# MIDDLE SCHOOL MATH

The Waldorf Curriculum includes developmental stages for learning mathematics. The elementary grade levels are a time for students to play with numbers and develop a love of math. In 5th and 6th grades, students consolidate the skills introduced earlier (such as fractions and long multiplication). In grades 7th and 8th the algebraic “real math” begins as they learn to think more abstractly. Now middle schooler’s thinking explodes as they learn to think more logically and critically, and engage deeply in problem solving.

## Middle School Youth Needs

As children approach adolescence their emotion life expands in many ways. Mathematics can offer an important support in this stage: subjective opinions are not required! Mathematical certainty allow the 6th grader to learn self-confidence and gain trust in intellectual thought processes!

Pure mathematics is, in its way, the poetry of logical ideas.  —Albert Einstein

## Math Research & Innovations

What does a growth mindset around math look like? It means being open to the curiosity of math rather than seeing it just as computation. Students in our middle school remember that mistakes are important, taking work risks in a safe learning environment that welcomes see the benefit of using visual models, understand that speed is not their focus but deep thinking is!

Jo Boaler, Stanford University, explains why mathematics can be so traumatic for many people and shows a different way that people can relate to mathematics. She also shares the latest brain science to show the ways our brains process mathematics, the importance of visual learning and the importance of self belief to our learning and our experiences.

# Integrations with Math

The expectations of mathematics are based on mastery of the topics at specific grade levels with the understanding that the themes and big ideas re-occur throughout our K-8th curriculum at varying degrees of difficulty, requiring different levels of mastery. During the 6th grade students work deeply with Number Sense and the interrelationship between division, fractions, decimals, and percentages – that is – ratio.

#### 1) Number Sense, Properties, and Operations

Students work with repeating decimals; decimal/fraction conversions; exponents; divisibility; prime factorization as well as thorough practice of the four processes

#### 2) Patterns, Functions, and Algebraic Structures

Mental math; “math tricks” such as casting out nines; integrated puzzle problems

#### 3) Data Analysis, Statistics, and Probability

Business mathematics brings the students in touch with daily life and practical knowledge of finance at a time when the students are really asking, “When will I be applying this?” – statistical graphs; formulae; currency exchange rates; sales tax

#### 4) Shape, Dimension, and Geometric Relationships

Geometric drawing from perspective drawings in art (compass & straight edge); basic Euclidean geometric constructions; measurement & area

# 21ST CENTURY SKILLS & READINESS IN MATH

### Information Literacy

The study of mathematics empowers students to organize and interpret quantitative data. To be informationally literate, mathematics students must be able to use learning tools and clearly communicate using mathematical language.

### Collaboration

In mathematics, students communicate using mathematical language. Students exchange ideas, strategies, solutions, justifications, and proofs with others. In turn, they themselves interpret and evaluate the work others.

Work with practical mathematical problems offers the seventh grader a framework for energetic thinking fostering intellectual engagement! The world of problem solving is now opening – no longer sufficient to merely get an answer!

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. In 7th grade students are growing more comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later.

#### 1) Number Sense, Properties, and Operations

Exponents & square roots; percentage; ratios; ratio in a square; ratio in a circle (pi); mental math; math tricks

#### 2) Patterns, Functions, and Algebraic Structures

Algebra with rational numbers: simplifying expressions; solving equations

#### 3) Data Analysis, Statistics, and Probability

Rates; distance, time, speed problems; puzzle problems

#### 4) Shape, Dimension, and Geometric Relationships

Area; rectangles; parallelograms; non-right triangles; the shear and stretch; similar figures; geometric drawing & construction; pentagon & the golden ratio; Pythagorean Theorem; angle theorems

# 21ST CENTURY SKILLS & READINESS IN MATH

### Self Direction

The discipline of mathematics requires a positive disposition and self-direction. We cultivate a sense of monitoring and assessing one’s mathematical thinking. This approach includes perseverance in searching for patterns, relationships, and meaningful solutions.

In 8th grade, students check their answers to problems using different methods, and are able to ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students are able to consider the meaning of a problem and look for ways to begin. They analyze givens, constraints, relationships, and goals. Students can consider the form and meaning of the solution and plan a solution pathway rather than merely jumping into a solution attempt.

#### 1) Number Sense, Properties, and Operations

Base systems of numbers; square root algorithm; calculations using Pythagorean theorem; percentage changes

#### 2) Patterns, Functions, and Algebraic Structures

Proportions and ratio; algebra; order of operations; distributive property

#### 3) Data Analysis, Statistics, and Probability

Dimensional analysis (converting metric U.S.); polynomial curves; puzzle problems

#### 4) Shape, Dimension, and Geometric Relationships

Area and volume; Platonic & Archimedean solids; drawing conic sections

# 21ST CENTURY SKILLS & READINESS IN MATH

### Critical Thinking and Reasoning

Waldorf students notice patterns that exist in nature and society; mathematics provides the grammar and structure that make it possible to describe these patterns. Mathematics is a discipline grounded in critical thinking and reasoning. In mathematics, students set up problems, devise and carry out strategies. Students then also evaluate the solutions, and justify these methods, strategies, and solutions.

### Invention

As new ideas are contributed, the field of mathematics changes. Invention is a key element as students make and test conjectures, create mathematical models of real-world phenomena, generalize results, and connections among ideas, strategies and solutions.

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