# Illinois Learning Standards

## Stage A - Math

### 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 by 2's, 5’s, and 10’s from zero. **
2. Recognize ‘how many’ in sets of objects. **
3. Demonstrate the concept of odd and even using manipulatives.
4. Develop initial understanding of place value and the base-ten number system using manipulatives. **
5. Describe numeric relationships using appropriate vocabulary.
6. Differentiate between cardinal and ordinal numbers in quantifying and ordering numbers.
7. Connect number words and numerals to the quantities they represent. **
8. Describe parts of a whole using 1/2, 1/3, and 1/4.
9. Order concrete representations of unit fractions.

#### 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 one-step addition and subtraction number sentences and word problems using concrete materials.
2. Construct number sentences to match word problems.
3. Demonstrate and describe the effects of adding and subtracting whole numbers using appropriate mathematical notation and vocabulary. **
4. Explore and apply properties of addition and subtraction.
5. Compute using fact families.

#### 6C —

##### Students who meet the standard can compute and estimate using mental mathematics, paper-and-pencil methods, calculators, and computers. (Choice of method)
1. Develop and use strategies for whole number computations with a focus on addition and subtraction. *
2. Use mental math counting strategies.
3. Describe reasonable and unreasonable sums and differences.
4. Utilize a calculator for counting patterns.

#### 6D  —

##### Students who meet the standard can solve problems using comparison of quantities, ratios, proportions, and percents.
1. Compare two or more sets, 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. Determine the attributes of an object that are measurable (e.g., length and weight are measurable; color and texture are not).
2. Compare and order objects according to measurable attributes. **
3. Measure objects using non-standard units.
4. Explore and describe chronological events (e.g., calendars, timelines, seasons).
5. Identify units of money and the value of each.
6. Count like sets of coins.

#### 7B —

##### Students who meet the standard can estimate measurements and determine acceptable levels of accuracy. (Estimation)
1. Estimate nonstandard measurements of length, weight, and capacity.

#### 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 appropriate nonstandard measurement units to measure length, weight, and capacity (e.g., number of handfuls of cubes to fill a container).

#### 8A—

##### Students who meet the standard can describe numerical relationships using variables and patterns. (Representations and algebraic manipulations)
1. Describe common and uncommon attributes (all, some, none) in a set.
2. Recognize, describe, and extend patterns such as sequences of sounds, motions, shapes, or simple numeric patterns, and translate from one representation to another (e.g., red-blue-red-blue translates to snap-clap-snap-clap). **
3. Describe given patterns using letters.
4. Analyze repeating 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 qualitative change, (e.g., student grows taller). **

#### 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 simple number sentences with variables (e.g., missing addend problems).

#### 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 real life word problems 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. Identify two- and three-dimensional shapes. **
2. Model two-dimensional geometric shapes by drawing or building. **
3. Describe and interpret relative positions in space and apply concepts of relative position (e.g., above/below). **
4. Recognize and describe shapes that have line symmetry. **
5. Identify geometric shapes and structures in the environment. **
6. Explore the effects of translations (slides), reflections (flips), and rotations (turns) with concrete objects.

#### 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 the same shape.
2. Compare and sort two- and three-dimensional objects.

#### 9C—

##### Students who meet the standard can construct convincing arguments and proofs to solve problems. (Justifications of conjectures and conclusions)
1. Recognize and explain a geometric pattern.

#### 10A—

##### Students who meet the standard can organize, describe and make predictions from existing data. (Data analysis)
1. Organize, describe, and label simple data displays such as pictographs, tallies, tables, and bar graphs.
2. Compare numerical information derived from tables and graphs.

#### 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 to answer a simple question.

#### 10C—

##### Students who meet the standard can determine, describe and apply the probabilities of events. (Probability including counting techniques)
1. Identify possible and impossible results of probability events using concrete materials.
2. Determine all possible outcomes of a given situation.

* 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.