Phase One: Defining Mathematics Lesson Plan

Notes for the Educator

The Core of Mathematics: How the Emily Co. Curriculum Approaches this Subject

This lesson is designed to be delivered during Phase One: Introduction to Languages.

This lesson aims to introduce the essential description of what is mathematical.

There is a core body of topics in mathematics that we must cover during the years of elementary school.

Below is the students’ very first mathematics lesson, creating a fundamental understanding of the subject.

Required Mathematics Lesson #1: What Is Mathematical?

Prerequisites

This required lesson, part of the Introduction to Languages coursework, is designed to be introduced to the student during Phase One: Independence, as one of their required mathematics lessons. You can learn more about Phase One: Independence by clicking here.

In their course Introduction to Languages, they should have already completed the following required lessons:

Introduction to English
The Alphabet
Reading Basics
Creating Your Own Language

They should have already completed these lessons before they begin this one.

If the student is not yet reading at grade level, they will use the video lecture primarily and follow along with the written one as they listen. They will need parent or teacher assistance writing out the numbers and words in their learning journal.

Don’t stress. This lesson seems advanced, but you’ll be reviewing it a little each day for weeks until it comes naturally to them. You can spend as long as you need to on this lesson- take months, if that’s your student’s natural pace.

The Goal Setting Session

The goals for all students during this lesson are:

to learn what the subject of mathematics includes and begin to define what is mathematical
to familiarize ourselves with the counting numbers and other common symbols in the language of mathematics, such as the addition, subtraction, and equal signs, and the shapes
to learn what addition and subtraction are, when we might use them in real life situations, and how these tasks are performed.

Parents/teachers and students should also sit down and identify at least one personal goal for the student based on their own passions in life, to be met during the course of this lesson. You can view suggested goal examples and read our guide to conducting a goal setting session by clicking here.

In a perfect world, about 3 months (12 weeks) should be spent on this lesson, so take your time. Review the article version of the lecture, and/or the video format of the lecture, three times per week with your child and guide them through the material.

Recommended Extracurricular Activities for this Lesson

Lego block sets
Together, count the cars you pass on the highway while driving
Have students draw something in their learning journal every day, and while you supervise make brief observations about the space, colors, shapes, sizes, perspective and angles in their creative work. Below each drawing in their learning journal, have them choose 2 emotional words to describe how the drawing makes them feel and write them out together.
Painting, with no rules
Music instrument lessons (learning a musical instrument can help with mathematics performance)

Instructions for the Parent

Preview this lesson and research anything you don’t understand for yourself. Make sure you’re fully comfortable with the material and prepared to answer questions about the topics before presenting it to the student.

Instructions for the Student

You will listen to this lecture multiple times during the 3-month duration of this lesson.

Each time you view the video lecture, read along with the written version of the lecture.

You can print out this article and highlight all the words you don’t know and concepts you don’t understand.

These highlighted sections will be the jumping off point and guide for your independent research. Paste them into your learning journal, and also include notes about your thoughts and feelings, and drawings that the material inspires you to create.

There are also recommended videos for you to view, and articles for you to read, which will hopefully communicate why this subject is important for you to learn.

The Five-Min Lectures

#1 What is Math?

The formal definition of mathematics from the Oxford Languages dictionary is: the abstract science of number, quantity, and space.

Mathematics may be studied in its own right (pure mathematics), or as it is applied to other disciplines such as physics and engineering (applied mathematics):

The mathematical aspects of something allow us to track and manage inventories. Mathematics is a global language designed to help us track and manage inventories. It is an international language devised to help us keep records of what objects we have in our possession. The numbers and signs in mathematics are like the letters in the other languages. People all over the world learn how to use math with these same symbols. This language allows them to communicate with each other about what they have, how much they have in stock, what the objects are worth, the measurements that would allow us to replicate the object, and more.

So mathematics is a language devised for tracking quantity (how much) and qualities (how much it costs, designs so we can create a new one, even how many people like the object). Once applied, mathematics can be used to track patterns and changes in all of this information, so we might work with all this information to seek the results and share the results with other people.

#2 What are the different types of mathematics?

Here are some examples of mathematical topics and their applications. All quoted definitions are taken from the Oxford Language Dictionary:

Arithmetic is “the branch of mathematics dealing with the properties and manipulation of numbers.” It begins with understanding the counting numbers. There is a total number of objects we have, and this total is represented by the symbol = which is called the equal sign, followed by the number amount. Then we can use operations like addition and subtraction to add to or remove from the total. Addition is when we add additional objects together to create a larger sum. The addition symbol + communicates we are adding more objects to the total. Subtraction is used for when we remove the objects from our inventory and are left with less as the total. The subtraction symbol – communicates we have less than what we started out with. We’ll learn more about how to use addition and subtraction in the next lesson.

Geometry is “the branch of mathematics dealing with properties and relations of points, lines, surfaces, solids, and higher dimensional analogs.” It allows us to draw out and understand objects’ sizes, dimensions, shapes, length, width, weight, and other measurements. Applied this allows us to reproduce the objects. Some examples of applied geometry are the pictured instructions to a Lego set, or the instructions to build a piece of furniture. These instructions are communicating the information you need to replicate what they’ve built, including details about what it should look like and how it should all fit together when it’s finished.

