Components

K-4 Benchmark

Number Sense

• Demonstrate understanding of whole and fractional numbers, and place value in whole numbers using objects, pictures, or symbols.

• Identify, compare, and order whole numbers and simple fractions.

• Demonstrate an understanding of the properties of the whole numbers system.

• Show understanding of whole number operations (+, -, x, ¸ ) using blocks, sticks, beans, pictures, symbols, etc.

• Add, subtract, multiply and divide whole numbers.

• Use mental arithmetic, pencil and paper, or calculator as appropriate to the task involving whole numbers.

• Identify situations involving whole numbers in which estimation is useful.

• Use estimation to predict computation results and to determine the reasonableness of answers, for example, estimating a grocery bill.

Measurement

• Understand concepts of perimeter, area, and volume.

• Use directly measurable attributes such as length, perimeter, area, volume/capacity, angle, weight/mass, time, money, and temperature to describe and compare objects.

• Understand that measurement is approximate.

• Know when to estimate and use estimation to predict and determine when measurements are reasonable, or to obtain approximations e.g. estimating the length of the playground by pacing it off.

• Understand the benefits of using standard units of measurement for measuring length, area, and volume.

• Understand appropriate units of measure for time, money, length, area, volume/capacity, weight/mass, and temperature.

• Select and use appropriate tools for measuring time, money, length, area, volume, mass, and temperature.

Geometric Sense

• Use attributes of geometric shapes and properties of parallel and perpendicular to identify, name, compare, and sort geometric shapes and figures.

• Recognize geometric shapes in the surrounding environment, for example, identify rectangles within windows.

• Understand concepts of symmetry, congruence, and similarity.

• Draw and build simple shapes and figures using appropriate tools, such as a straightedge, ruler, protractor, or nets.

• Locate and describe the location of objects on a number line, map, or a coordinate grid in the first quadrant.

• Understand and draw simple geometric transformations using translations (slides), reflections (flips), or rotations (turns).

Probability and Statistics

• Understand the difference between certain and uncertain events.

• Know how to list all possible outcomes of simple experiments.

• Understand and use experiments to investigate the probabilities of uncertain events.

• Collect data in an organized way.

• Organize and display data in numerical and graphical forms such as tables, charts, pictographs, and bar graphs.

• Understand measures of central tendency such as mean, median, and mode in describing data.

• Identify how data can be used to support a point of view.

• Predict outcomes of simple activities and compare predictions to experimental results.

• Understand and make inferences based on experimental results using coins, number cubes, spinners, etc.

Algebraic Sense

• Recognize, extend, and create patterns of numbers, shapes, or objects such as beans, toothpicks, pattern blocks, cubes, colored tiles.

• Write a rule for a pattern based on a single arithmetic operation between terms, such as a function machine.

• Understand equality and inequality and use =, >, and < in number sentences.

• Identify and use appropriate symbols and notations in reading and writing open sentences, for example, 3X = 18.

• Evaluate simple expressions using blocks, sticks, beans, pictures, etc.

• Solve simple equations using blocks, sticks, beans, pictures, etc.

Components

K-4 Benchmark

Investigate situations

• Recognize and extend patterns in everyday situations.

• Apply and adapt a variety of appropriate strategies (e.g. use manipulatives, draw pictures, work backwards, etc.).

• Organize, interpret, and compare relevant information using bar graphs, tables, pictographs, and Venn diagrams.

Formulate questions and define the problem

• Ask questions that extend problems.

• Clarify the problem and identify the question being asked.

• Distinguish between relevant and irrelevant information.

Construct solutions

• Use models, patterns, words, pictures, or numbers to organize information and solve problems (e.g. Which blocks will fit on this shelf? Show all the rectangular regions you can make using 24 tiles).

• Solve single- and/or multi-step problems.

• Solve problems with multiple, viable solutions.

Components

K-4 Benchmark

Analyze information

• Interpret information from familiar situations (e.g. explain why shapes are sorted in a certain way or why a number may or may not fit a pattern).

• Generalize relationships or situations (e.g. answer questions such as “will that always be true?”).

Predict results

• Make and test conjectures based on collected data (e.g. if, then statements).

Draw conclusions and verify results

• Use models, patterns, words, pictures, or numbers to explain/justify methods used to solve problems.

• Check for reasonableness of answers when solving problems.

• Evaluate results (e.g. “Jim says two given figures have the same area, is he correct? Why or why not?”).

Components

K-4 Benchmark

Gather information

• Create a plan for gathering relevant information (e.g. creating surveys and/or questionnaires).

• Formulate questions designed to access and extract relevant information.

• Use available technology to retrieve mathematical information from a variety of sources.

Organize and interpret information

• Transfer data from surveys, tables, or other sources to appropriate graphical displays using appropriate labels and titles.

Represent and share information

• Express mathematical ideas using mathematical language, models, charts, tables, graphs, and symbols.

• Explain or describe mathematical information for the purpose of informing or persuading.

Components

K-4 Benchmark

Relate concepts and procedures within mathematics

• Represent information in multiple ways.

• Describe how two given models are equivalent (e.g. match an array to the correct equation).

Relate mathematical concepts and procedures to other disciplines

• Make calculations based on information interpreted from a graph or chart.

• Use previously learned information in new contexts.

• Understand the contributions to mathematics by different cultures, etc.

Related mathematical concepts and procedures to real life situations

• Recognize mathematics in everyday situations.

• Identify how mathematics is used in career settings.