MTH 227 - Teaching Fractions and Decimals

Was previously MA 227

1. Explain and justify rational number concepts, including fractions, decimals, integers, and proportional reasoning, with attention to representations, models, and operations.
2. Communicate mathematical strategies and reasoning for rational number problems using accurate and precise language, models, multiple representations, and mathematical discourse.
3. Analyze PK–8 student thinking related to rational numbers and proportional reasoning using student work, discourse, and formative assessment evidence.
4. Apply current PK–8 state and national mathematics recommendations to the design and instruction of fractions, decimals, and  integers, and their operations, as well as proportional reasoning.
5. Use research-based pedagogical practices to support students’ mathematical communication, reasoning, and conceptual understanding of rational number ideas in PK–8 learners.
6. Plan, facilitate, and reflect on standards-aligned instruction on fractions, decimals, integers, and/or proportional reasoning that responds to and advances student thinking and incorporates formative assessment.

A. Core Teaching Practices

1. Lead whole-class and small-group mathematical discussions

2. Explain and model mathematical content, practices, and strategies

3. Build respectful and inclusive relationships with students

B. Elicit, Interpret, and Respond to Student Thinking

1. Elicit and analyze students’ mathematical thinking

2. Examine developmental progressions in students’ reasoning about rational numbers

3. Use evidence of student thinking to inform instructional decisions

C. Field Experience and Instructional Reflection

1. Apply current PK-8 state and national mathematics recommendations to plan instruction

2. Implement standards-aligned mathematics instruction with elementary students

3. Evaluate and reflect on instructional practices and student learning

II. Mathematical Content

A. Fraction Concepts and Operations

1. Meanings and models of fractions

a. Fractional parts, unit fractions, and fractions greater than one

b. Partitioning, iterating, and unitizing

c. Magnitude of fractions and number line representations

d. Area, length, and set models for fractions

2. Fraction equivalence, comparison, and estimation

a. Conceptual and procedural understandings of equivalence

b. Comparing fractions using benchmarks, common units, and reasoning strategies

c. Estimating fraction values using benchmarks and magnitude reasoning

d. Common misconceptions and instructional implications

3. Fraction operations

a. Meanings and problem structures for fraction addition and subtraction

b. Direct modeling, estimation, and invented strategies

c. Estimating results of fraction operations and assessing reasonableness

d. Development and justification of algorithms for fraction addition and subtraction

e. Meanings and problem structures for fraction multiplication

f. Fraction multiplication as scaling and iteration

g. Estimation strategies for fraction multiplication

h. Development and justification of multiplication algorithms

i. Meanings and problem structures for fraction division (partitive and measurement)

j. Estimation strategies for fraction division

k. Development and justification of division algorithms

B. Decimal Concepts and Operations

1. Decimal place value and representations

a. Extending the place-value system to decimals

b. Connections between fractions and decimals

c. Terminating and repeating decimals as extensions of fraction representations

2. Comparing and estimating with decimals

a. Ordering and comparing decimals using place value and benchmarks

b. Estimating decimal values and reasoning about magnitude

c. Common misconceptions related to decimal magnitude

3. Decimal operations

a. Estimation and number sense with decimal operations

b. Development and justification of algorithms for addition, subtraction, multiplication, and division

c. Reasoning about decimal operations using place value and powers of ten

C. Percents and Proportional Reasoning

1. Percents as hundredths and connections to fractions and decimals

2. Representing and solving percent problems using multiple models

3. Ratios as comparisons of quantities

4. Proportional relationships, unit rates, and scaling

5. Representations of proportional reasoning

a. Tables

b. Double number lines

c. Strip/bar diagrams

d. Graphs

D. Integers and the Real Number System

1. Structure of the real number system

2. Integers and their opposites

3. Absolute value and distance on the number line

4. Meanings and models for integer operations

a. Helium/sandbag (vertical) model for addition and subtraction

b. Bar diagrams for addition, subtraction, multiplication, division

c. Two-color counter models for addition, subtraction, multiplication, division

d. Walking the number line for addition, subtraction

5. Negative exponents and scientific notation

6. Connections among fractions, decimals, percents, and proportional reasoning

Facilitated Discussion: 10-60%

Collaborative Learning: 30-60%

Technology Supplemented Learning: 10-30%

Alternative grading will be used in this class.
Mandatory Course Components:
Service Learning with students grades PK-6, Math Play Activities
Equivalent Courses:
None.