High Quality Instructional Materials (HQIM)
High-quality curricular (instructional) materials exhibit a coherent sequence of lessons that target learning of grade-appropriate skills and knowledge through instructional strategies that are well supported by research and other characteristics such as engaging content and inclusive design. High-quality instructional materials have an increased positive impact on student learning when paired with curriculum-specific, ongoing professional learning. Gateway Regional School District has selected new high quality instructional materials in many subject areas with the incredible support of our dedicated teachers, and continues to review instructional materials for quality. Please see our state reporting on high quality instructional materials for specific resources being used in our schools!
Family Friendly Curriculum Frameworks Guides
Pre-K
The Commonwealth of Massachusetts sets expectations, or standards, for what every student will know and be able to do in school. This guide is designed to help you understand those standards and partner with teachers to support your child’s learning during pre-kindergarten. If you have questions about this information or your child needs extra help, please talk to your child’s teacher.
Kindergarten
The Commonwealth of Massachusetts sets expectations, or standards, for what every student will know and be able to do in school. This guide is designed to help you understand those standards and partner with teachers to support your child’s learning during kindergarten. If you have questions about this information or your child needs extra help, please talk to your child’s teacher.
Grade 1
The Commonwealth of Massachusetts sets expectations, or standards, for what every student will know and be able to do in school. This guide is designed to help you understand those standards and partner with teachers to support your child’s learning during first grade. If you have questions about this information or your child needs extra help, please talk to your child’s teacher.
Grade 2
The Commonwealth of Massachusetts sets expectations, or standards, for what every student will know and be able to do in school. This guide is designed to help you understand those standards and partner with teachers to support your child’s learning during second grade. If you have questions about this information or your child needs extra help, please talk to your child’s teacher.
Grade 3
The Commonwealth of Massachusetts sets expectations, or standards, for what every student will know and be able to do in school. This guide is designed to help you understand those standards and partner with teachers to support your child’s learning during third grade. If you have questions about this information or your child needs extra help, please talk to your child’s teacher.
Grade 4
The Commonwealth of Massachusetts sets expectations, or standards, for what every student will know and be able to do in school. This guide is designed to help you understand those standards and partner with teachers to support your child’s learning during fourth grade. If you have questions about this information or your child needs extra help, please talk to your child’s teacher.
Grade 5
The Commonwealth of Massachusetts sets expectations, or standards, for what every student will know and be able to do in school. This guide is designed to help you understand those standards and partner with teachers to support your child’s learning during fifth grade. If you have questions about this information or your child needs extra help, please talk to your child’s teacher.
Grade 6
The Commonwealth of Massachusetts sets expectations, or standards, for what every student will know and be able to do in school. This guide is designed to help you understand those standards and partner with teachers to support your child’s learning during sixth grade. If you have questions about this information or your child needs extra help, please talk to your child’s teacher.
Grade 7
The Commonwealth of Massachusetts sets expectations, or standards, for what every student will know and be able to do in school. This guide is designed to help you understand those standards and partner with teachers to support your child’s learning during seventh grade. If you have questions about this information or your child needs extra help, please talk to your child’s teacher.
Grade 8
The Commonwealth of Massachusetts sets expectations, or standards, for what every student will know and be able to do in school. This guide is designed to help you understand those standards and partner with teachers to support your child’s learning during eighth grade. If you have questions about this information or your child needs extra help, please talk to your child’s teacher.
High School
The Commonwealth of Massachusetts sets expectations, or standards, for what every student will know and be able to do in school. This guide is designed to help you understand those standards and partner with teachers to support your child’s learning during high school. If you have questions about this information or your child needs extra help, please talk to your child’s teacher.
Curriculum Maps
Kindergarten
MATHEMATICS
The big ideas in kindergarten include: representing and comparing whole numbers, initially with sets of objects; understanding and applying addition and subtraction; and describing shapes and space. More time in kindergarten is devoted to numbers than to other topics.
