# Family and Community Resources for Imagine Learning Illustrative Mathematics

## New Core K–12 Math Instructional Resources

In 2023, Imagine Learning Illustrative Mathematics (IM) became the primary math resource provider for the School District of Philadelphia. Learn more about Imagine Learning IM below to find family and student resources.

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• Learn number names and counting sequences.
• Count the number of objects and compare numbers.
• Understand subtraction as “taking apart” and “taking from”.
• Build understanding of number facts that add up to 5.
• Build a foundation of place value by working with numbers 11-19.

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• Represent and solve problems involving addition and subtraction.
• Understand and apply properties of operations and the relationship between addition and subtraction.
• Add and subtract within 20 and work with addition and subtraction equations.
• Extend the counting sequence and understand place value by using properties of operations to add and subtract.
• Measure lengths indirectly and by iterating length units.

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• Represent and solve problems involving addition and subtraction,
• Solidify their fluency of addition and subtraction within 20, and
• Understand place value and use it to add and subtract.
• These big three buckets of work can be taught together and a number line is one of the most powerful models to support this work.

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• Develop understanding of multiplication and division and strategies for multiplication and division within 100.
• Develop understanding of fractions, especially unit fractions (fractions with numerator 1).
• Develop understanding of the structure of rectangular arrays and of area.
• Describe and analyze two-dimensional shapes.

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• Use the four operations, addition, subtraction, multiplication and division, with whole numbers to solve problems.
• Understand place value for multi-digit whole numbers.
• Perform multi-digit arithmetic by using place value understanding and properties of operations.
• Understand fraction equivalence and ordering to build fractions with whole numbers.
• Understand decimal notation for fractions, and compare decimal fractions.

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• Understand the place value system.
• Perform operations with multi-digit whole numbers and decimals to hundredths.
• Use equivalent fractions to add, subtract, multiply and divide fractions.
• Understand and explore concepts of volume, and relate volume to multiplication and addition.

Unit 1 Area and Surface Area

Unit 2 Introducing Ratios

Unit 3 Unit Rates and Percentages

Unit 4 Dividing Fractions

Unit 5 Arithmeticin Base Ten

Unit 6 Expressions and Equations

Unit 7 Rational Numbers

Unit 8 Data Sets and Distributions

• Understand ratio concepts and ratio reasoning to solve problems.
• Divide fractions by using previous understandings of multiplication and division.
• Apply numbers to the system of rational numbers.
• Learn algebraic expressions, solve one-variable equations, and inequalities.
• Analyze quantitative relationships between dependent and independent variables.

Unit 1 Scale Drawings

Unit 2 Introducing Proportional Relationships

Unit 3 Measuring Circles

Unit 4 Proportional Relationships and Percentages

Unit 5 Rational Number Arithmetic

Unit 6 Expressions, Equations, andI nequalities

Unit 7 Angles, Triangles, and Prisms

Unit 8 Probability and Sampling

• Students will analyze proportional relationships and use them to solve real-world and mathematics problems.
• They will apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.
• Students will use properties of operations to generate equivalent expressions.
• They will solve real-life and mathematical problems using numerical and algebraic expressions.

Unit 1 Rigid Transformations and Congruence

Unit 2 Dilations, Similarity, and IntroducingSlope

Unit 3 Linear Relationships

Unit 4 Linear Equations and Linear Systems

Unit 5 Functions and Volume

Unit 6 Associations in Data

Unit 7 Exponents and Scientific Notation

Unit 8 Pythagorean Theorem and Irrational Numbers

• Students will work with radicals and integer exponents.
• They will understand the connections between proportional relationships, lines and linear equations.
• Students will analyze and solve linear equations and pairs of simultaneous linear equations.
• They will define, evaluate, and compare functions and use functions to model relationships between quantities.
• Students will understand congruence and similarity using physical models, transparencies, or geometric software.

Unit 1 One-variable Statistics

Unit 2 Linear Equations, Inequalities, and Systems

Unit 3 Two-Variable Statistics

Unit 4 Functions

Unit 5 Introductionto Exponential Functions

Unit 6 Introduction to Quadratic Functions

• Summarize and analyze data, using one-variable Statistics.
• Compare and contrast data sets by using summary statistics and their graphical representations.
• Analyze graphs as well as interpret them in the context of real-world situations.
• Simplify algebraic expressions.
• Solve one-variable equations and inequalities as well as graph the solution sets.
• Solve systems of equations and inequalities with one or two variables; using a variety of graphical and analytical strategies.
• Explore linear and exponential models individually before comparing and contrasting them.
• Use two-variable statistics to make inferences with mathematical tools such as correlation and regression.
• Explore more complex geometric situations and deepen explanations of geometric relationships, moving towards formal mathematical arguments.
• Important differences exist between this Geometry course and the historical approach taken in Geometry classes. For example, transformations are emphasized early in this course.
• Learn polynomial, rational, and radical functions.
• Work with expressions that define functions.
• Expand and improve abilities to model situations that solve equations including quadratic equations over the set of complex numbers, and that solve exponential equations using the properties of logarithms.