractions; describe the strategies used.
Lessons: 8.5, 8.6, 8.7, 8.8, 8.12   classroom tests
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 A.3. Students solve problems requiring multiple operations (addition, subtraction, multiplication and division) and use the conventions of order of operations (no exponents expected).

 Patterns, Functions and Algebra Goal 3 Evaluate numeric expressions containing grouping symbols and nested grouping symbols; insert grouping symbols and nested grouping symbols to make number sentences true; describe and use the precedence of multiplication and division over addition and subtraction.
Lessons: 2.1, 2.3, 7.5   classroom tests
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 RATIONAL NUMBER




 A.4. Students understand, name, compare, illustrate, compute with and use fractions.
 a. Add and subtract fractions with unlike denominators.
 Operation and Computation Goal 4: Use mental arithmetic, paperandpencil algorithms, and calculators to solve problems involving the addition and subtraction of fractions and mixed numbers; describe the strategies used and explain how they work.
Lessons: 5.2, 5.3, 6.8, 6.9, 6.10, 8.1, 8.2, 8.3, 8.4   classroom tests
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 b. Multiply a fraction by a whole number.
 Operation and Computation Goal 5: Use area models, mental arithmetic, paperandpencil algorithms and calculators to solve problems involving the multiplication of fractions and mixed numbers; use diagrams, a commondenominator method and calculators to solve problems involving the division of fractions; describe the strategies used. Lessons: 8.5, 8.6, 8.7, 8.8, 8.12   classroom tests
 classroom quizzes
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  report cards
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 A.5. Students understand and use number notation and place value in numbers with three decimal places.
 a. Compare, order, read, round, and interpret decimals with up to three decimal places.
 Number and Numeration Goal 1: Read and write whole numbers and decimals; identify places in such numbers and the values of the digits in those places; use expanded notation to represent whole numbers and decimals. Lessons: 1.1, 2.2, 2.4, 2.5, 2.7, 2.10, 3.2, 5.6, 5.7, 5.8, 7.2, 7.3, 9.2 Goal 6: Compare and order rational numbers; use area models, benchmark fractions and analyses of numerators and denominators to compare and order fractions and mixed numbers; describe strategies used to compare fractions and mixed numbers. Lessons: 2.10, 5.2, 5.3, 5.5, 5.6, 5.7, 6.8, 7.1, 7.7, 8.1, 8.4, 12.3, 12.4   classroom tests
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 b. Add and subtract decimals with up to three decimal places.
 Operations and Computation Goal 1: Use mental arithmetic, paperandpencil algorithms, and calculators to solve problems involving the addition and subtractions of whole numbers and decimals, and signed numbers; describe the strategies used and explain how they work. Lessons: 2.2, 2.3, 2.9, 7.8, 7.9, 7.10, 10.1, 10.2   classroom tests
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 c. Multiply and divide decimals with up to three decimal places by a 2digit whole number.
 Operations and Computation Goal 3: Use mental arithmetic, paperandpencil algorithms and calculators to solve problems involving the multiplication of whole numbers and decimals and the division of multi digit whole numbers and decimals by whole numbers; express remainders as whole numbers and fractions as appropriate; describe the strategies used and explain how they work. Lessons: 1.5, 2.7, 2.8, 2.9, 4.1, 4.2, 4.4, 4.5, 4.6, 10.1, 10.2, 12.8   classroom tests
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 d. Develop the concept of a fraction as division through expressing fractions with denominators of two, four, five, and ten, as decimals and decimals as fractions.
 Number and Numeration Goal 5: Use numerical expressions to find and represent equivalent names for fractions, decimals and percents; use and explain multiplication and division rules to find equivalent fractions and fractions in simplest form; covert between fractions and mixed numbers; convert between fractions, decimals and percents. Lessons: 1.3, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 5.10, 5.11, 5.12, 6.5, 6.6, 6.8, 6.9, 6.10, 8.1, 8.2, 8.3, 8.4, 8.7, 8.8, 8.9, 8.10, 8.12, 12.1, 12.4, 12.5, 12.6   classroom tests
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 A.6. Students understand concepts of positive and negative integers.
 a. Place positive and negative integers on a number line or scale.
 Measurement and Reference Frames Goal 4: Use ordered pairs of numbers to name, locate, and plot points in all four quadrants on a coordinate grid. Lessons: 7.7, 9.1, 9.2, 9.3, 9.7   classroom tests
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 b. Compare and order positive and negative integers.
 Measurement and Reference Frames Goal 4: Use ordered pairs of numbers to name, locate, and plot points in all four quadrants on a coordinate grid. Lessons: 7.7, 9.1, 9.2, 9.3, 9.7   classroom tests
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 c. Find the distance between two integers in a context.
 Measurement and Reference Frames Goal 4: Use ordered pairs of numbers to name, locate, and plot points in all four quadrants on a coordinate grid. Lessons: 7.7, 9.1, 9.2, 9.3, 9.7   classroom tests
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 REAL NUMBERS