The mathematical work for kindergarten is partitioned into 8 units:
- Math in Our World
- Numbers 1–10
- Flat Shapes All Around Us
- Understanding Addition and Subtraction
- Composing and Decomposing Numbers to 10
- Numbers 0–20
- Solid Shapes All Around Us
- Putting it All Together
In these materials, particularly in units that focus on addition and subtraction, teachers will find terms that refer to problem types, such as Add To, Take From, Put Together or Take Apart, Compare, Result Unknown, and so on. These problem types are based on common addition and subtraction situations, as outlined in Table 1 of the Mathematics Glossary section of the Common Core State Standards.
Grade 1
MATHEMATICS
The big ideas in grade 1 include: developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; developing understanding of whole-number relationships and place value, including grouping in tens and ones; developing understanding of linear measurement and measuring lengths as iterating length units; and reasoning about attributes of, and composing and decomposing geometric shapes.
The mathematical work for grade 1 is partitioned into 8 units:
- Adding, Subtracting, and Working with Data
- Addition and Subtraction Story Problems
- Adding and Subtracting within 20
- Numbers to 99
- Adding within 100
- Length Measurements within 120 units
- Geometry and Time
- Putting it All Together
In these materials, particularly in units that focus on addition and subtraction, teachers will find terms that refer to problem types, such as Add To, Take From, Put Together or Take Apart, Compare, Result Unknown, and so on. These problem types are based on common addition and subtraction situations, as outlined in Table 1 of the Mathematics Glossary section of the Common Core State Standards.
Grade 2
MATHEMATICS
The big ideas in grade 2 include: extending understanding of the base-ten number system, building fluency with addition and subtraction, using standard units of measure, and describing and analyzing shapes.
The mathematical work for grade 2 is partitioned into 9 units:
- Adding, Subtracting, and Working with Data
- Adding and Subtracting within 100
- Measuring Length
- Addition and Subtraction on the Number Line
- Numbers to 1,000
- Geometry, Time, and Money
- Adding and Subtracting within 1,000
- Equal Groups
- Putting it All Together
In these materials, particularly in units that focus on addition and subtraction, teachers will find terms that refer to problem types, such as Add To, Take From, Put Together or Take Apart, Compare, Result Unknown, and so on. These problem types are based on common addition and subtraction situations, as outlined in Table 1 of the Mathematics Glossary section of the Common Core State Standards.
Grade 3
MATHEMATICS
The big ideas in grade 3 include: developing understanding of multiplication and division and strategies for multiplication and division within 100; developing understanding of fractions, especially unit fractions (fractions with numerator 1); developing understanding of the structure of rectangular arrays and of area; and describing and analyzing two-dimensional shapes.
The mathematical work for grade 3 is partitioned into 8 units:
Grade 4
MATHEMATICS
The big ideas in grade 4 include: developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.
The mathematical work for grade 4 is partitioned into 9 units:
- Factors and Multiples
- Fraction Equivalence and Comparison
- Extending Operations to Fractions
- From Hundredths to Hundred-thousands
- Multiplicative Comparison and Measurement
- Multiplying and Dividing Multi-digit Numbers
- Angles and Angle Measurement
- Properties of Two-Dimensional Shapes
- Putting it All Together
Grade 5
MATHEMATICS
The big ideas in grade 5 include: developing fluency with addition and subtraction of fractions, developing understanding of multiplication and division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions), extending division to two-digit divisors, developing understanding of operations with decimals to hundredths, developing fluency with whole number and decimal operations, and developing understanding of volume.
The mathematical work for grade 5 is broken into 8 units:
- Finding Volume
- Fractions as Quotients and Fraction Multiplication
- Multiplying and Dividing Fractions
- Wrapping Up Multiplication and Division with Multi-digit Numbers
- Place Value Patterns and Decimal Operations
- More Decimal and Fraction Operations
- Shapes on the Coordinate Plane
- Putting it All Together
Grade 6
MATHEMATICS
Grade 6 begins with a unit on reasoning about area and understanding and applying concepts of surface area. It is common to begin the year by reviewing the arithmetic learned in previous grades, but starting instead with a mathematical idea that students haven’t seen before sets up opportunities for students to surprise the teacher and themselves with the connections they make. Instead of front-loading review and practice from prior grades, these materials incorporate opportunities to practice elementary arithmetic concepts and skills through warm-ups, in the context of instructional tasks, and in practice problems as they are reinforcing the concepts they are learning in the unit.
