Mathematics: Grades 5-6

MATHEMATICS: GRADE 5

Students will be engaged and inspired by the rigorous mathematical environment created in our collaborative and hands-on classrooms. Building on the strong foundations provided by our research-based mathematics program, students are given the ability to think critically and creatively as they explore mathematical content and practice important skills. Our classrooms strive to promote effective reasoning and immerse students in mathematical problem-solving situations with their peers. In 5th grade mathematics, the curriculum is designed to address content and skills in the following areas.

Numbers and Operations
Apply place value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals.
• We will understand and explain the value of digits in a larger number
• We will explain patterns of zeroes in an answer when multiplying by powers of 10
• We will explain patterns of decimal placement when a decimal is multiplied or divided by powers of 10
• We will use whole-number exponents to show powers of 10
• We will read, write, and compare decimals to thousandths
• We will read and write decimals to the thousandths place in various forms
• We will compare two decimals to thousandths using the >,=, and < symbols correctly
• We will use place value understanding to round decimals to any place

Extend an understanding of operations with whole numbers to perform operations including decimals.
• We will multiply multi-digit whole numbers
• We will divide four-digit numbers (dividends) by two-digit numbers (divisors)
• We will illustrate and explain a division problem using equations, arrays, and/or models
• We will add, subtract, multiply, and divide decimals to hundredths using what we have learned about place value
• We will relate the strategies used to add, subtract, multiply and divide decimals to hundredths to a written problem
• We will use the understanding of equivalency to add and subtract fractions
• We will add and subtract fractions with unlike denominators
• We will solve word problems that involve addition and subtraction of fractions
• We will use fractions and general number sense to estimate if an answer makes sense
• We will explain how a fraction represents the division of the numerator by the denominator
• We will use visual models to solve problems involving division of whole numbers where the quotient is a fraction or mixed number
• We will multiply a fraction times a fraction
• We will find the area of a rectangle with fractional sides in using various representations
• We will think about multiplication as the scaling of a number
• We will explain how to multiply a given number and make it smaller or larger
• We will generate equivalent fractions by multiplying by one
• We will solve real world problems that involve multiplication of fractions and mixed numbers
• We will use what we know about division to divide fractions by whole numbers or whole numbers by fractions
• We will divide a fraction by a whole number (non-zero) correctly

Algebraic Concepts
Interpret and evaluate numerical expressions using order of operations.
• We will use and evaluate parentheses and brackets in numerical expressions
• We will change a simple word expression into a mathematical expression
• We will explain the relationship between two number expressions without calculating the answers

Analyze patterns and relationships.
• We will generate numerical patterns using two given rules
• We will identify relationships between the numbers on the graph

Geometry
Graph points in the first quadrant on the coordinate plane and interpret these points when solving real world mathematical problems.
• We will create and label a coordinate plane
• We will explain how numbers in an ordered pair effects the direction/distance of the point
• We will create, plot, and label ordered pairs of numbers on a coordinate plane
• We will graph and interpret coordinate pairs of numbers and relate them to real world problems

Classify two-dimensional figures using an understanding of their properties.
• We will explain the hierarchy of a class of two-dimensional figures based on properties

MATHEMATICS: GRADE 6

Young mathematicians will be engaged by the rigorous mathematical environment created in our collaborative, hands-on classrooms. Building on the strong foundations provided by our research-based mathematics program, students will be given the ability to think critically and creatively as they explore mathematical content and practice important skills. Our teachers strive to promote effective reasoning and immerse students in mathematical problem-solving situations with their peers. The 6th grade curriculum is designed to address content and skills in the following areas.

Numbers and Operations
Understand ratio concepts and use ratio reasoning to solve problems.
• We will explain how a ratio is comparing two quantities
• We will explain the concept of a unit rate and how it relates to a ratio
• We will change a ratio to a unit rate
• We will make a table of equivalent fractions
• We will fill in the missing values from ta table of equivalent ratios
• We will plot pairs of numbers (from ratios) on a coordinate plane
• We will solve problems involving rates like unit pricing and constant speed
• We will solve problems involving percent’s when a part is given and the percent

Extend previous understandings of multiplication and division to divide fractions by fractions.
• We will know that a fraction can represent a quotient and we will find that quotient using models and equations

Identify and choose appropriate processes to compute fluently with multi-digit numbers.
• We will add, subtract, multiply, and divide multi-digit decimal numbers to solve problems

Develop and/or apply number theory concepts to find common factors and multiples.
• We will find the greatest common factor (GCF) of two whole numbers
• We will find the least common multiple (LCM) of two whole numbers less than or equal to 12
• We will express the sum of two whole numbers using the distributive property
Apply and extend previous understandings of numbers to the system of rational numbers.
• We will explain how positive and negative numbers relate to real world examples and the meaning of zero in each case
• We will explain how each rational number has an opposite value
• We will locate a rational number on the number line
• We will plot an ordered pair of rational numbers on the coordinate plane
• We will explain the meaning of ordering rational numbers in a real world situation
• We will explain how the absolute value of a number relates to its distance from zero
• We will explain how the absolute value of a number is used in real world situations to show magnitude
• We will use the coordinate plane to solve real world problems
• We will find the vertical or horizontal distance between two points on the coordinate plane

Algebraic Concepts
Apply and extend previous understandings of arithmetic to algebraic expressions.
• We will simplify expressions with exponents
• We will translate a written mathematical expression into a symbolic expression
• We will identify sum, term, product, factor, quotient, and coefficient
• We will view a “chunk” of the expression as a single “thing”
• We will substitute numbers for variables in a number sentence and simplify
• We will solve real world problems with a formula
• We will apply the order of operations to simplify a number sentence with no parentheses
• We will apply the properties of operations to make equivalent expressions

Understand the process of solving a one-variable equation or inequality and apply to real-world and mathematical problems.
• We will understand that solving an equation means to find the values that make it true
• We will determine whether a value makes an equation/inequality true or false
• We will write an expression with variables to represent a real world problem
• We will understand that a variable can represent an unknown number or set of numbers
• We will solve real-world problems involving non-negative rational numbers
• We will write an inequality to represent a condition in a real-world situation
• We will identify when an inequality has an infinitely many solutions
• We will graph solution sets of an inequality on a number line
Represent and analyze quantitative relationships between dependent and independent variables.
• We will explain the difference between independent and dependent variables
• We will write an expression from a real-world problem that relates independent and dependent quantities
• We will explain the relationship between dependent and independent variables using graphs and tables

Geometry
Apply appropriate tools to solve real world and mathematical problems involving area, surface area, and volume.
• We will find the area of any triangle
• We will find the area of other polygons by dividing them into triangles and/or rectangles
• We will calculate the volume of the right rectangular prism
• We will draw polygons in the coordinate plane given coordinates for the vertices
• We will find the vertical or horizontal distance of a side of the polygon
• We will find the surface areas of 3D figures

Measurement, Data and Probability
Demonstrate an understanding of statistical variability by displaying, analyzing, and summarizing distributions
• We will create dot, histogram, and box plots
• We will calculate measures of center and measures of variability
• We will explain the patterns and any striking deviations being described by the measures of center and measures of variability
• We will explain why a particular measure of center or measure of variability may be used based on the context of the data gathered