 No performance indicator. Although no performance indicators are stated, students are expected to have instructional experiences in which they use only rational numbers. 



 B. DATA: Students make measurements and collect, display, evaluate, analyze and compute with data to describe or model phenomena and to make decisions based on data. Students compute statistics to summarize data sets and use concepts of probability to make predictions and describe the uncertainty inherent in data collection and measurement. It is expected that when working with measurements students:
 understand that most measurements are approximations and that taking repeated measurements reveals this variability;
 understand that a number without a unit is not a measurement, and that an appropriate unit must always be attached to a number to provide a measurement;
 understand that the precision and accuracy of a measurement depends on selecting the appropriate tools and units; and use estimation comparing measures to benchmarks appropriate to the type of measure and units.
 MEASUREMENT AND APPROXIMATION




 B.1. Students understand and use measures of elapsed time, temperature, capacity, mass, and use measures of mass and weight.
 a. Select and use appropriate tools and units (mass in grams, weight in pounds) for these measures.
 Measurement and Reference Frames Goal 1: Estimate length with and without; measure length with tools to the nearest 1/8 inch and millimeter; estimate the measure of angles with and without tools; use tools to draw angles with given measures. Lessons: 2.1, 3.3, 3.4, 3.5, 3.6, 3.9, 3.10, 4.3, 5.10, 5.11, 6.2, 6.3, 11.7, 12.6 Goal 3: Describe relationships among U.S. customary units of length; among metric units of length; and among U.S. customary units of capacity. Lessons: 9.4, 9.5, 9.10, 11.3, 11.5, 11.6   classroom tests
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 b. Solve and justify problems with these measures.
 Measurement and Reference Frames Goal 2: Describe and use strategies to find the perimeter of polygons and the area of circles; choose and use appropriate formulas to calculate the areas of rectangles, parallelograms, and triangles, and the volume of a prism; define pi as the ratio of a circle's circumference to its diameter. Lessons: 3.5, 9.4, 9.5, 9.6, 9.8, 9.9, 10.8, 10.9, 11.3, 11.4, 11.5, 11.6, 11.7   classroom tests
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  report cards
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 DATA ANALYSIS




 B.2. Students read, construct, and interpret line graphs.

 Data and Chance Goal 1: Collect and organize data or use given data to create bar, line, and circle graphs with reasonable titles, labels, keys and intervals. Lessons: 2.5, 5.9, 5.11, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 7.6, 8.11, 9.7, 10.4, 10.5, 10.6, 11.2, 11.3, 11.5, 12.7   classroom tests
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  report cards
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 power school
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 B.3. Students find and use median, mode, and range for a set of data.

