Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as [...]

Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a [...]

Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations [...]

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two [...]

Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length [...]

Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons comparisons are valid only when two decimals [...]

Use place value understanding to round multi-digit whole numbers to any place. (Grade 4 expectations in this domain are limited [...]

Fluently add and subtract multi-digit whole numbers using the standard algorithm. (Grade 4 expectations in this domain are limited to [...]

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using [...]

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the [...]

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, [...]

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, [...]

Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of [...]

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve [...]

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle [...]

An angle is measured with reference to a circle with its center at the common endpoint of the rays, by [...]

An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is [...]

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of [...]

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can [...]

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, [...]

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to [...]

Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Grade 4 expectations in this domain [...]

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is [...]

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for [...]

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which [...]

Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple [...]

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not [...]

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the [...]

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on [...]

Model how information is broken down into smaller pieces, transmitted as packets through multiple devices over networks and the Internet, [...]

Discuss real-world cybersecurity problems and how personal information can be protected.

Organize and present collected data visually to highlight relationships and support a claim.

Use data to highlight or propose cause-and-effect relationships, predict outcomes, or communicate an idea.

Compare and refine multiple algorithms for the same task and determine which is the most appropriate.

Create programs that use variables to store and modify data.

Create programs that include sequences, events, loops, and conditionals.

Decompose (break down) problems into smaller, manageable subproblems to facilitate the program development process.

Modify, remix, or incorporate portions of an existing program into one's own work, to develop something new or add more [...]

Use an iterative process to plan the development of a program by including others' perspectives and considering user preferences.

Observe intellectual property rights and give appropriate attribution when creating or remixing programs.

Test and debug (identify and fix errors) a program or algorithm to ensure it runs as intended.

Take on varying roles, with teacher guidance, when collaborating with peers during the design, implementation, and review stages of program [...]

Describe choices made during program development using code comments, presentations, and demonstrations.

Discuss computing technologies that have changed the world, and express how those technologies influence, and are influenced by, cultural practices.

Brainstorm ways to improve the accessibility and usability of technology products for the diverse needs and wants of users.

Seek diverse perspectives for the purpose of improving computational artifacts.