#### Grades K-5

*Math In Focus*

*Singapore Math Comes to the United States*

Since 1995 Singapore has scored at the top on the Trends in International Math and Science Study (TIMSS). Math in Focus is the U.S. Edition of Singapore’s most widely used program.

**Behind the Math in Focus instructional success story**

**A focused and coherent syllabus**.*Math in Focus*introduces fewer topics in each grade, but teaches them to greater depth. Topics are taught to mastery, so they build from year to year across grade levels without repetition.**A visual and balanced approach**.*Math in Focus*is highly visual, following a concrete-to-pictorial-to-abstract progression.**A focus on number and operations**.*Math in Focus*is sequenced in a way that ensures students develop and maintain strong number sense. Students spend the majority of the first half of the year studying number. This provides the foundation necessary to move on to more complex and abstract thinking.**An emphasis on problem solving using model-drawing**.*Math in Focus*utilizes model-drawing strategies that help students solve both routine and nonroutine problems.**A recognition of the importance of attitudes and metacognition**. The Singapore Ministry of Education’s mathematics framework emphasizes the importance of attitude and the ability to self-monitor while problem solving to achieve success in math.*Math in Focus*provides students with the tools they need to break down complex concepts and problems, which in turn develops positive attitudes.

#### Grades 6-8

*Connected Mathematics Project (CMP)*

With funding from the National Science Foundation (NSF) in 1991-1996, and in 2000-2006, the Connected Mathematics Project (CMP) developed a complete mathematics curriculum for middle school teachers and students. CMP helps students and teachers develop understanding of important mathematical concepts, skills, procedures, and ways of thinking and reasoning, in number, geometry, measurement, algebra, probability and statistics. CMP is based on research, and was field-tested in diverse sites across the country with approximately 45,000 students and 390 teachers. Each unit, in both 1991-1996 and 2000-2006 development periods, went through at least 3 cycles of field testing. A growing body of research and evaluation reports (*2006 Evaluation Booklet**, **New Studies**, **CMP Literature Review 2010**) indicates that CMP outperforms non-CMP curricula on tests of problem-solving ability, equals or outperforms non-CMP curricula on skills tests, and promotes long term retention.*

#### Guiding Principles for Development

The authors were guided by the following principles in the development of the Connected Mathematics materials. These statements reflect both research and policy stances in mathematics education about what works to support students’ learning of important mathematics.

- The “big” or key mathematical ideas around which the curriculum is built are identified.
- The underlying concepts, skills, or procedures supporting the development of a key idea are identified and included in an appropriate development sequence.
- An effective curriculum has coherence-it builds and connects from investigation to investigation, unit-to-unit, and grade-to-grade.
- Classroom instruction focuses on inquiry and investigation of mathematical ideas embedded in rich problem situations.
- Mathematical tasks for students in class and in homework are the primary vehicle for student engagement with the mathematical concepts to be learned. The key mathematical goals are elaborated, exemplified, and connected through the problems in an investigation.
- Ideas are explored through these tasks in the depth necessary to allow students to make sense of them. Superficial treatment of an idea produces shallow and short-lived understanding and does not support making connections among ideas.
- The curriculum helps students grow in their ability to reason effectively with information represented in graphic, numeric, symbolic, and verbal forms and to move flexibly among these representations.
- The curriculum reflects the information- processing capabilities of calculators and computers and the fundamental changes such tools are making in the way people learn mathematics and apply their knowledge of problem-solving tasks.

*Connected Mathematics* is different from many more familiar curricula in that it is problem centered. The following section elaborates what we mean by this and what the value added is for students of such a curriculum.

#### Brief Description of Units

## 6th Grade## Prime Time## Factors and Multiplesnumber theory, including factors, multiples, primes, composites, prime factorization ## Bits and Pieces I## Understanding Rational Numbersmove among fractions, decimals, and percents; compare and order rational numbers; equivalence ## Shapes and Designs## Two-Dimensional Geometryregular and non-regular polygons, special properties of triangles and quadrilaterals, angle measure, angle sums, tiling, the triangle inequality ## Bits and Pieces II## Understanding Fraction Operationsunderstanding and skill with addition, subtraction, multiplication, and division of fractions ## Covering and Surrounding## Two-Dimensional Measurementarea and perimeter relationships, including minima and maxima; area and perimeter of polygons and circles, including formulas ## Bits and Pieces III## Computing With Decimals and Percentsunderstanding and skill with addition, subtraction, multiplication, and division of decimals, solving percent problems ## How Likely Is It?## Probabilityreason about uncertainty, calculate experimental and theoretical probabilities, equally-likely and non-equally-likely outcomes ## Data About Us## Statisticsformulate questions; gather, organize, represent, and analyze data; interpret results from data; measures of center and range |
## 7th Grade## Variables and Patterns## Introducing Algebravariables; representations of relationships, including tables, graphs, words, and symbols ## Stretching and Shrinking## Similaritysimilar figures; scale factors; side length ratios; basic similarity transformations and their algebraic rules ## Comparing and Scaling## Ratio, Proportion, and Percentrates and ratios; making comparisons; proportional reasoning; solving proportions ## Accentuate the Negative## Positive and Negative Numbersunderstanding and modeling positive and negative integers and rational numbers; operations; order of operations; distributive property; four-quadrant graphing ## Moving Straight Ahead## Linear Relationshipsrecognize and represent linear relationships in tables, graphs, words, and symbols; solve linear equations; slope ## Filling and Wrapping## Three-Dimensional Measurementspatial visualization, volume and surface area of various solids, volume and surface area relationship ## What Do You Expect?## Probability and Expected Valueexpected value, probabilities of two-stage outcomes ## Data Distributions## Describing Variability and Comparing Groupsmeasures of center, variability in data, comparing distributions of equal and unequal sizes |
## 8th Grade## Thinking With Mathematical Models## Linear and Inverse Variationintroduction to functions and modeling; finding the equation of a line; inverse functions; inequalities ## Looking for Pythagoras## The Pythagorean Theoremsquare roots; the Pythagorean Theorem; connections amongcoordinates, slope, distance, and area; distances in the plane ## Growing, Growing, Growing## Exponential Relationshipsrecognize and represent exponential growth and decay in tables, graphs, words, and symbols; rules of exponents; scientific notation ## Frogs, Fleas and Painted Cubes## Quadratic Relationshipsrecognize and represent quadratic functions in tables, graphs, words and symbols; factor simple quadratic expressions ## Kaleidoscopes, Hubcaps and Mirrors## Symmetry and Transformationssymmetries of designs, symmetry transformations, congruence, congruence rules for triangles ## Say It With Symbols## Making Sense of Symbolsequivalent expressions, substitute and combine expressions, solve quadratic equations, the quadratic formula ## Shapes of Algebra## Linear Systems and Inequalitiescoordinate geometry, solve inequalities, standard form of linear equations, solve systems of linear equations and linear equalities. ## Samples and Populations## Data and Statisticsuse samples to reason about populations and make predictions, compare samples and sample distributions, relationships among attributes in data sets |