Stage B - Mathematics

Descriptors

6A - Students who meet the standard can demonstrate knowledge and use of numbers and their many representations in a broad range of theoretical and practical settings. (Representations)

1. Count with understanding, including skip counting from any number by 2’s and 10’s.
2. Extend initial understanding of place value and the base-ten number system using multiple models. **
3. Describe numeric relationships using comparison notation.
4. Use cardinal and ordinal numbers appropriately.
5. Recognize and explain the concept of odd and even numbers.
6. Describe parts of a set using 1/2, 1/3, and 1/4.
7. Represent, order, label, and compare unit fractions using concrete materials.

6B - Students who meet the standard can investigate, represent and solve problems using number facts, operations, and their properties, algorithms, and relationships. (Operations and properties)

1. Solve two-step addition and subtraction number sentences and word problems.
2. Demonstrate the relationship between addition and subtraction.
3. Explore multiplication and division through equal grouping and equal sharing of objects.**
4. Connect repeated addition to multiplication.
5. Demonstrate fluency with basic addition and subtraction facts.**

6C - Students who meet the standard can compute and estimate using mental mathematics, paper-and-pencil methods, calculators, and computers. (Choice of method)

1. Explain and use mental math strategies to solve simple addition and subtraction problems.
2. Estimate sums and differences of one- or two-digit numbers.
3. Analyze situations to determine whether exact numbers or estimates are appropriate.
4. Utilize a calculator to solve addition and subtraction problems.

6D - Students who meet the standard can solve problems using comparison of quantities, ratios, proportions, and percents.

1. Compare unit fractions, using manipulatives, to solve problems.

7A - Students who meet the standard can measure and compare quantities using appropriate units, instruments, and methods. (Performance and conversion of measurements)

1. Identify the type of measure (e.g., weight, height, volume, temperature) for each measurable attribute.
2. Measure objects using standard units.
3. Order events chronologically.
4. Tell time using an analog clock.
5. Describe relationships within units of time, money, and length (e.g., 12 inches in a foot).
6. Count, compare, and order sets of unlike coins.
7. Show equivalent amounts of money.
8. Explore and explain making change using manipulatives.

7B - Students who meet the standard can estimate measurements and determine acceptable levels of accuracy. (Estimation)

1. Estimate elapsed time for a given task.
2. Estimate standard measurements of length, weight, and capacity.
3. Estimate the amount of money needed to make purchases.

7C - Students who meet the standard can select and use appropriate technology, instruments, and formulas to solve problems, interpret results, and communicate findings. (Progression from selection of appropriate tools and methods to application of measurements to solve problems)

1. Select an appropriate unit and tool for measurement. **
2. Explore and describe perimeter and area of real objects.
3. Solve problems using money and time.

8A - Students who meet the standard can describe numerical relationships using variables and patterns. (Representations and algebraic manipulations)

1. Sort, classify, and order objects by multiple properties.**
2. Create rules for multiple sortings in a single set.
3. Recognize, describe, and extend geometric and numeric patterns.
4. Create patterns concretely and numerically to match a given letter description (e.g., AAB) and make predictions.
5. Extend numeric patterns involving addition and/or subtraction (e.g., 1, 3, 5, … what are the next two terms?).
6. Change patterns by manipulation of concrete materials.
7. Describe missing units in a pattern.
8. Analyze growing patterns.

8B - Students who meet the standard can interpret and describe numerical relationships using tables, graphs, and symbols. (Connections of representations including the rate of change)

1. Describe and compare quantitative change (e.g., student grows two inches in one year). **

8C - Students who meet the standard can solve problems using systems of numbers and their properties. (Problem solving; number systems, systems of equations, inequalities, algebraic functions)

1. Solve word problems involving unknown quantities.
2. Apply the relationship of addition and subtraction families to solve for an unknown quantity.

8D - Students who meet the standard can use algebraic concepts and procedures to represent and solve problems. (Connection of 8A, 8B, and 8C to solve problems)

1. Solve problems and justify solutions using patterns.

9A - Students who meet the standard can demonstrate and apply geometric concepts involving points, lines, planes, and space. (Properties of single figures, coordinate geometry and constructions)

1. Investigate and predict the results of putting together and taking apart two- and three-dimensional shapes (e.g., put two triangles together to make a quadrilateral). **
2. Describe and interpret direction and distance in navigating space, and apply concepts of direction and distance (e.g., nearer/farther). **
3. Perform translations (slides), reflections (flips), and rotations (turns) with concrete objects.
4. Create and complete shapes that have line symmetry.

9B - Students who meet the standard can identify, describe, classify and compare relationships using points, lines, planes, and solids. (Connections between and among multiple geometric figures)

1. Identify objects that are congruent.
2. Compare and contrast attributes of two- and three-dimensional objects using appropriate vocabulary.

9C - Students who meet the standard can construct convincing arguments and proofs to solve problems. (Justifications of conjectures and conclusions)

1. Justify an extension of a pattern.

10A - Students who meet the standard can organize, describe and make predictions from existing data. (Data analysis)

1. Organize and interpret simple data displays such as pictographs, tallies, tables, and bar graphs.
2. Make predictions from simple data.

10B - Students who meet the standard can formulate questions, design data collection methods, gather and analyze data and communicate findings. (Data Collection)

1. Gather data by creating and using interview questions.

10C - Students who meet the standard can determine, describe and apply the probabilities of events. (Probability including counting techniques)

1. Identify and discuss likely, unlikely, and impossible probability events.
2. Communicate and display results of probability events in order to make predictions of future events.

* National Council of Teachers of Mathematics. Principles and Standards for School Mathematics. Reston, Va: National Council of Teachers of Mathematics, 2000.
** Adapted from: National Council of Teachers of Mathematics. Principles and Standards for School Mathematics. Reston, Va: National Council of Teachers of Mathematics, 2000.

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