Adult Literacy Fundamental Mathematics (ALFM)
Goal Statement
Adult Literacy Fundamental Level Mathematics (ALF-M) will give students a strong foundation of basic skills, concepts, mathematical vocabulary, and problem solving strategies to prepare them to meet personal, career or further academic goals.
The ALF-M levels are six designated levels that range from pre-numeracy to readiness for the Intermediate ABE level. Learning Outcomes for all six levels are categorized as CONCEPTS, OPERATIONS/ APPLICATIONS or SKILLS & STRATEGIES FOR LEARNING. The outcomes in each of the six ALF-M levels are cumulative and reflect all the skills encompassed by the previous ALF-M level. In many cases, it is necessary to spiral back to review concepts mastered at previous ALF-M levels.
Students are expected to develop conceptual understanding as well as skills. They are expected to apply the learned mathematical concepts and skills to a variety of problem-solving situations. They are to be encouraged to develop automaticity and estimation skills in order to increase their confidence and competence in mathematics.
Level 1 Math
Students need to demonstrate competency in these outcomes before progressing to the next level. In assessment, it may be determined that some of the outcomes have already been met. In this case, students will focus on the outcomes which still need to be achieved.
Learning Outcome
Students will be able to . . . |
Sub-outcomes/skills
By achieving this broader outcome, students will demonstrate that they can also . . . |
Sample Practice Tasks
Students can develop/practice the skills needed to achieve this outcome by . . . |
- Evaluate 2-digit expressions using addition and subtraction, without carrying or borrowing/trading
- Identify place value to 100
- Round whole numbers to the nearest 10, 100, 1000
- Order whole numbers to 100
- Represent mathematical ideas in concrete, pictorial, and symbolic forms
- Use mathematical vocabulary and language to communicate concepts
- Identify value of Canadian currency
- Translate a 1 step addition or subtraction word problem into a mathematical expression
- Identify regular shapes: rectangle, square, triangle, and circle
- Recognize common base time units (seconds, minutes, etc.)
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- Read and write whole numbers up to 100
- Recognize vertical and horizontal format for adding and subtracting
- Count by multiples of 2, 5, 10, up to 1000
- Apply or use examples of keywords
- Compare whole numbers
- Estimate value of numbers
- Solve for the perimeter of a rectangle, triangle, and square
- Draw and label the sides of a regular shape (rectangle, square, triangle)
- Planning the steps necessary for a feast
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- Counting by multiples of 2, 5, and 10
- Show the relationship between manipulatives and numbers up to 20
- Drawing and labeling regular shapes (rectangle, square, triangle, circle)
- Plan and produce a food product based on a recipe.
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Level 2 Math
Students need to demonstrate competency in these outcomes before progressing to the next level. In assessment, it may be determined that some of the outcomes have already been met. In this case, students will focus on the outcomes which still need to be achieved.
Learning Outcome
Students will be able to . . . |
Sub-outcomes/skills
By achieving this broader outcome, students will demonstrate that they can also . . . |
Sample Practice Tasks
Students can develop/practice the skills needed to achieve this outcome by . . . |
- Evaluate multi-digit expressions using addition, subtraction with carrying or borrowing/trading
- Identify place value to 1,000,000
- Round whole numbers up to 1,000,000 place value
- Read, write and compare whole numbers to 1,000,000 in digits and words
- Represent mathematical ideas in concrete, pictorial and symbolic forms
- Use mathematical vocabulary and language to communicate concepts
- Add and subtract currency up to $2
- Translate 1-step addition, subtraction and multiplication word problems into a mathematical expression
- Convert, add and subtract time units
- Convert to and from 12-hour notation to 24-hour notation
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- Show the relationship between multiplication and repeated addition
- Recall multiplication facts up to 12 x 12
- Write numbers in expanded notation to 10,000
- Estimate sums and differences
- Multiply two whole numbers that are less than or equal to 10
- Multiply one-digit numbers by 10, 100, 1000
- Use key words: multiplier, multiple, multiplication, multiply, product, double/twice, triple, quadruple, by, of, carrying, borrowing, times, expanded notation, perimeter
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- Memorize 12 x 12 multiplication chart
- Write numbers as repeated additions or multiplication
- Calculate perimeter of a square and a rectangle
- Make change up to $1
- Scheduling
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Level 3 Math
Students need to demonstrate competency in these outcomes before progressing to the next level. In assessment, it may be determined that some of the outcomes have already been met. In this case, students will focus on the outcomes which still need to be achieved.
Learning Outcome
Students will be able to . . . |
Sub-outcomes/skills
By achieving this broader outcome, students will demonstrate that they can also . . . |
Sample Practice Tasks
Students can develop/practice the skills needed to achieve this outcome by . . . |
- Evaluate expressions using multiplication and division with carrying and with/without remainder
- Divide and multiply whole numbers by 10, 100’s, and 1000’s.
