The math facts and concepts that we’ll be highlighting in the coming weeks and months should be well known by every student in grade 6 and up. They form the fabric of knowledge — the foundation necessary for success in the middle school and high school math classrooms. Most teachers assume that their students know this information. When facts and concepts are at a student’s fingertips, new material encountered becomes an extension of things they already know. Without them, it seems like every new topic has to be learned from the beginning — and the prospect of that can be daunting.
Each time we post for this age group, we recommend that you spend a few minutes with your student asking them questions based on the facts and concepts presented. If you feel they would be more comfortable doing the exercise alone, that’s okay too. The important thing is that they stop to ponder what they do — and do not — know. They’ll be pleasantly surprised by how many things they have already internalized. Moreover, they’ll be inspired to study and learn the ones they haven’t (yet).
Wholes and Parts
• The whole equals the sum of its parts.
• Each part equals the whole minus the sum of the other parts.
→ What are examples for each of these concepts?
Zero – 0
• Zero counts “the number of” when the answer is “none.”
• Zero is an even number.
• Zero is the only number that is neither positive nor negative.
• Any number plus its opposite is zero. [3 + -3 = 0]
• Any number plus zero is equal to that number. [369 + 0 = 369]
• Any number minus zero is equal to that number. [24 – 0 = 24]
• Every number is a factor of zero. That is, every number “goes into” zero exactly no (0) times, with “nothing left-over.”
• Division by zero is not possible.
→ Are any of these concepts confusing to you? If so, go back to ponder the concept. Why is the stated fact true? How would you prove it if asked by a teacher? Consider working with a number line to support your thought process.
One – 1
• One (1) times any number is equal to that number. [667 x 1 = 667]
• Any number divided by one (1) is equal to that number. [42 ÷ 1 = 42]
• One (1) is a factor of every number. [6 = 1 x 6]
• Negative one (-1) is a factor of every number. [6 = -1 x -6]
• Every number times its reciprocal equals one (1). [2/3 x 3/2 = 1]
• A proper fraction has a value less than one whole (1).
• An improper fraction has a value greater than one whole (1).
• Unity is the fraction that has a value equal to one whole (1).
→ Are any of these concepts confusing to you? If so, go back to ponder the concept. Why is the stated fact true? How would you prove it if asked by a teacher?
🎯 Understanding these values will help when working with upper-level fractions
and algebraic theory.