## Common Core State Standards for Mathematics

Grade(s) K-12 resources related to the following standard:
Standards for Mathematical Practice
Look for and make use of structure.

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This article talks about the origins of our number system and the important roles zero plays in it. The author informs the reader that the early number systems of the Egyptians, the Babylonians, the Romans and Greeks were developed for counting but not for calculations. Not until we had a base ten number system with place value and a symbol for zero did our number system become useful.
Reference Materials, Article
Grade Level: 3, 4, 5, 6+
This 440-page report explores how students in pre-K through grade 8 learn mathematics, with a focus on number and operations, and recommends how teaching, curricula, and teacher education should change to improve mathematics learning. (A 39-page summary, Helping Children Learn Mathematics, is catalogued separately.) The authors identify five interdependent components of mathematical proficiency and describe how students develop this proficiency. The report presents a portrait of mathematics learning: research findings on what children know about numbers before they arrive in pre-K and the implications for instruction; details on the processes by which students acquire mathematical proficiency; what is known from research about teaching for mathematics proficiency and developing proficiency in teaching. Visitors to this website may read the full text online, download a copy (pdf), or purchase a hard copy.
Reference Materials
Grade Level: Pre-K, K, 1, 2, 3, 4, 5, 6+
This virtual manipulative allows a teacher or student to represent a linear equation and solve it through the use of a balance beam. Unit blocks (representing 1s) and x-boxes (representing the unknown), are placed on the pans of a balance beam. Once the beam balances to represent the given linear equation, the learner can choose to perform any arithmetic operation to both sides of the equation keeping the beam balanced. The goal, of course, is to get a single X-box on one side, with however many unit blocks needed for balance thus giving the value of x. There is also the option of creating your own equations to solve.
Activity, Interactive Media
This interactive Java learning tool, which was constructed using the cross-platform open educational resource GeoGebra, allows a teacher to demonstrate and explore evaluating algebraic expressions with students. Choose from four algebraic expressions and use sliders to select the value of the variable (-10 to 10) and any parameters. Show or hide the algebraic expression, the expression with substitution, the notation shown for multiplication or division, and the result. Values range from -10 to 10 and can be integers or intervals of one tenth.
Demonstration, Interactive Media
This interactive Java learning tool allows a teacher to demonstrate and explore with students number line models for two simple variable expressions for multiplication. The first expression is a variable with an understood coefficient of one and the second is the multiplication of a variable by a coefficient. Sliders are used to select the value of the variable (-10 to 10) and the coefficient (0 to 10). Check boxes show or hide the algebraic expression, the expression with substitution, the notation shown for multiplication, the result, and a model for the multiplication, shown as jumps along a number line.
Demonstration, Interactive Media
This unit consists of four lessons in which students explore several meanings and representations of multiplication, including number lines, sets, arrays, and balance beams. They also learn about the commutative property of multiplication, the results of multiplying by 1 and by 0, and the inverse property of multiplication. Students write story problems and create pictographs. The unit includes activity sheets, assessment ideas, links to related applets, reflective questions for students and teachers, extensions and a bibliography of children's literature with a multiplication focus.
Activity, Instructional Strategy, Lesson Plans, Unit of Instruction
In this 14-min video British teacher Rosalind Caren demonstrates group activities designed to develop number sense, fluency with addition and subtraction fact families, and reasoning skills. Caren exhibits effective questioning techniques and routines. Headteacher/math coordinator Kate Frood describes the guiding principles and expectations of teaching at the school. Following a class observation Frood provides constructive feedback to Caren and her teaching assistants.
Instructional Strategy, Lesson Plans, Video