- Translate multiplication and division into mathematical expressions to solve multi-step word problems reflecting real life situations
- Demonstrate division by regrouping
- Use mathematical vocabulary and language to communicate concepts
- Recognize basic metric units
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- Memorize division and multiplication facts
- Recognize the relationship between X and -/-
- Estimate products and quotients
- Solve single and multi-step multiplication and division word problems reflecting real life situations
- Apply multiplication and division to real life situations
- Apply or use examples of keywords
- Define basic prefixes of metric system
- Calculate area of a square and rectangle
- Compare and contrast perimeter and area informally, using a drawing or a shape
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- Check a division question using multiplication
- Check multiplication with division
- Determine a number’s divisibility between 2, 3, 5 and 9
- Solve single and multi-step multiplication and division word problems reflecting real life situations
- Calculate unit prices using whole numbers
- Find quotient keywords
- Calculate the lowest price comparing unit prices of similar products
- Make change up to $100
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Level 4 Math
Students need to demonstrate competency in these outcomes before progressing to the next level. In assessment, it may be determined that some of the outcomes have already been met. In this case, students will focus on the outcomes which still need to be achieved.
Learning Outcome
Students will be able to . . . |
Sub-outcomes/skills
By achieving this broader outcome, students will demonstrate that they can also . . . |
Sample Practice Tasks
Students can develop/practice the skills needed to achieve this outcome by . . . |
- Evaluate decimal expressions using addition subtraction, multiplication, and division
- Identify place value to 10 000ths
- Round decimal numbers to a given place value
- Order decimal numbers
- Evaluate multi-step decimal expressions
- Solve word problems
- Convert measurements within the metric system
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- Read and write decimals
- Apply or use examples of keywords: decimal, decimal place value, per, of, by
- Convert between dollars and cents
- Compare decimal values
- Translate word problems into mathematical expressions and/or equations
- Convert metric units without a conversion chart
- Apply and use metric examples of length, mass, capacity, and temperature
- Calculate perimeter and area of squares and rectangles
- Add and subtract same units and mixed metric units
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- Calculate unit price
- Solve for the best buy
- Calculate household expenses (make a budget)
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Level 5 Math
Students need to demonstrate competency in these outcomes before progressing to the next level. In assessment, it may be determined that some of the outcomes have already been met. In this case, students will focus on the outcomes which still need to be achieved.
Learning Outcome
Students will be able to . . . |
Sub-outcomes/skills
By achieving this broader outcome, students will demonstrate that they can also . . . |
Sample Practice Tasks
Students can develop/practice the skills needed to achieve this outcome by . . . |
- Use mathematical vocabulary and language to communicate the concept of fractions
- Recognize the relationship between fractions and decimals
- Reduce fractions
- Convert between improper fractions and mixed numbers
- Identify equivalent fractions
- Evaluate fraction expressions using addition, subtraction, multiplication and division
- Translate a word problem into a mathematical equation and solve
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- Define and use keywords like fraction, numerator, denominator, mixed numbers, equivalent fractions, whole numbers, long division, greater than, lesser than, equals, simplify
- Express a number as a product of prime numbers or composite numbers, recognize prime numbers, greatest common factor, simplify
- Comparison of fractions and long division of whole numbers
- Group equivalent fractions
- Calculate perimeter and area of squares and rectangles
- Determine least common denominator (LCD), least common multiple (LCM)
- Simplify and write equivalent fractions using addition, subtraction, multiplication, division, common denominator
- Use critical thinking in real-life math applications
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- Label parts of a fraction – 2/3 (numerator and denominator)
- Use an image to show a proper fraction and mixed number (e.g., drawing, manipulatives, shapes, etc.)
- Find the odd one (e.g., 1/2, 2/4, 3/6, 8/9)
- Use common fraction function on a calculator
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Level 6 Math
Students need to demonstrate competency in these outcomes before progressing to the next level. In assessment, it may be determined that some of the outcomes have already been met. In this case, students will focus on the outcomes which still need to be achieved.
Learning Outcome
Students will be able to . . . |
Sub-outcomes/skills
By achieving this broader outcome, students will demonstrate that they can also . . . |
Sample Practice Tasks
Students can develop/practice the skills needed to achieve this outcome by . . . |
- Evaluate expressions using fractions, decimals and percent
- Represent proportion as a statement of equivalence between two ratios
- Write the relationship between two numbers or quantities as a rate
- Analyze data tables and graphs (bar, line, circle)
- Apply mathematical concepts and procedures to tasks of daily living
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- Convert a decimal to a percent, percent to decimal, a fraction to a percent, a percent to a fraction
- Recognize percent notation as a denominator of 100
- Compare a decimal to a percent, percent to decimal, a fraction to a percent, a percent to a fraction
- Explain or show with examples the different elements of a graph
- Identify different types of graphs (bar, line, circle, pictograph)
- Estimate percentages
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- Find a percent of a number
- Explain or use examples of key words: ratio, rate proportion, percent “of” commission, tax, discount, simple interest
- Find a number when a percent is given
- Find a percent of a number
- Determine if proportions are equal, using two different methods
- Solve a proportion for a missing term
- Express the relationship between two numbers as a percent
- Estimate percentages (mental shopping), calculate discounts, tips on service, tax, calculate wage increase, and budget
- Apply ratio and proportion to solve problems involving real life situations
- Calculate discounts, mark ups, budgets, payment schedules, wage increases, sale prices, taxation, commission and duty
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