# Course Descriptions

Making Sense of Numbers (MSN) is the foundational course with content focused on the base ten structure of our number system. Meaningful distributed instruction is the mathematical practice emphasized to support children’s development of number sense.

Big Ideas:

• Understand that each place represents 10 times that of the place to its right.
• Understand that numbers can be decomposed and composed to compute and increase flexibility with numbers.
• Understand that invented strategies use the properties of operations.

Making Sense of Operations (MSO) focuses on the four basic operations (addition, subtraction, multiplication, and division) for whole and rational numbers. Meaningful distributed instruction is implemented to build children’s development of symbolic procedures.

Big Ideas:

• Understand that the four operations are related.
• Understand that the properties of operations contribute to the efficiency of solving math computation.
• Understand that the properties of operations allow computations to be performed flexibly.
• Understand that the properties of operations are needed to justify the correctness of computational algorithms.
• Understand that there are meaningful ways to learn the basic facts.
• Understand that fraction operations connect to whole number operations.

Making Sense of Geometry (MSG) centers on two and three dimensional shapes and their properties. The implementation focus iinvolves problem-based instructional tasks and their uses in instruction differentiated for learners.

Big Ideas:

• Understand that what makes shapes alike and different can be determined by an array of geometric properties.
• Understand that shapes can be moved in a plane or in space. These changes can be described in terms of translations, reflections, and rotations.
• Understand that shapes can be described in terms of their location in a plane or in space.
• Understand that shapes can be seen from different perspectives.

Making Sense of Measurement (MSM) focuses on ways to measure one-, two-, and three-dimensional attributes, develop connections among them, and make sense of standard formulas. Classroom discourse is the implementation focus.

Big Ideas:

• Understand that objects have measurable attributes.
• Understand how to compare two objects with a common measurable attribute.
• Understand how to estimate and measure lengths indirectly and by iterating length units.
• Understand how to solve problems involving measurement, estimation, conversions of intervals of time, liquid volumes, and masses of objects.

Making Sense of Algebraic Thinking I (MSAT I) connects the generalization of the four basic operations to various expressions. The implementation focus involves problem-based instructional tasks.

Big Ideas:

• Understand the relationship between addition and subtraction, as well as multiplication and division.
• Understand the application of operations within equations and how to represent and solve equations utilizing the operations of addition, subtraction, multiplication, and division.
• Understand how to write and interpret numerical expressions.

Making Sense of Algebraic Thinking II (MSAT II) applies algebraic thinking to the description of patterns to produce functions and to the description of relationships. The implementation focus is to use and flexibly move among multiple connected representations (e.g., words, symbols, tables, graphs, etc).

Big Ideas:

• Understand the application of operations within equations and how to represent and solve equations utilizing the operations of addition, subtraction, multiplication, and division.
• Understand how to write and interpret numerical expressions.
• Understand how to reason about and solve equations with variables and inequities.
• Understand ratio concepts and use of ratio reasoning to solve problems.

Making Sense of Rational Numbers (MSRN) focuses on unit fractions, equivalent fractions, and decimal notations. The implementation focus involves problem-based instructional tasks.

Big Ideas:

• Understand how to build fractions from unit fractions.
• Understand how to use equivalent fractions as a strategy to add or subtract fractions.
• Understand how to write decimal notation for fractions and compare decimal fractions.
• Understand how to compute multi-digit numbers and find common factors and multiples.

Making Sense of Data (MSD) centers on learning the components of statistical investigations, including the collection, representation, description, and interpretation of data. The implementation focus is to use assessment for learning.

Big Ideas:

• Understand how to classify objects and count the number of objects in each category.
• Understand how to represent and interpret data.
• Understand statistical variability.
• Understand how to summarize and describe distribution.

Teaching Mathematics to Struggling Learners: Building Your Confidence is the foundational course focused on the theory of best practice for struggling learners, understanding the Iowa Multi-Tiered Support System (MTSS), and implementation of one Do the Math unit.

Teaching Struggling Learners: Addition, Subtraction, and Place Value focuses on diagnosing and addressing student difficulties and developing mathematical content knowledge for teaching in the areas of addition, subtraction, and place value.

Teaching Struggling Learners: Multiplication and Division focuses on diagnosing and addressing student difficulties and developing mathematical content knowledge for teaching in the areas of multiplication and division.

Teaching Struggling Learners: Fractions focuses on diagnosing and addressing student difficulties and developing mathematical content knowledge for teaching in the area of fractions.