Module 1: Mathematical Operations - Course Guide

Module Overview:

In this module students will learn about the basic order of operations to use when evaluating numerical expressions. Students will learn about how to use parentheses, brackets or braces in mathematical expressions. Students will learn about translating words into math and the meaning of math expressions. Students will learn about how to use their knowledge about mathematical translation to solve word problems. Students will learn about creating numerical patterns and identifying relationships between patterns. They will learn about relationships between different sequences and how to find them and learn about ordered pairs and how they can be created from sequences.

Module Materials:

Lesson # Lesson Title Material(s)
1 Introduction to Operations *Math 5A Workbook, ISBN 978-1-63916-100-3 (optional);
2 Parentheses, Brackets, and Braces None
3 Translating Words to Math None
4 Translating Math to Words None
5 Meaning of Mathematical Expressions None
6 Translating Mathematical Expressions None
7 Patterns and Sequences None
8 Relationships Between Sequences None
9 Ordered Pairs None
10 Patterns and Graphs None

Module Objectives:

Lesson # Lesson Title Objective(s)
1 Introduction to Operations
  1. Evaluate expressions using the basic order of operations.
2 Parentheses, Brackets, and Braces
  1. Use symbols such as parentheses, brackets, or braces in numerical expressions.
  2. Evaluate expressions that use parentheses, brackets, or braces.
3 Translating Words to Math
  1. Translate words into numerical expressions.
4 Translating Math to Words
  1. Translate mathematical expressions to words.
5 Meaning of Mathematical Expressions
  1. Recognize the meanings of numerical expressions.
6 Translating Mathematical Expressions
  1. Translate words to mathematical expressions.
  2. Write simple expressions that include all operations.
  3. Recognize the meanings of numerical expressions.
  4. Evaluate mathematical expressions using order of operations.
7 Patterns and Sequences
  1. Create numerical patterns using different rules.
  2. Identify patterns in a numerical sequence given a pattern rule.
  3. Extend or duplicate a pattern in a number sequence.
  4. Use a two-column table to record the inputs and outputs of the given numerical pattern.
8 Relationships Between Sequences
  1. Identify and explain the relationships between corresponding terms of patterns.
9 Ordered Pairs
  1. Generate and graph ordered pairs from the corresponding terms of sequences.
  2. Plot ordered pairs on a coordinate plane.
10 Patterns and Graphs
  1. Identify patterns and relationships between ordered pairs on a graph.
  2. Make predictions based on trends identified in data on a graph.
  3. Generate and graph a numerical pattern when given a rule in the form y = ax or y = x + a.
  4. Recognize an additive and a multiplicative numerical pattern.

Module Key Words:

Key Words
numerical expression
order of operations
evaluate
parentheses
brackets
braces
translation
translate
operation
arithmetic number pattern
arithmetic sequence
term
prediction
input
output
input-output table
sequence
corresponding
relationship
corresponding term
ordered pair
coordinate plane
plot
graph
pattern
trend
positive
negative
unrelated
additive pattern
multiplicative pattern

Module Assignments:

Lesson # Lesson Title Page # Assignment Title
1 Introduction to Operations 6 Assignment
2 Parentheses, Brackets, and Braces 6 Assignment
6 Translating Mathematical Expressions 5 Assignment
7 Patterns and Sequences 9 Assignment
9 Ordered Pairs 5 Assignment

Learning Coach Notes:

Lesson # Lesson Title Notes
1 Introduction to Operations
2 Parentheses, Brackets, and Braces In their Math notebook, have your student record the steps for the order of operations when parenthesis, brackets, and braces are involved.
3 Translating Words to Math In their math notebook, have your student explain the following: translation and the math operation words.
4 Translating Math to Words Give your student 5 different math problems and have them write them into words in their Math notebook.
5 Meaning of Mathematical Expressions In their Math notebook, have your student summarize what they learned about Mathematical Expressions in this lesson.
6 Translating Mathematical Expressions In their Math notebook, have your student describe the steps involved to translate a mathematical expression.
7 Patterns and Sequences
8 Relationships Between Sequences In their Math Notebook, have your student summarize the steps they can follow to discover relationships in sequences.
9 Ordered Pairs In their Math Notebook, have your student explain the following: ordered pair, coordinate plane, corresponding terms, and how to graph ordered pairs.
10 Patterns and Graphs In their Math notebook, have your student explain the three types of trends when looking at data.

Module Guiding Questions:

When a student starts a lesson ask them questions to check for prior knowledge and understanding and to review concepts being taught. At the end of the lesson ask the questions again to see if their answer changes.

Lesson Title Question
Introduction to Operations
  1. What does PEMDAS stand for?
Parentheses, Brackets, and Braces
  1. What is the order of operations when parentheses, brackets, and braces are in a problem?
Translating Words to Math
  1. What keywords are in word problems that let you know what operation to use?
Translating Math to Words
  1. How can you put math problems into words?
Meaning of Mathematical Expressions
  1. How is an expression different from an equation?
Translating Mathematical Expressions
  1. What does it mean to evaluate a mathematical expression?
Patterns and Sequences
  1. What is an arithmetic pattern?
Relationships Between Sequences
  1. How do you find the rule to a number pattern?
Ordered Pairs
  1. What is an ordered pair?
Patterns and Graphs
  1. How can you analyze data on a graph?

Module Video Questions:

When a student watches a video take time to ask them questions about what they watched. Suggested questions for the videos in this module are listed here. Suggestion: Have the student watch the entire video first all the way through. Then have them watch the video a second time, as they watch it pause the video and ask the questions.

Lesson Title Video Question
Introduction to Operations Introduction to Operations
  1. What does PEMDAS stand for?
Parentheses, Brackets, and Braces Parentheses, Brackets, Braces
  1. What is the order of operations when parentheses, brackets, and braces are in a problem?
Translating Words to Math Translating Words to Math
  1. What are some keywords that indicate addition?
  2. What are some keywords that indicate subtraction?
  3. What are some keywords that indicate multiplication?
  4. What are some keywords that indicate division?
Translating Mathematical Expressions Translating Mathematical Expressions
  1. What were the steps used to solve the problems in this video?
Patterns and Sequences Patterns and Sequences
  1. What are some steps you can follow to help figure out a pattern?
Relationships Between Sequences Relationships Between Sequences
  1. What are some steps you can follow to look for in relationships to sequences?
Ordered Pairs Ordered Pairs
  1. How do you graph ordered pairs?
Patterns and Graphs Patterns and Graphs
  1. What is a trend?
  2. How do professionals rely on trends?

Module Suggested Read Aloud Books:

Take time to read to your student or have them read aloud to you. Read a different book each day. While reading the book point out concepts being taught. You may purchase these books or find them at your local library. Suggested things to discuss while reading the book:

  • What is the main idea?
  • What are three things new you learned?
  • How does this book relate to what you are learning about?

# Book Author Lexile Level
1 The Story of the Order of Operations: PEMDAS Mrs. Kim Huffstetler
2 A-B-A-B-A―a Book of Pattern Play Brian P. Cleary

Module Outing:

Take some time to apply what your student is learning to the real world. Suggested outings are below.

# Outing