Math
District 90 believes that all students are capable of achieving high levels of mathematics and is committed to ensuring continuous development, growth, and achievement for all learners. Mathematics instruction in District 90 provides the opportunity for all students to have an engaging and challenging curriculum which focuses on developing students’ deep understanding of mathematical concepts.
K-5 Math
In grades K-5, the core resource for math is Savvas Investigations in Number, Data and Space.
In kindergarten, students focus on counting, number and operations, measurement, geometry, and data. Throughout the year, students:
- Fluently counting to—-and counting out sets of —-20
- Rote count by 1s and 10s and 100; when counting by 1st, start from a number other than 1
- Represent and solve addition and subtraction story problems within 10
- Fluently add and subtract within 5
- Identify and describe familiar 2-D and 3-D shapes
- Make 2-D and 3-D shapes
- Understand length and width of objects
- Sort a set of objects by a given attribute and order the groups based on the number in each
More information from Investigations: Kindergarten Scope and Sequence and Math in Kindergarten
In first grade, students focus on number and operations, geometry, measurement, fractions and data. Throughout the year, students:
- Understand ten ones as one ten, and teen numbers as one ten and some more ones
- Understand that the multiples of 10 through 90 refer to 1-9 tens and 0 ones
- Understand that you can count on/back to add/subtract
- Add and subtract with numbers within 20 demonstrating fluency for addition and subtraction within 10
- Solve add to and take from problems with unknown change
- Solve comparison story problems with a bigger or smaller unknown
- Match a 2-D representation of a 3-D shape to the outline of one of its faces
- Demonstrate accurate measuring techniques when measuring an object or distance with multiple units
- Tell and write time to the half hour
- Understand that halves, or fourths apply to wholes divided into two (four) equal parts
- Partition circles and rectangles into two and four equal parts
More information from Investigations: Grade 1 Scope and Sequence andMath in Grade 1
In second grade, students focus on number and operations, geometry, measurement, fractions and data. Throughout the year, students:
- Understand that 100 can be seen as 1 hundred, as 10 tens, and as 100 ones
- Understand that the multiples of 100 are made up of a number of hundreds
- Understand that 3-digit numbers represent amounts of hundreds, tens, and ones
- Read, write, count and compare numbers up to 1000
- Represent and solve addition and subtraction problems with 3-digit numbers
- Solve two-step problems about money; recognize and identify coins and their value
- Fluently subtract 2 digit numbers
- Fluently add and subtract within 100
- Solve problems that involve equal groups
- Make a rectangle out of same size equal squares and specify the number of rows and the number of squares in each row
- Recognize that (halves, thirds, fourths) of the same whole can look different
- Partition 2-D shapes into halves, thirds, and fourths and name the regions
- Recognize that, when measuring the same length, larger units yield smaller counts
- Estimate and measure lengths in inches, feet, centimeters and meters
- Organize a set of data into up to four categories
- Create, describe, and interpret a variety of data representations, including picture graphs and bar graphs
More information from Investigations: Grade 2 Scope and Sequence and Math in Grade 2
In third grade, students focus on number and operations, rational numbers,measurement, data, and geometry Throughout the year, students:
- Understand the meaning of multiplication
- Understand and work with an array/area model of multiplication
- Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division
- Solving multiplication and division problems, including multi-step problems and problems with multiple solutions
- Use knowledge of place value to read, write, sequence and round numbers to 1000
- Solve addition and subtraction problems using strategies
- Fluently add and subtract within 1000 using strategies and algorithms based on place value
- Understand and find area and perimeter
- Solve problems involving measurement of liquid volume and mass
- Describe and classify 2-D figures
- Describe and summarize a set of data, describing concentrations of data and what those concentrations mean in terms of the situation the data represent.