Algebra is “the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.” So this branch of mathematics incorporates letters from English and other symbols from various other languages. Integrating information from additional languages besides just mathematics allows us to do more. In Algebra you often use the information you already have provided to deduce what is missing from that information. So the information you already have includes clues to figuring out something you don’t yet know. The letters from other languages represent the clue indicators in this process.

Statistics is “the practice or science of collecting and analyzing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample.” So statistics works with parts of a whole. How much of the pizza was eaten? How many people enjoyed this content? The answers to information like this can be expressed using a fraction or percentage, which we’ll learn about later in a different lesson. Statistics is most often applied in social studies and marketing studies.

There are other advanced specialties of mathematics, such as trigonometry, calculus, and differential equations, which you will learn about later if you pursue further education. There is even a branch of mathematics dedicated to trying to predict the future!

All of the mathematics you learn in Emily Co. coursework will be applicable to your daily life.

Vocabulary List

Search for the following words in the online dictionary and add their meanings to your learning journal. Include doodles/drawings. Highlight your favorite words.

Mathematical
Concept
Abstract
Concrete
Applied
Problem
Number
Zero
One
Two
Three
Four
Five
Six
Seven
Eight
Nine
Ten
Eleven
Twelve
Thirteen
Fourteen
Fifteen
Sixteen
Seventeen
Eighteen
Nineteen
Twenty
Thirty
Forty
Fifty
Sixty
Seventy
Eighty
Ninety
Hundred
Thousand
Million
Billion
Calculation
Reckoning
Tally
Question
Arithmetic
Equal
Addition
Subtraction
Dimension
Measurement
Unknown
Shape
Square
Rectangle
Triangle
Circle
Hexagon
Octagon
Statistic

Recommended Viewing List

This viewing list is designed to be a jumping off point for your research. You don’t have to review everything on this list- start off by browsing and following your natural curiosity. Delve deeper if you’d like.

Learning Journal Activities

Activity #1: The Counting Numbers
Write out the counting numbers 0-100 on individual lines in your notebook. Do this in various colors of ink. You can choose the color for each number based on your intuition.
Next to each of the counting numbers, write the first word that comes to mind. This process is called word association. It tells you what you already think, know, feel.
Then, look up the symbolic meaning of the numbers in various cultures, and take some notes on the meanings from the mythologies that catch your eye and interest you.
Activity #2: Shapes and Sizes
Learn how to draw a circle, square, rectangle, triangle, hexagon, and octagon. Label them. Decorate them by coloring each of them a different color. Then, measure each side of each shape with a ruler and write down how many centimeters each line equals beside it.
Activity #3: Addition and Subtraction
Draw the addition symbol. Next to it, write out the meaning of the addition symbol.
Draw the subtraction symbol. Next to it, write out the meaning of the subtraction symbol.

Then walk the child through the basics of addition and subtraction by having them use their fingers. (On their fingers have them count the total amount of some objects you see, and then remove some of the objects, and have them count out the new total on their fingers.) Don’t get frustrated with them- it takes as long as it takes. Role model good learning habits and self-esteem.

Integration and Imaginative Play Meditation

The Storefront

Come up with an idea for a store you’d like to run. It can be a pet shop, a car dealership, or anything else you can imagine as a store. This store is stocked with an inventory of items. In the pet shop example, there would be pet food, live animals, and cleaning supplies in the inventory. In the car dealership example, there would be a variety of cars in the inventory.

List what you would sell at your store in your learning journal. Then draw a picture of each of the items your store sells. Then, label each item with a number of how many you would have in the store’s inventory to sell to customers. Lastly, determine how much each item is worth and write down a dollar amount to indicate how much 1 of that item would cost.

Then, run your store using stuffed animals, toy cars, or whatever you are selling. Your parents and siblings are your first customers! Explain to them what you have in inventory at your shop, and sell them what they want. Use play money and exchange goods.

Practical Applications Project

The Yard Sale

As a family, set up a real-life yard sale with old toys and items from the house. Count how many of each type of item you have, and assign each item a price. Allow the child to participate in each step and explain to them the process as you go through it. Allow them to be present on the day of the yard sale and role model to them how to keep track of the inventory and prices, and how to deal with customers. Make sure to take some family photos or videos to include in the Learning Journal.

Proofs and Presentations Stage

Review the Learning Journal and highlight anything in it that you’d like to learn more about or still don’t understand. Go over it together.

Oral Narration Session

At the end of the 12 weeks, have the child sum up their answers out loud to the following questions. Their answers should be recorded as voice memos, which are added to the virtual edition of their learning journal.

What is mathematics?
Is there anything about mathematics you like? Dislike?
What would you use mathematics for?
Count as high as you can!
What are the different shapes?
How do you use a ruler to measure the length of an object? Show me.
Why might we need to know the shape and measurements of the objects we have?
What is addition?
What is subtraction?
What is the price, at a store?
What are the different ways a store owner would use math to run their business?

Self-Assessment Guide

The student is ready to move on when they can count to 100, have a grasp of what the subject of mathematics is, have completed all learning activities, and can answer the above oral narration questions to the parent’s satisfaction. They do not need to know how to perform addition and subtraction yet, but they should be introduced to counting on their fingers, have a basic understanding allowing them to provide a simple definition of addition and subtraction and how they might be applied in daily situations.