Washington Academic Standards

Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.

Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

Understand that the two digits of a two-digit number represent amounts of tens and ones.

Flexibly, efficiently, and accurately add within 100, including adding a two-digit number and a onedigit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

Flexibly, efficiently, and accurately solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and/or equations with a symbol for the unknown number to represent the problem.

Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Demonstrate that equal shares of identical wholes need not have the same shape.

Flexibly, efficiently, and accurately use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.

Flexibly, efficiently, and accurately solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Flexibly apply and extend previous understandings of multiplication to multiply a fraction by a whole number using visual models in the context of word problems.

Flexibly, efficiently, and accurately add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Flexibly and efficiently solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Assess the reasonableness of answers using mental and estimation strategies.

Flexibly, efficiently, and accurately write and evaluate numerical expressions involving whole-number exponents.

Flexibly, efficiently, and accurately solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Flexibly, efficiently, and accurately apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram showing the distance between two numbers is the absolute value of their difference, understand the concept of opposite quantities combining to zero (additive inverse), representing operations on number lines, and interpreting real-world scenarios in context.

Flexibly, efficiently, and accurately apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers including the distributive property and properties of operations. Understand integers can be divided as long as the divisor isn't zero, resulting in rational numbers and convert rational numbers into decimals using long division, recognizing that the decimal form either ends in 0s or repeats eventually, and interpreting realworld contexts.

Recognize and represent proportional relationships between quantities, including using equivalent ratios in a table, graphing on the coordinate plane to see of the graph is a straight line through origin, identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions, write equations for proportional relationships, and analyze graphs to understand what the data points tell them about the real-world situation, focusing on points like (0, 0) which represents no change and (1, r) where r is the unit rate.

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation, understanding the probability of a compound event is a fraction of the outcomes of the sample space. Design and use a simulation to generate frequencies for compound events.

Flexibly, efficiently, and accurately solve linear equations in one variable with one solution, infinitely many solutions, or no solutions and solve linear equations with rational number coefficients where solution paths may require using the distributive property and combining like terms.

Flexibly, efficiently, and accurately explain a proof of the Pythagorean Theorem and its converse.