- Measure to the nearest fourth inch and represent measurement data to the nearest fourth inch on a line plot
More information from Investigations: Grade 3 Scope and Sequence and Math in Grade 3
In fourth grade, students focus on number and operations, rational numbers, analyzing patterns and rules, measurement, data, and geometry Throughout the year, students:
- Visualizing multiplication
- Reasoning about numbers and their multiples and factors
- Solving multiplicative comparison problems
- Extending knowledge of the number system to 1,000,000
- Fluently add and subtract multi-digit whole numbers
- Understanding the meaning of fractions and decimals
- Comparing the values of fractions and decimals
- Computing with rational numbers
- Modeling situations with mathematics
- Generating and analyzing patterns
- Describing and measuring angles
- Understanding and determining area
- Representing, describing, summarizing, and comparing data
- Identifying mirror symmetry in shapes
More information from Investigations: Grade 4 Scope and Sequence and Math in Grade 4
In fifth grade, students focus on number and operations, rational numbers, analyzing patterns and rules, measurement, data, and geometry Throughout the year, students:
- Visualizing multiplication
- Reasoning about numbers and their multiples and factors
- Solving multiplicative comparison problems
- Extending knowledge of the number system to 1,000,000
- Fluently add and subtract multi-digit whole numbers
- Understanding the meaning of fractions and decimals
- Comparing the values of fractions and decimals
- Computing with rational numbers
- Modeling situations with mathematics
- Generating and analyzing patterns
- Describing and measuring angles
- Understanding and determining area
- Representing, describing, summarizing, and comparing data
- Identifying mirror symmetry in shapes
More information from Investigations: Grade 5 Scope and Sequence and Math in Grade 5
Math in Grades 6-8
District 90 believes that all students are capable of achieving high levels of mathematics and is committed to ensuring continuous development, growth, and achievement for all learners. Mathematics instruction in District 90 provides the opportunity for all students to have an engaging and challenging curriculum which focuses on developing students’ deep understanding of mathematical concepts. The backbone of this instruction comes from Amplify Desmos.
6th Grade Math:
This course begins with a student of area and surface area. Students will calculate the area of polygons by decomposing, rearranging, enclosing and composing shapes. They also represent polyhedra with nets and calculate surface area. Next, students are introduced to the concept of ratios. They represent ratios using double number lines, tables, and tape diagrams and use ratio reasoning to solve problems. Students then apply ratio reasoning to unit rates and recognize that equivalent ratios have the same unit rates. They use a variety of strategies and representations of percentages to determine missing percentages, parts and wholes. Students will extend what they learned about dividing whole numbers to divide fractions by fractions. They answer questions like “How many groups?” of “How many in one group?” They use a variety of strategies, such as making tape diagrams, creating common denominators, and rewriting equivalent multiplication problems using the reciprocal. Next, students develop and use a variety of strategies for representing, adding, and subtracting, multiplying and dividing multi-digit decimals. Students write and solve equations of the form `x+p=q` and `px=q` in and out of context. As part of this unit, students explore what equivalent expressions with variables are and use the distributive property to write equivalent expressions. Students are introduced to different ways of representing relationships: using tables, equations, and graphs. Finally, students describe locations on the number line and situations in context using positive and negative numbers. They also compare and order positive and negative numbers and their absolute values. Students extend what they learned about the coordinate plane in Grade 5 to include points with positive and negative coordinates. Students solve real-world and mathematical problems by graphing points, and draw polygons given coordinates for the vertices.
7th Grade Math:
The course begins with a study of scaled drawings. Students will describe how scaling affects lengths, angles, and areas in scaled copies. Next, students will continue to build on their work in 6th grade to use tables to recognize proportional relationships and calculate the constant of proportionality. Students will write and use equations to analyze proportional relationships. Students will take a break from proportional relationships to focus on circles and then return to proportional relationships and percentages. Students will represent proportional relationships using tape diagrams, tables, double number lines and equations to solve problems involving proportional relationships and percent change. Students will transition to operations with positive and negative numbers. In this unit students will perform all four operations with positive and negative numbers using a variety of strategies. Next, students are introduced to equations and expressions including finding solutions for linear equations in one variable and basic equations involving exponents. Student understanding of ratios and rates combined with a basic understanding of equations leads students to study proportional relationships with special emphasis on circumference and area of a circle as an example and nonexample of proportional relationships. This is followed by looking at percentage concepts and applications such as sales tax, tipping, and markup. They learn about rational numbers less than zero expanding their understanding of arithmetic to negative numbers. A brief study of data and statistics concludes the new concepts in the course.
