# Mathematics

Fluency with addition and subtraction of fractions, and developing undertstanding of mutliplication and division of fractions.

Extending division to 2-digit divisors, intergrading decimal fractions into the place value system and developing understanding of operations with decimals to the hundreths, and developing fluency with whole number and decimal operations.

Developing understanding of volume.

Curriculum Map - Year at a Glance

Trimester I

I. Add and Subtract Fractions with Unlike Denominators

Big Idea: Real world problems can be solved by combining or separating groups.

Essential Questions:

◊ How are fractions related to decimals?

◊ How are common denominators used to compare fractions?

◊ What are some ways that fractions can be combined or separated?

◊ How are fractions used to represent numbers in the real world situations?

Domains: Operations & Algebraic Thinking / Numbers and Operations - Fractions

Big Idea: Real world problems can be solved by combining or separating groups.

Essential Questions:

◊ How can addition and subtraction of decimals be represented by objects, pitures, words, and numbers?

◊ What are some ways that decimals can be combined and separated?

◊ How are decimals used to represent numbers in the real world?

Domains: Number & Operations in Base Ten

Trimester II

III. Multiply Whole Numbers & Decimals

Big Idea: Real world problems can be solved by combining or separating groups.

Essential Questions:

◊ What patterns do you notice in the placement of the decimal when we multiply by powers of ten?

◊ How is repeated addition related to multiplication?

◊ How can you apply the conversion of measurement units to real-life problems?

Domains: Number & Operations in Base Ten

IV. Divide Whole Numbers & Decimals

Big Idea: Real world problems can be solved by separating or combining groups.

Essential Questions:

◊ What patterns do you notice when dividing by powers of ten?

◊ How does using the algorithm help you to divide more efficiently?

◊ Compare and explain how the size of factors is related to the size of the product?

◊ How can we apply the conversion of measurement units to real-life problems?

Domains: Number & Operations in Base Ten / Number and Operations - Fractions

VII. Multiply Fractions

Big Idea: Parts build up to wholes.

Essential Questions:

◊ What is the whole?

◊ What is the relationship between the whole and the fraction?

◊ How can you apply the multiplication of fractions to real-life problems?

Domains: Number & Operations in Base Ten

I. Fluency with Whole Numbers and Deciamls - Place Value, Multiplication, and Expressions.

Big Idea: Different Values can be represented in many ways.

Essential Questions:

◊ What patterns can we identify in the base ten system?

◊ How does the position of a number determine its value?

◊ How can we simplify the problem solving process?

◊ What kinds of models can be used to represent decimals?

Domains: Operation & Algebraic Thinking / Number & Operations in Base Ten

VII. Multiply Fractions

Big Idea: Parts build up to wholes.

Essential Questions:

◊ What is the whole?

◊ What is the relationship between the whole and the fraction?

◊ How can you apply the multiplication of fractions to real-life problems?

Domains: Number & Operations in Base Ten

VIII. Divide Fractions

Big Idea: Wholes break down to parts.

Essential Questions:

◊ What is the unit fraction?

◊ What is the relationship of the fraction to the whole?

◊ How can you apply the division of fractions to real-life problems?

Domains: Number & Operations in Base Ten

IX Algebra: Patterns and Graphing

Big Idea: The relationship between values can be represented visually.

Essential Questions:

◊ How is the coordinate system used?

◊ How can you identify relationships between pairs of numbers in a table?

◊ How are lists, tables, charts, and diagrams used to illustrate mathematical relationships?

Domains: Operations & Algebraic Thinking / Measurement & Data / Geometry

X Convert Units of Measurement

Big Idea: Real-World problems can be solved by conversion in units of measurement.

Essential Questions:

◊ What is the relationship in the Customary Units of measurement?

◊ What is the relationship in the Metric System?

◊ How can you apply the conversion of measurement units to real-life problems?

Domains: Measurement & Data

XI (a) Volume

Big Idea: Objects can be measured and compared by their attributes.

Essential Questions:

◊ What is volume?

◊ How are area and volume alike and different?

◊ How do we measure volume?

◊ Why is volume represented in cubic units?

◊ Does volume change when you change the measurement material? WHy or why not?

◊ How can you find the volume of cubes and recangular prisms?

◊ Why is it important to know how to measure volume?

Domains: Measurement & Data / Geometry

XI (b) Geometry

Big Idea: Objects can be described, classified, and analyzed by their characteristics.

Essential Questions:

◊ How do parallel, perpendicualr, and congruent lines relate and help identify teo-dimensional shapes?

◊ How do characteristics help identify geometric figures?

◊ How can you classify two-dimensional shapes in a hierarchy based on their properties?

Domains: Measurement & Data / Geometry