 Data and Chance Goal 2: Use the maximum, minimum, range, median, mode, and mean and graphs to ask and answer questions, draw conclusions, and make predictions. Lessons: 2.1, 2.5, 2.6, 3.1, 3.2, 3.9, 5.10, 5.11, 5.12, 6.1, 6.4, 6.5, 6.6, 6.7, 7.6, 10.7, 10.8, 10.9, 12.7   classroom tests
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 PROBABILITY




 No performance indicator. Although no performance indicators are stated, students are expected to have experiences with probability in grade four, but it is not expected that the knowledge will be secure.




 C. GEOMETRY: Students use measurement and observation to describe objects based on their sizes and shapes; model or construct twodimensional and threedimensional objects; solve problems involving geometric properties; compute areas and volumes based on object properties and dimensions; and perform transformations on geometric figures. When making or calculating measures, students use estimation to check the reasonableness of results.  GEOMETRIC FIGURES




 C.1. Students identify, describe and classify solid figures.
 a. Identify edges, vertices, and faces in threedimensional figures.
 Geometry Goal 2: Describe, compare, and classify plane and solid figures using appropriate geometric terms; identify congruent figures and describe their properties. Lessons: 3.6, 3.7, 3.8, 3.10, 9.3, 9.6, 9.8, 9.9, 11.1, 11.2, 11.4, 11.7   classroom tests
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 b. Describe and classify solid figures according to the number of edges, faces, and vertices as well as the shapes of faces.
 Geometry Goal 2: Describe, compare, and classify plane and solid figures using appropriate geometric terms; identify congruent figures and describe their properties. Lessons: 3.6, 3.7, 3.8, 3.10, 9.3, 9.6, 9.8, 9.9, 11.1, 11.2, 11.4, 11.7   classroom tests
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 GEOMETRIC MEASUREMENT




 C.2. Students find the area of triangles and quadrilaterals.
 a. Know how to derive and use the formula A= (1/2) bh for the area of a triangle.
 Geometry Goal 2: Describe, compare, and classify plane and solid figures using appropriate geometric terms; identify congruent figures and describe their properties. Lessons: 3.6, 3.7, 3.8, 3.10, 9.3, 9.6, 9.8, 9.9, 11.1, 11.2, 11.4, 11.7   classroom tests
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 b. Find the area of parallelograms.
 Geometry Goal 2: Describe, compare, and classify plane and solid figures using appropriate geometric terms; identify congruent figures and describe their properties. Lessons: 3.6, 3.7, 3.8, 3.10, 9.3, 9.6, 9.8, 9.9, 11.1, 11.2, 11.4, 11.7   classroom tests
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  report cards
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 power school
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 C.3. Students understand how to find the volume and surface area of rectangular prisms.
 a. Know how to build solids with unit cubes and find their volume.
 Geometry Goal 2: Describe, compare, and classify plane and solid figures using appropriate geometric terms; identify congruent figures and describe their properties. Lessons: 3.6, 3.7, 3.8, 3.10, 9.3, 9.6, 9.8, 9.9, 11.1, 11.2, 11.4, 11.7   classroom tests
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  report cards
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 power school
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 b. Recognize and estimate the relative sizes of one cubic meter and one cubic centimeter or one cubic inch and one cubic foot.
 Geometry Goal 2: Describe, compare, and classify plane and solid figures using appropriate geometric terms; identify congruent figures and describe their properties. Lessons: 3.6, 3.7, 3.8, 3.10, 9.3, 9.6, 9.8, 9.9, 11.1, 11.2, 11.4, 11.7   classroom tests
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 c. Know how to derive and use the formula (length x width x height) for the volume of a rectangular prism.
 Geometry Goal 2: Describe, compare, and classify plane and solid figures using appropriate geometric terms; identify congruent figures and describe their properties. Lessons: 3.6, 3.7, 3.8, 3.10, 9.3, 9.6, 9.8, 9.9, 11.1, 11.2, 11.4, 11.7   classroom tests
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 d. Create nets to aid visualization and computation.