One of the design principles of these materials is that students should encounter plenty of examples of a mathematical or statistical idea in various contexts before that idea is named and studied as an object in its own right. For example, in the first unit, students will generalize arithmetic by writing simple expressions before they study algebraic expressions as a class of objects in the sixth unit. Sometimes this principle is put into play several units before a concept is developed more fully, and sometimes in the first several lessons of a unit, where students have a chance to explore ideas informally and concretely, building toward a more formal and abstract understanding later in the unit.
The 6th Grade units are:
6.3 Unit Rates and Percentages
6.7 Rational Numbers
Grade 7
Grade 8
High School
Curriculum Maps
Kindergarten
MATH
The big ideas in kindergarten include: representing and comparing whole numbers, initially with sets of objects; understanding and applying addition and subtraction; and describing shapes and space. More time in kindergarten is devoted to numbers than to other topics.
The mathematical work for kindergarten is partitioned into 8 units:
- Math in Our World
- Numbers 1–10
- Flat Shapes All Around Us
- Understanding Addition and Subtraction
- Composing and Decomposing Numbers to 10
- Numbers 0–20
- Solid Shapes All Around Us
- Putting it All Together
In these materials, particularly in units that focus on addition and subtraction, teachers will find terms that refer to problem types, such as Add To, Take From, Put Together or Take Apart, Compare, Result Unknown, and so on. These problem types are based on common addition and subtraction situations, as outlined in Table 1 of the Mathematics Glossary section of the Common Core State Standards.
Grade 1
MATH
The big ideas in grade 1 include: developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; developing understanding of whole-number relationships and place value, including grouping in tens and ones; developing understanding of linear measurement and measuring lengths as iterating length units; and reasoning about attributes of, and composing and decomposing geometric shapes.
The mathematical work for grade 1 is partitioned into 8 units:
- Adding, Subtracting, and Working with Data
- Addition and Subtraction Story Problems
- Adding and Subtracting within 20
- Numbers to 99
- Adding within 100
- Length Measurements within 120 units
- Geometry and Time
- Putting it All Together
In these materials, particularly in units that focus on addition and subtraction, teachers will find terms that refer to problem types, such as Add To, Take From, Put Together or Take Apart, Compare, Result Unknown, and so on. These problem types are based on common addition and subtraction situations, as outlined in Table 1 of the Mathematics Glossary section of the Common Core State Standards.
Grade 2
MATH
The big ideas in grade 2 include: extending understanding of the base-ten number system, building fluency with addition and subtraction, using standard units of measure, and describing and analyzing shapes.
The mathematical work for grade 2 is partitioned into 9 units:
- Adding, Subtracting, and Working with Data
- Adding and Subtracting within 100
- Measuring Length
- Addition and Subtraction on the Number Line
- Numbers to 1,000
- Geometry, Time, and Money
- Adding and Subtracting within 1,000
- Equal Groups
- Putting it All Together
In these materials, particularly in units that focus on addition and subtraction, teachers will find terms that refer to problem types, such as Add To, Take From, Put Together or Take Apart, Compare, Result Unknown, and so on. These problem types are based on common addition and subtraction situations, as outlined in Table 1 of the Mathematics Glossary section of the Common Core State Standards.
Grade 3
MATH
The big ideas in grade 3 include: developing understanding of multiplication and division and strategies for multiplication and division within 100; developing understanding of fractions, especially unit fractions (fractions with numerator 1); developing understanding of the structure of rectangular arrays and of area; and describing and analyzing two-dimensional shapes.
The mathematical work for grade 3 is partitioned into 8 units:
Grade 4
MATH
The big ideas in grade 4 include: developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.
