Number Properties
 Kindergarten

#### Core Ideas

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
• Count with understanding and recognize “how many” in a set of objects.
• Develop a sense of whole numbers and represent and use them in flexible ways.
• Develop understanding of the relative magnitude and position of whole numbers.
• Use multiple models to develop initial understandings of the base-ten number system.
• Connect number words and numerals to the quantities they represent, using various physical models and representations.

#### Core Ideas

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
• Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
• Develop understanding of the relative magnitude of whole numbers and the concepts of sequences, quantity, and the relative positions of numbers.
• Understand conservation of quantity and number.
• Use multiple models to illustrate understandings of the base-ten number system and place value concepts.
• Understand that fractions are equal partitions.

#### Core Ideas

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
• Understand whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
• Understand the relative magnitude of whole numbers and the concepts of sequences, quantity, and the relative position of numbers.
• Demonstrate an understanding of the base-ten number system and place value concepts.
• Represent commonly used fractions such as 1/2, 1/3, and 1/4 in a variety of ways.

Apple Farm Field Trip

• See Related Classroom Video Visit: Word Problem Clues
Tracy Lewis leads a re-engagement lesson on the language of word problems, helping students to use word clues to identify mathematical operations. Students explore errors and strategies as they look together at student work. In addition to the lesson, the multimedia documentation of Tracy Lewis's teaching includes a pre-teaching planning conversation with Anthony Rogers, Leslie Thornley, and Camille Paris, and a follow-up faculty debrief with observing teachers. VIDEO >>

#### Core Ideas

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
• Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
• Develop understanding of the relative magnitude of whole numbers and the concepts of sequence, quantity, and the relative positions of numbers.
• Understand the place-value structure of the base-ten number system including being able to represent and compare whole numbers and decimals (in the context of dollars and cents).

House Numbers

#### Core Ideas

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
• Develop an understanding of fractions as a part of a whole unit, as part of a collection, and as a location on a number line.
• Use models, benchmarks, and equivalent forms to judge the size of friendly fractions.
• Recognize and generate equivalent forms of commonly used fractions.

Sum Bugs

#### Core Ideas

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
• Use models, benchmarks, and equivalent forms to judge the size of fractions.
• Recognize and generate equivalent forms of commonly used fractions and decimals.
• Understand the place-value structure of the base-ten number system including being able to represent and compare rational numbers.
• Describe classes of numbers according to characteristics such as the nature of their factors.

Fruity Fractions

Breakfast Time

#### Core Ideas

• Understand number systems, the meanings of operations, and ways of representing numbers, relationships, and number systems.
• Understand fractions, decimals, and percents as parts of whole units and as parts of a collection.
• Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.
• Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line.
• Understand the meaning and effects of operations with fractions and decimals.
• Use factors, multiples, prime factorization, and relatively prime numbers to solve problems.
• Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators, and paper-and-pencil, depending on the situation, and apply selected methods.
• Develop and analyze algorithms for operations on fractions and decimals, and develop fluency in their use.
• Understand and use proportional reasoning to represent quantitative relationships.
• Understand and use the associative and commutative properties of addition to simplify computations with fractions, decimals, and whole numbers.

Percent Cards

#### Core Ideas

• Understand number systems, the meanings of operations, and ways of representing numbers, relationships, and number systems.
• Develop, analyze, and explain methods for solving problems involving proportional reasoning, such as scaling and finding equivalent ratios.
• Develop meaning of integers and represent and compare quantities with them.
• Understand the meaning and effects of operations with rational numbers.
• Understand and use the inverse relationships of a series of operations to simplify computations and solve problems.
• Develop and analyze algorithms for computing with rational numbers.
• Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with rational numbers.
• Develop and use strategies to estimate the results of rational number computations, and judge the reasonableness of results.
• Work flexibly with fractions, decimals, and percents to solve problems.

Sale!

#### Core Ideas

• Understand number systems, the meanings of operations, and ways of representing numbers, relationships, and number systems.
• Develop meaning for percents greater than 100 and less than 1.
• Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation.
• Understand and use the inverse relationships of squaring and finding square roots to simplify computations and solve problems.
• Demonstrate how and when to use the operations of exponents and roots.
• Compare and contrast the properties of rational and irrational numbers.