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# Math

## Curriculum

### Kindergarten

• Counting within 100
• Compare quantities to 20
• Instantly recognize small quantities
• One-to-one correspondence and cardinality
• Represent, model, and solve addition and subtraction problems within 10
• Fluently add and subtract within 5
• Compose and decompose teen numbers
• Compare and order objects according to measureable attributes
• Sort and classify objects
• Identify, compose, and compare basic shapes

• Numbers 0 - 120
• Fluently add and subtract within 10
• Solve a variety of addition and subtraction problems within 20
• Use place value and materials to add within 100
• Identify and combine coins
• Organize, represent, and interpret data
• Measure of lengths using non-standard units
• Time to the nearest hour/half hour
• Describe, compose, and decompose shapes

• Place value to 1000
• Mentally add and subtract within 20
• Fluently add and subtract within 100
• Use models to add and subtract within 1000
• Money problems
• Time to 5 minutes
• Addition and subtraction fluency to 20
• Attributes of shapes
• Partitioning circles and rectangles; equal shares and fractions
• Measure and estimate length
• Rectangular arrays
• Create and interpret simple graphs

• Understand fractions as numbers
• Create equivalences and compare fractions
• Compare shapes use them to represent fractions
• Fluently add and subtract within 1,000
• Solve two- step word problems involving the four operations
• Multiplication facts
• Represent and solve multiplication and division problems
• Scaled picture and bar graphs
• Measure lengths to the half and quarter inch
• Area and perimeter
• Tell time and solve time interval problems
• Volume and mass

• Generalize place value understanding
• Addition and subtraction of multi-digit numbers
• Extend multiplication and division
• Number patterns
• Factors, multiples, and square, prime, and composite numbers
• Represent, order and compare fraction
• Factors and Multiples
• Create line plots to display data
• Attributes of geometric figures including angle measurement
• Add and subtract fractions with like denominators

• Generalize place value concepts to decimal numbers
• Multiply and divide multi-digit whole numbers and decimals to hundredths.
• Multiply fractions
• Begin fraction and whole number division
• Patterns, functions, and algebraic structures
• Perimeter, area, and volume
• Flexible problem solving of multi-digit whole numbers and decimals
• Line plots and fractional amounts
• Geometric attributes and coordinate graphing
• Measurement conversions

## Assessment

#### Universal Screeners

All students in Grades K-5 take a math screener in the Fall to assess student math skills and guide teachers in grouping students for instruction and helping struggling students. A winter and spring screener may also be given in grades K-4.

#### BVSD End of Year Assessments

BVSD gives a district created common assessment at the end of Grade 2 and a transition test at the end of Grade 5.

#### CMAS

Students in Grades 3,4,5 take the Math State Test.

## Learning Materials

Math Expressions has been used in Elementary BVSD classrooms since the 2013 - 2014 school year. It was selected for being a rigorous, well articulated, research based program that aligns closely with the Colorado Academic Standards for Mathematics.

Math Expressions- Models, Methods, and Icons provides for you an overview of expectations, computational techniques as well as some of the instructional methods of Math Expressions.

## Parent Resources

### Think Central

Think Central is a powerful and extensive website for parents and students using Math Expressions, the adopted curricular materials for BVSD elementary schools. In this site you will find information about the program, get access to student texts, find out about strategies, terminology, and the research and philosophy behind the program.

• Think Central Overview for Parents (PDF, PPT)
• Video on how to find Homework and Remembering pages.
• Video Overview of Basic Functionality
• Student Welcome Letters (English, Español)
• Education Place: Education place is essentially a completely new site within Think Central. Here you will find other games, lots of information, and explanatory videos. Use this Education Place Guide to help you navigate those resources.

### MegaMath

MegaMath is a series of games and activities that accompany Math Expressions. Ask your teacher which activities are appropriate for the current unit of study.

You can also link directly to the activity associated with the current lesson by opening the Student Activity Book on Think Central, navigating to the correct lesson, and then following the link, via the link button, to Mega Math.

MegaMath - Spanish

## Curriculum

6th Grade MathIn Grade 6, math focuses on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.

7th grade mathematics focuses on 4 areas, (1) understanding and applying proportional relationships; (2) operations with rational numbers including variable expressions and linear equations; (3) solving problems involving scale drawings, informal geometric constructions, and area of 2-dimensional figures, surface area and volume of 3-dimensional shapes; (4) drawing inferences about populations based on samples.

8th Grade Mathematics, focuses on three critical areas: (1) formulating and reasoning about expressions and equations including solving linear equations and system of equations; (2) understanding the concept of a function and using functions to describe quantitative relationships; (3) analyzing two-and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.

Advanced CoursesML Algebra 1- Algebra 1 is an introduction to abstract reasoning and algebraic symbolism. Students will solve equations and systems of equations, and they will use functions to represent patterns and make predictions. The focus is on linear, exponential, and quadratic functions in problem-solving sitations. Students will engage daily with the Standards for Mathematical Practice. Students will also employ algebraic methods to summarize data and to compare data sets. Learn more

ML Advanced Algebra 1- Advanced Algebra 1 is an in-depth study of algebraic symbolism, systems of equations, graphing, problem-solving, and probability and statistics. The students will build upon their previous knowledge to further understand the characteristics and representations of various functions, and relations including: linear, exponential, and quadratic equations, inequalities, complex numbers, and rational algebraic expressions. As an advanced course, this course goes beyond the curriculum expectations of a standard course offering by increasing the depth and complexity. Students are engaged in dynamic, high‐level learning via the Standards for Mathematical Practice. The pace of an advanced course may be faster than that of the Algebra 1 course. Learn more

ML Geometry 1- Geometry presents a thorough study of the structure of the postulational system and development of formal synthetic proof. It considers the topics of congruence, parallelism, perpendicularity, properties of polygons, similarity, and the relationships of circles, spheres, lines, and planes with respect to space as well as the plane. Basic principles of probability will be introduced. The maintenance of algebraic skills will be emphasized. Learn more

ML Advanced Geometry 1- Advanced Geometry presents a thorough study of the structure of the postulate system and development of formal two-column proof. It considers the topics of congruence, parallelism, perpendicularity, properties of polygons, similarity, and the relationships of circles, spheres, lines, and planes with respect to space as well as the plane. Basic principles of probability will be introduced. Use of algebraic skills is expected. As an advanced course, this course goes beyond the curriculum expectations of a standard course offering by increasing the depth and complexity. Students are engaged in dynamic, high‐level learning via the Standards for Mathematical Practice. The pace of an advanced course may be faster than that of the M41 Geometry course. Learn more

## Assessment

Students in grades 6, 7, and 8 take the CMAS math test.

Students in grades 6 and 7 take a BVSD End of Course assessment.

ALL students preparing to enroll in Algebra 1 the following year take an Algebra Readiness Test.

All Algebra 1/Advanced Algebra 1 students take an end of year assessment.

## Parent Resources

The Connected Math for Families website is a great place to start. There are also great overview documents of each unit of study.

## Curriculum

BVSD provides many course options and pathways for high school math, including academic support, advanced, AP, and IB options.

See here for all the high school math course options.

Math options may vary by school. Check your school's course catalog to see what is being offered.

## Assessment

All students enrolled in Algebra 1/Advanced Algebra 1 take an End-of-Year Summative Assessment.

All students enrolled in Geometry/Advanced/Pre-IB Geometry take an End-of-Year Summative Assessment.

All students in grades 9-10 take the PSAT and all students in grade 11 take the SAT.