# Horizons

## Content

#### multiplication and division facts to 100 (extending computational fluency)

Lesson 1-40: Multiplication and division by powers of 10, Multiplications and division of decimals and fractions

#### operations with integers (addition, subtraction, multiplication, division, and order of operations)

Lessons 1-40: Negative exponents, powers of negative numbers, product of powers, power of a power, power of a product

• Multiplications and division of decimals and fractions
• Order of operations, simplifying expressions, factors
• Prime factorization, GCF, LCM, divisibility tests
• Signed numbers, absolute value
• Squares and square roots, cubes and cube roots
• Like terms, number terminology

#### operations with decimals (addition, subtraction, multiplication, division, and order of operations)

Lessons 1-40: Negative exponents, powers of negative numbers, product of powers, power of a power, power of a product

• Multiplications and division of decimals and fractions
• Order of operations, simplifying expressions, factors
• Prime factorization, GCF, LCM, divisibility tests
• Signed numbers, absolute value
• Squares and square roots, cubes and cube roots
• Like terms, number terminology

#### relationships between decimals, fractions, ratios, and percents

Lessons 1-40: Negative exponents, powers of negative numbers, product of powers, power of a power, power of a product

• Multiplications and division of decimals and fractions
• Order of operations, simplifying expressions, factors
• Prime factorization, GCF, LCM, divisibility tests
• Signed numbers, absolute value
• Squares and square roots, cubes and cube roots
• Like terms, number terminology

#### discrete linear relations, using expressions, tables, and graphs

Lessons 81-120 Functions, graphs of  functions

• Slope, y-intercept, slope-intercept form

#### two-step equations with whole-number coefficients, constants, and solutions

Lessons 1-40: Equations and inequalities with one variable

Lesson 81-120: Solving one-variable equations and inequalities

• Solving two-variable equations, adding and subtracting equations
• Two-variable equations with dependent and independent variables

• Algebra tiles
• Binomials, FOIL method, trinomials
• Dividing monomials and polynomials
• Dividing polynomials by monomials and binomials
• Multiplying monomials and polynomials
• Polynomial expressions
• Pythagorean formula, right triangles
• 30-60-90 and 45-45-90 triangles
• Compressions, dilations, reflections, rotations, translations
• Cosine, sine, tangent

#### circumference and area of circles

Lesson 81-120: Parts of a circle, tangents

• Perimeter and area of circle, square, rectangle, triangle, rhombus, parallelogram, trapezoid

#### volume of rectangular prisms and cylinders

Lesson 81-120: Volume, surface area, and lateral area of prism, cube, cylinder, cone,

pyramid, sphere

#### Cartesian coordinates and graphing

Lesson 81-120: Graphing coordinate points, linear equations, and inequalities
Functions, graphs of functions

#### combinations of transformations

Lesson 81-120: Adjacent, complementary, and supplementary angles, transversals

• Congruent triangles and polygons, symmetry

#### circle graphs

Lesson 81-120: Parts of a circle, tangents

#### experimental probability with two independent events

Lessons 41-80: Combined probabilities, mutually exclusive events

#### financial literacy — financial percentage

Lesson 81-120: Commission, discount, mark-up, sale price, profits, and royalties

#### line graphs

Supplementation Required

#### single-outcome probability, both theoretical and experimental

Supplementation Required

#### financial literacy — simple budgeting and consumer math

Lesson 81-120: Commission, discount, mark-up, sale price, profits, and royalties

## Curricular Competencies

### Reasoning/Analyzing

#### Use logic and patterns to solve puzzles and play games

Supplementation Required

#### Use reasoning and logic to explore, analyze, and apply mathematical ideas

Lesson 81-120: Commission, discount, mark-up, sale price, profits, and royalties

#### Estimate reasonably

Supplementation Required

#### Demonstrate and apply mental math strategies

Supplementation Required

#### Use tools or technology to explore and create patterns and relationships, and test conjectures

Supplementation Required

#### Model mathematics in contextualized experiences

Supplementation Required

### Understanding/Solving

#### Apply multiple strategies to solve problems in both abstract and contextualized situations

Can be covered through discussion regarding topics such as commission, discount, financial literacy that is applicable to differing cultural perspectives

#### Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving

Supplementation Required

#### Visualize to explore mathematical concepts

Supplementation Required

#### Engage in problem-solving experiences that are connected to place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures

Supplementation Required

### Communicating/Representing

#### Use mathematical vocabulary and language to contribute to mathematical discussions

Have student engage in using mathematical vocabulary

#### Explain and justify mathematical ideas and decisions

Have student engage in discussion about  mathematical concepts

#### Communicate mathematical thinking in many ways

Have student engage in using mathematical vocabulary

Have student engage in discussion about mathematical concepts

#### Represent mathematical ideas in concrete, pictorial, and symbolic forms

Use any lessons that involve concrete, pictorial and symbolic representations

### Connecting/Reflecting

#### Reflect on mathematical thinking

Supplementation Required

#### Connect mathematical concepts to each other and to other areas and personal interests

Supplementation Required

#### Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts

Supplementation Required