The mathematical work for grade 4 is partitioned into 9 units:
- Factors and Multiples
- Fraction Equivalence and Comparison
- Extending Operations to Fractions
- From Hundredths to Hundred-thousands
- Multiplicative Comparison and Measurement
- Multiplying and Dividing Multi-digit Numbers
- Angles and Angle Measurement
- Properties of Two-Dimensional Shapes
- Putting it All Together
Grade 5
MATH
The big ideas in grade 5 include: developing fluency with addition and subtraction of fractions, developing understanding of multiplication and division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions), extending division to two-digit divisors, developing understanding of operations with decimals to hundredths, developing fluency with whole number and decimal operations, and developing understanding of volume.
The mathematical work for grade 5 is broken into 8 units:
- Finding Volume
- Fractions as Quotients and Fraction Multiplication
- Multiplying and Dividing Fractions
- Wrapping Up Multiplication and Division with Multi-digit Numbers
- Place Value Patterns and Decimal Operations
- More Decimal and Fraction Operations
- Shapes on the Coordinate Plane
- Putting it All Together
Grade 6
MATH
Grade 6 begins with a unit on reasoning about area and understanding and applying concepts of surface area. It is common to begin the year by reviewing the arithmetic learned in previous grades, but starting instead with a mathematical idea that students haven’t seen before sets up opportunities for students to surprise the teacher and themselves with the connections they make. Instead of front-loading review and practice from prior grades, these materials incorporate opportunities to practice elementary arithmetic concepts and skills through warm-ups, in the context of instructional tasks, and in practice problems as they are reinforcing the concepts they are learning in the unit.
One of the design principles of these materials is that students should encounter plenty of examples of a mathematical or statistical idea in various contexts before that idea is named and studied as an object in its own right. For example, in the first unit, students will generalize arithmetic by writing simple expressions before they study algebraic expressions as a class of objects in the sixth unit. Sometimes this principle is put into play several units before a concept is developed more fully, and sometimes in the first several lessons of a unit, where students have a chance to explore ideas informally and concretely, building toward a more formal and abstract understanding later in the unit.
The 6th Grade units are:
6.3 Unit Rates and Percentages
6.7 Rational Numbers
Grade 7
MATH
As in grade 6, students start grade 7 by studying scale drawings, an engaging geometric topic that supports the subsequent work on proportional relationships in the second and fourth units. It also makes use of grade 6 arithmetic understanding and skill, without arithmetic becoming the major focus of attention at this point. Geometry and proportional relationships are also interwoven in the third unit on circles, where the important proportional relationship between a circle's circumference and its diameter is studied. By the time students reach the fifth unit on operations with rational numbers, both positive and negative, students have had time to brush up on and solidify their understanding and skill in grade 6 arithmetic. The work on operations on rational numbers, with its emphasis on the role of the properties of operations in determining the rules for operating with negative numbers, is a natural lead-in to the work on expressions and equations in the next unit. Students then put their arithmetical and algebraic skills to work in the last two units, on angles, triangles, and prisms, and on probability and sampling.
7.2 Introducing Proportional Relationships
7.4 Proportional Relationships and Percentages
7.5 Rational Number Arithmetic
7.6 Expressions, Equations and Inequalities
7.7 Angles, Triangles and Prisms
Grade 8
MATH
Students begin grade 8 with transformational geometry. They study rigid transformations and congruence, then dilations and similarity (this provides background for understanding the slope of a line in the coordinate plane). Next, they build on their understanding of proportional relationships from grade 7 to study linear relationships. They express linear relationships using equations, tables, and graphs, and make connections across these representations. They expand their ability to work with linear equations in one and two variables. 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 learn that linear relationships are an example of a special kind of relationship called a function. They apply their understanding of linear relationships and functions to contexts involving data with variability. 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. They wrap up the year with a study of the volumes of cones, cylinders, and spheres.
The mathematical work for grade 8 is partitioned into 9 units:
8.1 Rigid Transformations and Congruence
8.2 Dilations, Similarity, and Introducing Slope
8.4 Linear Equations and Linear Systems
8.7 Exponents and Scientific Notation
8.8 Pythagoran Theorem and Irrational Numbers