Number & Quantity

Counting, comparing, and operating with numbers and quantities in meaningful contexts.

K–12 objective ladder

• K D05.S1.K.01 Count objects up to 20 and say how many there are.
• 1 D05.S1.01.01 Count, read, and write whole numbers up to 120 and use them to say how many objects are in a group.
• 1 D05.S1.01.02 Add and subtract within 20 using objects, drawings, or counting strategies, and explain what the operation means.
• 2 D05.S1.02.01 Use place value of tens and ones to read, write, compare, and order two-digit numbers.
• 2 D05.S1.02.02 Add and subtract within 100 using models, drawings, or written methods, and explain the strategy used.
• 3 D05.S1.03.01 Use place value to 1,000 to read, write, round, and compare whole numbers.
• 3 D05.S1.03.02 Multiply and divide within 100 and explain the meaning of each operation using objects, drawings, and known facts.
• 4 D05.S1.04.01 Use place value to 1,000,000 to read, write, round, and compare multi-digit whole numbers.
• 4 D05.S1.04.02 Add, subtract, multiply, and divide multi-digit whole numbers, and use estimation to check that answers are reasonable.
• 5 D05.S1.05.01 Read, write, compare, and round decimals to the thousandths and connect them to fractions with denominators of 10 and 100.
• 5 D05.S1.05.02 Add, subtract, multiply, and divide fractions and decimals in real contexts such as sharing, cooking, and money.
• 6 D05.S1.06.01 Use ratios and rates to describe and compare real situations such as fair shares, recipes, and unit prices.
• 6 D05.S1.06.02 Use positive and negative numbers to represent real situations such as temperature and elevation, and locate and order them on a number line.
• 7 D05.S1.07.01 Use proportional relationships, including unit rates, scale, and percentages, to solve multi-step problems in real contexts.
• 7 D05.S1.07.02 Perform all four operations with rational numbers such as fractions, decimals, and integers, and explain each step of the reasoning.
• 8 D05.S1.08.01 Distinguish rational and irrational numbers and approximate square roots by locating them on the number line.
• 8 D05.S1.08.02 Use integer exponents and scientific notation to represent and compare very large and very small quantities, such as distances in space or the size of cells.
• 9 D05.S1.09.01 Work with real numbers, roots, and radicals in expressions and equations, explaining which properties justify each step.
• 9 D05.S1.09.02 Choose appropriate units and levels of precision when measuring and calculating, and interpret the results in context.
• 10 D05.S1.10.01 Use properties of exponents and roots to simplify expressions and solve problems involving exponential growth and decay.
• 10 D05.S1.10.02 Extend number reasoning to complex numbers and explain why new kinds of numbers arise from real problems.
• 11 D05.S1.11.01 Model and solve real problems with sequences and series, and interpret their meaning in financial or environmental contexts.
• 11 D05.S1.11.02 Use vectors and matrices to represent and manipulate quantities with both size and direction or with several dimensions.
• 12 D05.S1.12.01 Apply the ideas of limits and continuity informally to describe change, approximation, and the behavior of quantities.
• 12 D05.S1.12.02 Reason quantitatively about large systems such as populations, energy use, or carbon, using orders of magnitude and estimation, and critique the numbers used in public claims.

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