5年生のマスターメソッド数学の1年間：パート4/4

*Note: If your student has not taken (or is not signed up for) Parts 1, 2 and 3 of this series, please contact me first for placement advice.

This session is part of a larger series titled, Full Year of 5th Grade Mastery Method Math. Taken as a whole, this will offer a full year's worth of math at the general 5th grade level--focusing on all aspects of and operations with fractions, as well as basic Pre-Algebra concepts (solving for the unknown) and Geometry (area and circumference of circles) and an introduction to decimals and percents. This is a Mastery approach to math--each concept will be demonstrated, explained and practiced in a meaningful, in-depth way to achieve full understanding before moving on and connecting to the next topic. This approach is ideal both for students who love math and want to take a deep dive into each concept, as well as anxious math learners who get easily overwhelmed by jumping quickly between concepts and prefer to take their time to fully learn and understand each concept. In both cases, the mastery method can build confidence, create a positive math identity and set students on a trajectory of math success. Because of the small size of this class, I will be able to give each student the individual attention needed to ensure mastery. This course is geared towards the 5th grade student, but because the mastery method builds on previously internalized concepts and skills, specific age or assigned grade level is not as important as the prerequisite foundations of mathematical understanding. 

**Specifically for this class, students should come with a solid number sense for whole numbers and performing basic operations (adding, subtracting, multiplying and dividing) on single and multi-digit numbers. They should have a general understanding of fractions and be able to add, subtract, compare and find equivalent fractions (covered in Part 1); find common factors, simplify fractions, and convert between improper fractions and mixed numbers (covered in Part 2); and add and subtract mixed numbers, including regrouping and unlike denominators, and divide fractions (covered in Part 3). If you have questions about your learner’s placement level, please contact me. 

In this fourth session, we will begin by making a big deal that we will be studying Algebra! But algebra doesn’t have a big, scary thing! It’s really more like a fun puzzle--trying to solve for the unknown. We will learn how to “undo” equations by using opposite operations (inverses) to solve for the unknown, then plug our answer back into the equation to check our work. We will cover single step and multi-step solving for the unknown using multiplication, division, addition and subtraction, as well as fractions. Additionally, we will cover multiplying 3 fractions using canceling as a shortcut (one of my math joys!), and learn how to find the area and circumference of circles using the fractional estimate of pi. We will end with an introduction to decimals and percentages and their connection to fractions, before our end of the year assessment, review and celebration! Each week we will cover one topic over three days, following this pattern: 1) visual, interactive introduction using real world connections; 2) guided, group and individual practice; 3) review work, including previously mastered concepts such as multi-digit multiplication or finding perimeter and area,  so that understanding stays fresh and further connections can be made. (See below for the full weekly outline of topics).

I want my students to feel fully engaged in the learning process--to find meaning, confidence (and yes, even joy!) in mathematical problem solving. To make math fun and engaging, I will be presenting lessons through interactive slides, which will include clear visual representations, virtual manipulatives, and connections to math in the real world. Additionally, I will be using applications such as Nearpod (nearpod.com) to create further opportunities for students to engage with the material and with one another. Activities will include collaborative idea boards, typed or drawn responses, polls, matching games, quizzes and embedded games. These activities provide not only engagement and fun for students, but also give me as the teacher the opportunity for ongoing, informal assessment. Furthermore, the ability for me to share student answers anonymously can help those students who feel uncomfortable or anxious answering questions verbally. 

In order to better personalize instruction and keep track of student mastery, I will also be utilizing Google Classroom. This will allow me to post assignments, interactive slides, quizzes, additional resources and homework. Students will also be able to turn their homework in through Google classroom so that I can correct and return it to them.
*For students needing additional support in reaching mastery of a topic, I will be offering tutoring sessions each week, available by the ½ hour.

Week 1 : Solving for the Unknown: Multiplicative Inverse
Day 1: Interactive review of Reciprocals, division as opposite of multiplication, fractions as division
Day 2: Practice using the multiplicative inverse to solve for the unknown
Day 3: Review Work, Word Problems, and Games: Measurement: Length (12 inches = 1 foot)

Week 2 : Multiplying 3 Fractions with Canceling as Shortcut
Day 1: Interactive, real-world introduction to finding a fraction of a fraction of a fraction (multiplying 3 fractions)
Day 2: Practicing multiplying 3 fractions with more real world examples
Day 3: Review Work, Word Problems, and Games: Measurement: Mass (2,000 pounds= 1 ton)

Week 3: Solving for the Unknown: 2 Step using Multiplicative Inverse, Addition and Subtraction
Day 1: Interactive introduction to Multi-step solving for unknown: Undo through the opposite
Day 2: Practice multi-step solving for the unknown
Day 3: Review Work, Word Problems, and Games: Measurement: Distance (1 mile = 5,280 feet)

Week 4:  Area and Circumference of Circles
Day 1: Interactive visual introduction to area and circumference of circles
Day 2: Practice finding the area and circumference of circles with real world problem solving
Day 3: Review Work, Word Problems, and Games: Comparing measure and fractions using >, < , and =.

Week 5: Solving for the Unknown: Multi-Step with Fractions as coefficients
Day 1: Review undoing using opposite (including multiplicative inverse/reciprocal)
Day 2: Practice solving for the unknown with fractions
Day 3: Review Work, Word Problems, and Games:Finding the average

Week 6: Connections: Fractions, Decimals and Percent
Day 1: Interactive introduction to decimals using money (fractions as tenths and hundredths) and percents as parts of the whole (per hundred)
 Day 2: Practice converting fractions to decimals and percentages using tenths and hundredths
Day 3: Review Work, Word Problems, and Games: Roman numerals: I, V, and X

Week 7: Solving for the Unknown: Multi-Step with Fractions Everywhere!
Day 1: Focus on step-by-step problem solving: undoing using opposites and inverses
Day 2: Practice solving for the unknown in multi-step equations with fractions
Day 3: Review Work, Word Problems, and Games: Roman numerals: L, C, D, and M

Week 8: Review Week: Making connections
Day 1: How are division,  fractions, decimals and percentages all related? Multiplication and division? Addition and Subtraction?
Day 2: Why are fractions, division, decimals and percents important in the real world? 
Day 3: Review Work, Word Problems, and Games: Mixed review as needed

Week 9: Review Week
Day 1: Progress Assessment
Day 2: Review as needed
Day 3: Celebration!