# Horizons

## Content

#### small to large numbers (thousandths to billions)

Unit 1: Place value and number theory

Unit 2: Number order and integers

Unit 3: Addition & Subtraction: 2-6 digits, equations, missing addends, estimating, money, counting change

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

Unit 4: Multiplication: properties, terms, facts/common multiples/triple digit times single digit/two digit times a two digit/three digit times three digit/money by two digit number/missing factors/estimating products/exponents/four digit by four digit/five digit by five digit

Unit 5: Division: properties, terms, facts/one, two, and three digit divisors/dividing money/estimating quotients/averaging with remainders/four digit divisor

#### order of operations with whole numbers

Unit 2: Number order and integers

#### factors and multiples — greatest common factor and least common multiple

Unit 4: Multiplication: common multiples

Unit 8: Fractions: greatest common factor, common denominators

#### improper fractions and mixed numbers

Unit 8: Fractions: greatest common factor, common denominators

#### introduction to ratios

Supplementation Required

#### whole-number percents and percentage discounts

Unit 9: Decimals: fractions to decimals/word numbers to hundred thousandths/compare & order decimals/add decimals (horizontal and vertical)/subtract decimals/estimate decimals/multiply a decimal by a whole number/multiply two decimals/divide decimal by a whole number/extend quotient to tenths, hundredths, thousandths/interpret the remainder/divide by a decimal/divide and multiply by 10, 100, 1000/repeating decimals

Unit 14: Percent: understand the concept/finding a percent of a number/percent and decimals/percent and fraction/discount and sales tax

#### multiplication and division of decimals

Unit 9: Decimals: fractions to decimals/word numbers to hundred thousandths/compare & order decimals/add decimals (horizontal and vertical)/subtract decimals/estimate decimals/multiply a decimal by a whole number/multiply two decimals/divide decimal by a whole number/extend quotient to tenths, hundredths, thousandths/interpret the remainder/divide by a decimal/divide and multiply by 10, 100, 1000/repeating decimals

#### increasing and decreasing patterns, using expressions, tables, and graphs as functional relationships

Unit 10: Ratio: write simple ratios/multiply to find equal ratios/divide to find equal ratios/cross products/use cross products to solve for n/ratio as a percent

Unit 12: Graphs: bar/line/pictographs/circle/coordinate graphs/comparing graphs/mean, mode, median/graphing in all four quadrants

Unit 16: Problem Solving: find a pattern

#### one-step equations with whole-number coefficients and solutions

Unit 13: Equations: addition/subtraction/multiplication/division/writing equations for word problems/equal ratios

#### perimeter of complex shapes

Unit 6: Geometry: perimeter and area

#### area of triangles, parallelograms, and trapezoids

Unit 6: Geometry: perimeter and area

#### angle measurement and classification

Unit 7: Geometric Constructions: protractors/compass/measuring and constructing angles/construct a perpendicular bisector/bisect an angle/construct a regular hexagon/construct an equilateral triangle/construct a right triangle/construct a square/construct a parallelogram

#### volume and capacity

Unit 11: Measurement: standard and metric linear equivalent/standard and metric liquid equivalent/standard and metric weight equivalent/temperature reading and understanding/Fahrenheit and Celsius/millimeter, centimeter, decimeter, meter/decameter, hectometer, kilometer

#### triangles

Unit 6: Geometry: perimeter and area/area of a parallelogram/area of a triangle/area of a circle/volume of a cube/volume of a cylinder/surface area/shapes and solids/symmetry/congruent figures/line, line segment, ray, endpoint/parallel, intersecting, perpendicular/angles-rays, vertex, acute, obtuse, right/circles – diameter, radius, chord, central angle/types of triangles/polygons-sides, vertices, diagonals

Unit 7: Geometric Constructions: protractors/compass/measuring and constructing angles/construct a perpendicular bisector/bisect an angle/construct a regular hexagon/construct an equilateral triangle/construct a right triangle/construct a square/construct a parallelogram

#### combinations of transformations

Unit 12: Graphs: bar/line/pictographs/circle/coordinate graphs/comparing graphs/mean, mode, median/graphing in all four quadrants

#### line graphs

Unit 12: Graphs: bar/line/pictographs/circle/coordinate graphs/comparing graphs/mean, mode, median/graphing in all four quadrants

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

Supplementation Required

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

Unit 14: Percent: understand the concept/finding a percent of a number/percent and decimals/percent and fraction/discount and sales tax

Lesson 15: Applications: writing cheques/budgeting/banking/savings/understanding interest/computing interest/comparison buying/installment buying/using charts and tables

## 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

Supplementation Required

#### Estimate reasonably

Unit 8: Fractions: Round and estimate with fractions

Unit 9: Decimals: fractions to decimals/word numbers to hundred thousandths/compare & order decimals/add decimals (horizontal and vertical)/subtract decimals/estimate decimals

#### Demonstrate and apply mental math strategies

Supplementation Required

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

Use of manipulatives, calculator, graphic calculator, etc.

### Understanding/Solving

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

Lesson 15: Applications: writing cheques/budgeting/banking/savings/understanding interest/computing interest/comparison buying/installment buying/using charts and tables

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

Lesson 15: Applications: writing cheques/budgeting/banking/savings/understanding interest/computing interest/comparison buying/installment buying/using charts and tables

#### 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

Lesson 15: Applications: writing cheques/budgeting/banking/savings/understanding interest/computing interest/comparison buying/installment buying/using charts and tables

### Communicating/Representing

#### Explain and justify mathematical ideas and decisions

Supplementation Required

#### Communicate mathematical thinking in many ways

Unit 16: Problem Solving: choosing an operation/reasonable or unreasonable answers/too much information and too little information/multiple step problems/understanding remainders/make an organized list/draw a picture/find a pattern/use a chart, table, menu, schedule

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

Supplementation Required

### Connecting/Reflecting

#### Reflect on mathematical thinking

Supplementation Required

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

Unit 16: Problem Solving: choosing an operation/reasonable or unreasonable answers/too much information and too little information/multiple step problems/understanding remainders/make an organized list/draw a picture/find a pattern/use a chart, table, menu, schedule

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

Supplementation Required