Math Foundations V

In Foundational Math V students grow their arithmetic toolbox to include decimal place value and decimal operations. Students will master adding, subtracting, multiplying, and dividing decimals. They will continue to develop their mastery of fractions to include mixed number operations. This newfound knowledge will be used to evaluate numerical expressions using the order of operations. They will study the coordinate plane, conversion factors, volume, and classifying quadrilaterals. They will develop a sense that mathematics can utilize and expose patterns, in nature and manmade, by learning to identify these patterns and how to translate them into the language of mathematics. Students will gain fluency in multiplying numbers from 1 to 12 and memorizing basic divisibility rules. They will complete portfolio projects that deepen their understanding of the concepts, appreciate the role of mathematics in God’s creation, and lead them to explore real-world applications of mathematics. Throughout the course, students will be led to see mathematics in the world around us through patterns.

Experience The teaching of a new concept opens with a brief review of previously covered content. This review connects the previous lesson to the current lesson. The premise of the current lesson is presented via a question or idea. The students now have a puzzle or idea that they want to explore. As we delve deeper into answering the question at hand, we begin to discover the new mathematical concept. We use our prior knowledge and intuition to uncover a new truth about mathematics. Once this truth has been uncovered, we begin to work examples; first as a class and then as individuals or in groups. As our understanding of the concept deepens, we extend our knowledge base to include specific cases or situations that lead to minor adjustments in the truth that we have uncovered – thus expanding the truth. We use a variety of methods to uncover new truths. The most frequent method is a Socratic-style discussion that the entire class participates in. A discussion takes place that reveals the relevance of this truth in our mathematical studies or our daily lives (real-life application). 

Get to Know Foundational Math with Christina Royals

Delivery Each teacher has a unique presentation style in delivering the aforementioned experience. Sometimes the teacher leads the discussion using questions; following the example set by Socrates.. Sometimes a problem is presented and the students take the lead in finding a solution based on extending previous knowledge. Sometimes students participate in a hands-on activity to discover new truths. Sometimes a short lecture or presentation is required, however, we aim to minimize lecturing, especially before high school. 

Methodology Students continue to study the new truth and deepen their understanding of it via homework, classwork, projects, and assessments. Since our classes do not meet 5 days per week, students must spend time studying the concepts outside of class. This also helps students grow in their ability to think and work math concepts independently which is required for future math classes. For this reason, we ask that parents minimize the assistance that students are given on assignments. If a student receives an A on an assignment, it should be a true indication of their independent ability as the teacher interprets this A as independent mastery.

Review assignments or classroom review activities are utilized to assist students with opportunities to retain or improve their mastery. Assessments are directly or indirectly cumulative and serve as an opportunity to deepen their learning. Assessments are not meant to be a regurgitation of previous homework assignments.

Preparedness Students who are adequately prepared to take this course will have mastered (can work independently without prompting):

• Place Value to One Million
• Rounding, Adding, Subtracting, Multiplying, and Dividing Multi-Digit Whole Numbers (including Long Division)
• Adding and Subtracting Fractions (unlike denominators) and Mixed Numbers
• Convert Units of Time
• Classify Lines, Polygons, Triangles, and Symmetry
• Calculate Area and Perimeter

Quarter 1

1. Extend Place Value to Include Decimal Places
2. Read, Write, Round, and Compare Decimals
3. Adding and Subtracting Decimals
4. Estimating Sums, Differences, Products, and Quotients of Decimals
5. Multiply and Divide Multi-Digit Whole Numbers
6. Understand Powers and Exponents
7. Estimate Products of Multi-Digit Factors
8. Multiply Decimals

• The order in which topics are presented may vary according to instructor and course section.

Quarter 2

1. Dividing with Two Digit Divisors
2. Dividing Decimals by Whole Numbers and Decimals
3. Adding and Subtracting Fractions and Mixed Numbers
4. Multiplying a Fraction by a Fraction
5. Multiplying Mixed Numbers
6. Dividing a Fraction by a Whole Number

• The order in which topics are presented may vary according to instructor and course section.

Quarter 3

1. Understanding and Using the Coordinate Plane
2. Writing, Interpreting, and Evaluating Numerical Expressions
3. Identifying and Graphing Numerical Patterns

• The order in which topics are presented may vary according to instructor and course section.

Quarter 4

1. Convert Customary and Metric Units
2. Measurements on Line Plots
3. Volume of 3D and Composite Figures
4. Properties of and Classifying Quadrilaterals

• The order in which topics are presented may vary according to instructor and course section.

• Computer: You will need a stable, reliable computer, running with a processor with a speed of 1 GHz or better on one of the following operating systems: Mac OS X with Mac OS 10.7 or later; Windows 8, 7, Vista (with SP1 or later), or XP (with SP3 or later). We do not recommend using an iPad or other tablet for joining classes. An inexpensive laptop or netbook would be much better solutions, as they enable you to plug an Ethernet cable directly into your computer. Please note that Chromebooks are allowed but not preferred, as they do not support certain features of the Zoom video conference software such as breakout sessions and annotation, which may be used by our teachers for class activities.
• High-Speed Internet Connection: You will also need access to high-speed Internet, preferably accessible via Ethernet cable right into your computer. Using Wi-Fi may work, but will not guarantee you the optimal use of your bandwidth. The faster your Internet, the better. We recommend using a connection with a download/upload speed of 5/1 Mbps or better. You can test your Internet connection here.
• Webcam: You may use an external webcam or one that is built in to the computer. Webcam Recommendations: Good (PC only) | Best (Mac and PC)
• Headset: We recommend using a headset rather than a built-in microphone and speakers. Using a headset reduces the level of background noise heard by the entire class. Headset Recommendations: USB | 3.5mm
• Zoom: We use a web conferencing software called Zoom for our classes, which enables students and teachers to gather from around the globe face to face in real time. Zoom is free to download and easy to use. To download Zoom:
  1. Visit zoom.us/download.
  2. Click to download the first option listed, Zoom Client for Meetings.
  3. Open and run the installer on your computer.
  4. In August, students will be provided with instructions and a link for joining their particular class.
• Scanner: In this class, students frequently submit homework assignments by scanning pages from their workbooks. Students and/or their parents should have easy access to a scanner and the ability to use it.