Mathematics

Intellectual and Dispositional Standards

1. Demonstrate an understanding of what it means to do mathematics by regularly

explaining the meaning of problem situations and looking for multiple ways to solve

them, as well as displaying a sense of wonder about mathematics as a way of

knowing/understanding the world more clearly.

2. Demonstrate an ability to represent a mathematical problem situation quantitatively using quantitative reasoning, creating a logical representation with appropriate units and

accurate meanings of the quantities involved in the problem.

3. Demonstrate an ability to experiment with the use of multiple methods of representing

real-life problem situations (numbers, mathematical language, equations, charts, and

figures) in order to explain the connections between the situation and the representation.

4. Determine what the most appropriate tools are to help solve or make sense of a range of different problem situations by comparing/contrasting the strengths/weaknesses of different approaches to problem solving.

5. Develop and refine mathematical arguments (making connections between models and equations represented in these arguments) through frequent peer and student-to-teacher communication of mathematical reasoning.

6. Use developmentally appropriate, clear, and precise language when discussing

mathematical reasoning, specifying units of measure, the meaning of symbols being

discussed, and the various parts of graphical representations of that reasoning.

7. Use knowledge of mathematical rules and operations to identify patterns and the beauty, harmony, proportion, and radiance present in patterns.

8. Use knowledge of repetitive actions in counting and computation to make generalizations about mathematical models and algorithms.

9. Show interest in the pursuit of understanding mathematics for its own sake and as a way to solve problems addressing social justice issues in local and global communities.

10. Exhibit joy while solving difficult mathematical problems and operations, while also

recognizing the importance of inquiry and learning through mathematical processes.\

Content, Knowledge, and Skills Standards

Operations and Algebraic Thinking

1. Use the four operations (addition, subtraction, multiplication, and division) with whole

numbers to solve problems.

2. Represent verbal statements with mathematical equations using appropriate operations and be able to conceptualize and discuss mathematical equations verbally.

3. Solve multi-step word problems posed with whole numbers and having whole-number

answers using the four operations, including problems in which remainders must be

interpreted.

4. Represent word problems using equations with a letter standing for the unknown

quantity.

5. Assess the reasonableness of answers to word problems using mental computation and estimation strategies including rounding.

6. Gain familiarity with factors and multiples in the range 1-100.

7. Generate a number or shape pattern that follows a given rule.

Numbers and Operations

8. Understand place value for multi-digit numbers; for example, that a digit to the left

represents ten times more than a digit to its right.

9. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

10. Use place value understanding to round multi-digit whole numbers to any place.

11. Use place value understanding and properties of operations to perform multi-digit

arithmetic, including addition, subtraction, multiplication, and division.

12. Know multiplication facts and related division facts through 12 × 12.

13. Illustrate and explain multiplication and division calculations by using equations,

rectangular arrays, and/or area models.

14. Extend understanding of fraction equivalence and ordering by using visual fraction

models and common denominator/numerator strategies.

15. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers (e.g., decomposing fractions into a sum of fractions with similar denominators, adding/subtracting mixed numbers with like denominators).

16. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

17. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number; solve word problems involving multiplication of a fraction by a whole

number.

18. Understand decimal notation equivalence for fractions, and compare decimal fractions.

Measurement and Data

19. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit within a particular system of units.

20. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, money, and perimeter and area, including problems involving simple fractions or decimals, and problems that require expressing

measurements given in a larger unit in terms of a smaller unit.

21. Make a line plot to display a data set of measurements in fractions of a unit and solve problems involving addition and subtraction of fractions by using information presented in line plots.

22. Understand angle concepts and measure angles, including how angles are formed, how they are measured, and how they are compared.

Geometry

23. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular

and parallel lines and be able to identify these in two-dimensional figures.

24. Classify two-dimensional figures based on the presence or absence of parallel or

perpendicular lines, or the presence or absence of angles of a specified size; recognize

right triangles as a category and identify right triangles.

25. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts, identify line symmetric figures, and draw lines of symmetry.