 C.4. Students understand how to describe position and direction in two dimensions.
 a. Locate points on the Cartesian plane.
 Measurement and Reference Frames Goal 4: Use ordered pairs of numbers to name, locate, and plot points in all four quadrants of a coordinate grid. Lessons: 7.7, 9.1, 9.2, 9.3, 9.7   classroom tests
 classroom quizzes
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 performances/displays/presentations
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 large scale assessments: NWEA, MEA
  report cards
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 b. Determine horizontal and vertical distance on the coordinate plane.
 Measurement and Reference Frames Goal 4: Use ordered pairs of numbers to name, locate, and plot points in all four quadrants of a coordinate grid. Lessons: 7.7, 9.1, 9.2, 9.3, 9.7   classroom tests
 classroom quizzes
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 performances/displays/presentations
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 large scale assessments: NWEA, MEA
  report cards
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 power school
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 c. Measure angles in degrees.
 Geometry Goal 1: Identify, describe, compare, name and draw right acute, obtuse, straight, and reflex angles; determine angle measures in vertical and supplementary angles and by applying properties of sums of angle measures in triangles and quadrangles. Lessons: 3.3, 3.4, 3.5, 3.7, 3.8, 3.9, 3.10.   classroom tests
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 performances/displays/presentations
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 TRANSFORMATIONS




 C.5. Students reflect, slide, and rotate plane figures.
 a. Identify figures with rotational or line symmetry.
 Geometry Goal 3: Identify, describe, and sketch examples of reflections, translations, and rotations. Lessons: 3.8, 9.2, 9.3.   classroom tests
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 b. Create figures with rotational or line symmetry.
 Geometry Goal 3: Identify, describe, and sketch examples of reflections, translations, and rotations. Lessons: 3.8, 9.2, 9.3   classroom tests
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 c. Slide, rotate, or reflect figures to create patterns or demonstrate congruence.



 D. ALGEBRA: Students use symbols to represent or model quantities, patterns and relationships and use symbolic manipulation to evaluate expressions and solve equations. Students solve problems using symbols, tables, graphs and verbal rules choosing the most effective representation and converting among representations.
 SYMBOLS AND EXPRESSIONS




 D.1. Students create and evaluate simple expressions in the context of numbers and operations as described in Standard 2.1: Number* for this grade level. *Standard 2.1 referenced here in the language of Me. Dept. of Ed. Reg. 131 refers to Standard Aof this document.
 a. Create and evaluate expressions with no more than three variables.
 Patterns, Functions, and Algebra Goal 2: Determine whether number sentences are true or false; solve open number sentences and explain solutions; use a letter variable to write an open sentence to model a number story; use a panbalance model to solve linear equations in one unknown. Lessons: 2.4, 2.8, 4.6, 4.7, 7.4, 7.5, 7.9, 7.11, 9.8, 10.1, 10.2, 10.3 Goal 4: Describe and apply properties of arithmetic. Lessons: 1.1, 1.2, 1.7, 4.3, 12.1   classroom tests
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 EQUATIONS AND INEQUALITIES

 

 D.2. Students find the unknown in simple equations in the context of numbers and operations as described in Standard 2.1: Number* for this grade level such as: 3 9  k = 39  40 78 + b = 57 + 79 30 x A = 276 (3 + 4) x 6 = 6 x [ ] 3 x 15 = 3 x (10 + [ ] ) *Standard 2.1 referenced here in the language of Me. Dept. of Ed. Reg. 131 refers to Standard Aof this document.

 Patterns, Functions, and Algebra Goal 2: Determine whether number sentences are true or false; solve open number sentences and explain solutions; use a letter variable to write an open sentence to model a number story; use a panbalance model to solve linear equations in one unknown. Lessons: 2.4, 2.8, 4.6, 4.7, 7.4, 7.5, 7.9, 7.11, 9.8, 10.1, 10.2, 10.3 Goal 4: Describe and apply properties of arithmetic. Lessons: 1.1, 1.2, 1.7, 4.3, 12.1   classroom tests
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 FUNCTIONS AND RELATIONS




 D.3. Students use tables, rules, diagrams, and graphs to represent and analyze the relationship between quantities.





