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Number Sense: The student understands place value and how numbers relate, and fluently performs basic mental calculations and written operations.
Fact Fluency
Fact Fluency
Fact Fluency is the ability to efficiently recall the answers to basic arithmetic operations (addition, subtraction, multiplication, and division). While we believe it is important that students take time to think through solutions to more complex problems (e.g., when solving real-world problems), it is crucial that students can access basic math facts reasonably quickly and correctly. The lack of knowing basic math facts can become a big obstacle for students in understanding more complex concepts like regrouping, long division, multiplying multi-digit numbers, and fraction arithmetic.
Note: Some students may have learning differences that make certain aspects of math difficult. Our teachers use accommodations to help these students learn and work as effectively as possible.
Fact Fluency Expectations by Grade Level
Fact Fluency Expectations by Grade Level
By the end of each grade level, students should be fluent in the following operations:
FACT FLUENCY TIPS
FACT FLUENCY TIPS
Practice, practice, practice!
Students can use what they know to figure out what they don't know:
Math facts can be practiced anywhere, anytime:
At home? Practice with games like Bullwinkle, Salute, or Multiplication Squares. Cook with recipes using exact measurements and talk about the quantities. Double a recipe for an extra challenge! Grab a computer and practice with apps like Matific (grades K-3), IXL (grades 4-5), Hit the Button, or XtraMath (free parent registration required).
In the car? Practice facts orally (e.g., "Jaco, what is 6 plus 8?" "13" "That could be 6 + 7, try again" "Oh! 14!" "Great! What is 9 plus 7?"...). Listen to the Math Facts playlist in Spotify.
At the grocery store? Count how many items you put in the cart (counting). Estimate the total cost of the groceries (estimation and addition). Calculate the amount of change you'll receive (subtraction). Calculate the cost of products you want more than one of (multiplication). If a product contains multiple units, find the cost of one unit (e.g., a bar of chocolate has 8 squares and costs CHF 3.20, so 1 square would cost 3.20 ÷ 8 = CHF 0.40) (division).
Written Operations
Written Operations
In addition to fact fluency with basic operations, students should be able to solve more complex operations using written strategies. These strategies typically involve the use of algorithms (e.g., number bonds, vertical addition/subtraction/ multiplication, and long division), but may also include strategies like the area model for multiplication and division with partial quotients. Alternate strategies may be introduced depending on the needs of the students, but the goal is to teach students efficient methods for calculation.
Written Operations by Grade Level
Written Operations by Grade Level
WRITTEN OPERATIONS TIPS
WRITTEN OPERATIONS TIPS
Our math workbooks are a great source of problems for practicing written operations. Students are not expected to complete every problem in their workbooks for homework, so they can go back and find incomplete problems to practice. Students can check their answers with a parent or a calculator.
The workbook also has an example or two at the beginning of each section. Make sure to read through these to better understand what to do in that type of problem.
For students practicing division, a calculator will report a remainder as a decimal number (e.g., we teach students to write 19 ÷ 5 = 3 R 4, but a calculator will report 5.8). To check if a remainder is correct, divide the remainder by the divisor using a calculator. In the example above, you would calculate 4 ÷ 5 = 0.8, so 3 R 4 = 3.8, which is correct.
When working with apps like Matific (grades K-3) or IXL (grades 4-5), have paper and pencil out to work out the problems by hand.
Grid paper can help to line up numbers in their correct place to avoid place value errors.
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