![]() Velocity includes both speed and direction, thus velocity can be either positive or negative while speed can only be positive. Velocity: The velocity of an object is the change in position (displacement) over a time interval. Addressing this issue requires a more thorough exposition on Special Relativity, the first of Einstein’s two Relativity Theories. All you need to do is travel at light speed.” The practice is, admittedly, a bit more difficult. MOst of my students have been trhough this stuff a few times and so it's far, far more common for them to do the "two negatives make a positive" thing.The simple answer is, “Yes, it is possible to stop time. The "Reverse - reverse!!" idea works for some and happily doesn't often turn into "-7 + -4 = -11", I think because of the visual difference (there's a plus sign between the "reverse! Reverse!") and that multiplication is powerful enough to impose its nature on the whole problem, throwing it into reverse. The other analogy I make is starting w/ positive times negative being negative (via repeated addition). the visual part of it seems to be important. This doesn't stand a *chance* unless I have the table ready. If I go bakc in time, that would be negative time - and of course it would be worth more If I want to know how much its value has changed I can multiply the number of years by 2000. (Yes, I tell 'em life isn't that simple.) I show a table of a car's value, decreasing at 2000 per year. This Substitution Puzzle from gets quite challenging.ĭo let me know if you use an interesting method or resource for teaching the multiplication of negative numbers. For example, if a = 3, b = -2 and c = -5, find the values of: abc bc 2 (bc) 2 a 2b 3 and so on. This topic is revisited in later years when students are practising substitution. ![]() There's a great resource from MathsPad for this - Using a Calculator: Odd One Out. It's important that students know how to use their calculator properly. It may be worth exploring calculator behaviour too (ie some calculators require brackets when squaring a negative). The squaring and cubing (etc) of negatives is worth discussing - students should spot that an even power gives a positive value (eg what is the value of (-1) 100?). CIMT's negative numbers chapter has activities for practising multiplying negatives.Ĭolin Foster suggests that you ask students to make up ten multiplications and ten divisions each giving an answer of –8 (eg –2 × –2 × –2 or –1 × 8 etc).MathsPad has a great range of negative number puzzles including arithmagons (some of these resources are only available to subscribers).I really like Don Steward's ' Directed Number Gaps' activity - it works well with any year group.Here are a few resource recommendations for this topic: An example of a common mistake is shown below (taken from via Nix the Tricks). The latter is confusing and may lead to misconceptions. 'A negative times a negative equals a positive' is clearly preferable to 'two minuses make a plus'. The History of Negative Numbers from NRICH is worth reading.I was inspired to write this post after watching this excellent video ' A negative times a negative is a.' by Mathologer (my new favourite YouTube channel!).I enjoy James Tanton's curriculum essays: Why is negative times negative positive?.The FAQ pages on Math Forum always provide interesting answers: Why is a negative times a negative a positive?.It's a good idea to read about a topic before you teach it, even relatively simple topics that you've taught many times before. Perhaps start with a numerical example instead of a formal proof.ģ + (-3) = 0 Multiply everything by -4 3(-4) + (-3)(-4) = 0(-4) -12 + (-3)(-4) = 0 (-3)(-4) must equal 12 to make this statement true. I'm not sure how accessible it is to Year 7 students, but it's worth a go.Ī and b are positive a + (-a) = 0 ![]() Here's a proof that is clear and accessible to us experienced mathematicians. ![]()
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