8th Grade Math:
Students begin the course with transformational geometry. They study rigid transformations and congruence, then scale drawings, dilations, and similarity (this provides background for understanding the slope of a line in the coordinate plane). Next, they expand their ability to work with linear equations in one and two variables and deepen their understanding of equivalent expressions. They then build on their understanding of proportional relationships from the previous course to study linear relationships. They express linear relationships using equations, tables, and graphs, and make connections across these representations. Building on their understanding of a solution to an equation in one or two variables, they understand what is meant by a solution to a system of equations in two variables. They apply their understanding of linear relationships to contexts involving data with variability. They learn that linear relationships are an example of a special kind of relationship called a function. They extend the definition of exponents to include all integers, and in the process codify the properties of exponents. They learn about orders of magnitude and scientific notation in order to represent and compute with very large and very small quantities. They encounter irrational numbers for the first time and informally extend the rational number system to the real number system, motivated by their work with the Pythagorean Theorem.
STATE STANDARDS FOR MATH
The Common Core State Standards for mathematics are organized by content standards, which address topics, content, and skills. The Standards for Mathematical Practice address ways of thinking about mathematics, persevering in problem solving, use of appropriate tools, and mathematical reasoning. The balance of both content and conceptual understanding is essential in the development of proficiency for all students.
COMMON CORE STATE STANDARDS
The Common Core State Standards are organized by grade level and identify the content students will be learning that particular year. When the standards were constructed, an emphasis was placed on coherence and rigor to ensure that student learning builds from one grade to the next.
STANDARDS FOR MATHEMATICAL PRACTICE
The Standards for Mathematical Practice describe “processes and proficiencies” that students should acquire as their math learning progresses. These standards require students to articulate their reasoning, provide proof for solutions, persist in problem solving, and make connections across mathematical ideas.
ACCELERATED MATHEMATICS IN THE MIDDLE SCHOOL
Roosevelt Middle School offers four different mathematics pathways for students in order to meet the diverse needs of all our learners. The accelerated program, also known as ATP, provides math instruction at a faster pace of instruction. Eligibility is determined through the following means:
- Silicon Valley Math Initiative Tasks: students complete five problem-solving tasks, one for each of the five mathematical “big ideas” to assess grade-level proficiency with concepts, use of multiple strategies, creative problem solving, and ability to explain math reasoning. University of Illinois at Chicago’s Metro Chicago Math Initiative (MCMI) scores the completed tasks and proficiency levels are determined by norms established annually by the Silicon Valley Math Initiative.
- Measures of Academic Progress (MAP): eligible students must attain 90% on the math section of the assessment to be considered for ATP-1 or 95% for ATP-2.
- Teacher Assessment: teachers complete a checklist related to how student engage in mathematics (ability to persevere in problem solving, use of multiple strategies, ability to explain math thinking).
PLACEMENT PROCESS FOR ACCELERATED MATH IN MIDDLE SCHOOL
MIDDLE SCHOOL MATH COURSE DESCRIPTIONS
RESOURCES FOR PARENTS TO SUPPORT THEIR CHILD’S MATH LEARNING
The Council of Great City Schools has developed content and grade-specific parent roadmaps that provide detailed information for parents about the expectations of the Common Core in Mathematics. These roadmaps include examples of grade-level focus in the content area and can be accessed via this link https://www.cgcs.org/page/244.
The National PTA has partnered with the National Education Association to develop guides to help families support their children.