Course Profile: Fact Fluency and Number Sense

ADDIE Model

Course Profile: Fact Fluency for Multiplication & Related Division

Problem or Insight

There is a lack of understanding of numbers to assist in fact fluency in mathematics at the elementary and middle-school levels. Students are less inclined to memorize their times tables, and, even if they do, they lack the ability to manipulate numbers in order to make sense of them. If these needs are not addressed, there will continue to be a growing number of students who become easily stuck and frustrated due to a lack of mathematical fluency when it comes to more difficult concepts. Teachers often receive PD about the importance of fluency in reading and have an abundance of resources to support students… but math is often steps behind.

Learner Personas

Persona 1: Student is comfortable skip-counting to figure out multiplication and division facts but often gets frustrated with the amount of time that this takes. This student is unaware of the different strategies they can use to make this a quicker, easier experience.

Persona 2: Student who has memorized their times tables but is unable to approach numbers with flexible thinking. If this student does happen to forget a fact, they lack the strategies to figure it out in a concise way. They are not yet comfortable enough to use the distributive property to break down facts they find challenging.

Persona 3: Student who does not fully understand the concepts of multiplication and division… all they know is that it has something to do with “groups of” and resorts to drawing circles and dots to figure out even the simplest of facts.

Course Overview

This course will span four modules to support the suggested fact fluency sequence of teaching multiplication and related division facts. The first module will focus on foundational facts, and then move on to facts that build off of the foundations to build flexible thinking and comfort manipulating numbers.

Learning Environment

Learners: There is a large opportunity for students to receive the support they need to experience success in mathematics. Teachers are often swamped trying to reach curricular outcomes and don’t have the time to set aside to go ‘back to basics.’ In the past, students would be sent home with flashcards to memorize with their parents, but research is showing that it is more effective for students to build a conceptual understanding over rote memorization. “Number sense is the foundation for all higher-level mathematics” (Feikes & Schwingendorf, 2008).

Facilitators:

The fact that this course will be offered entirely online with videos and student practice means that it will create very little extra work for those facilitating the program. Students will be able to access this from home from a device, and parents won’t have to worry about trying to understand various strategies to help students gain that ever-important number sense foundation. Teachers and Educational Assistants will be able to ask students to access the modules online and check in with them to see what they learned and then build upon that learning.

The Domain and Discipline

This course will focus on fluency in basic mathematical facts through a variety of strategies to build number sense in learners. In turn, this will support learners when it comes to all outcomes in mathematics.

Learning Technologies

The learning technologies used can vary from computer to cellphone to tablet. All students from grades 3-8 in HTCSD have access to a shared Chromebook throughout the school day, and grade 7-8 students have 1:1 technology.

Access and Cost

Access to technology will not be an issue. There will also be no costs associated with this platform.

Course-Level Objectives

This course will assist students in meeting a variety of math outcomes from grades 3-8, as well as additional outcomes that require number sense.

• 3: Demonstrate understanding of multiplication to 5 x 5 and the corresponding division statements including:
  • representing and explaining using repeated addition or subtraction, equal grouping, and arrays
  • creating and solving situational questions
  • modelling processes using concrete, physical, and visual representations, and recording the process symbolically
  • relating multiplication and division.
    • Note: The focus of this outcome is for the students to become familiar with multiplication and division and strategies for mentally determining products and quotients. It is not intended that students memorize the basic facts.([C, CN, PS, R])
  • 3: Demonstrate an understanding of multiplication of whole numbers (limited to numbers less than or equal to 10) by:
    • applying mental mathematics strategies
    • explaining the results of multiplying by 0 and 1
    • ([C, CN, R])
  • 4: Demonstrate an understanding of multiplication (2- or 3-digit by 1-digit) by:
    • using personal strategies for multiplication, with and without concrete materials
    • using arrays to represent multiplication
    • connecting concrete representations to symbolic representations
    • estimating products
    • solving problems.
    • ([C, ME, PS, R, V])
  • 5: Demonstrate an understanding of division (1-digit divisor and up to 2-digit dividend) to solve problems by:
    • using personal strategies for dividing with and without concrete materials
    • estimating quotients
    • explaining the results of dividing by 1
    • solving problems involving division of whole numbers
    • relating division to multiplication.
    • ([C, CN, ME, PS, R, V])
  • 2: Analyze models of, develop strategies for, and carry out multiplication of whole numbers. ([C, CN, ME, PS, R, V])
  • 3: Demonstrate, with and without concrete materials, an understanding of division (3-digit by 1-digit) and interpret remainders to solve problems. ([C, CN, PS, R])
  • 2: Demonstrate understanding of factors and multiples (concretely, pictorially, and symbolically) including:
    • determining factors and multiples of numbers less than 100
    • relating factors and multiples to multiplication and division
    • determining and relating prime and composite numbers.
    • ([C, CN, ME, PS, R])
  • 4: Extend understanding of multiplication and division to decimals (1-digit whole number multipliers and 1-digit natural number divisors). ([C, CN, ME, PS, R])
  • 1: Demonstrate an understanding of division through the development and application of divisibility strategies for 2, 3, 4, 5, 6, 8, 9, and 10, and through an analysis of division involving zero. ([C, CN, ME,R])
  • Addition, subtraction, multiplication, and division of decimals to greater numbers of places, and the order of operations.
  • 2: Expand and demonstrate understanding of the addition, subtraction, multiplication, and division of decimals to greater numbers of decimal places, and the order of operations. ([C, CN, ME, PS, R, T])
  • 1: Demonstrate understanding of the square and principle square root of whole numbers concretely or pictorially and symbolically. ([CN, ME, R, T, V])
  • 4: Demonstrate understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially, and symbolically. ([C, CN, ME, PS])
  • 5: Demonstrate understanding of multiplication and division of integers concretely, pictorially, and symbolically. ([C, CN, PS, R, V])

Instructional Approach

• Pre-assessment reflections that allow learners to self-evaluate where they are at at the beginning of each module (formative assessment).
• Video lessons to teach strategies and skills to learn their multiplication and subsequent division facts.
• Activities (matching, flashcards) to allow practice on relevant facts within each module.
• Post-assessment reflection to allow learner to self-evaluate how they feel at the end of each module (formative assessment).
• Possibly the opportunity for bar-graph data collection to allow students to self-monitor their progress.

Major Platforms

• Canvas
• Lumi Education H5P
• 99math
• Wayground
• com

Educational Technologies

These platforms and technologies will provide students with online video lessons to learn/review strategies, online practice to apply those strategies and a self-assessment to see progress being made.

Course Design Pre-Planning