![]() ![]() Some sets include a few cards with definitions of basic subtraction terminology. These printable math flash cards include all subtraction facts from 0 through 20. (Duplex Print, No Answers) Addition 18 to 20. (Duplex Print, No Answers) Addition 13 to 17. (Duplex Print, No Answers) Addition 0 to 12. Print on both sides of the paper, no folding or gluing needed. Horizontal Addition - Duplex Print, No Answersįollowing are "duplex, no answers" addition flash card sets. ![]() No folding or gluing or duplex printing needed. Following are the addition sets with the answers removed. Horizontal Addition - No AnswersĪ visitor named Katrina requested flash card sets that don't include answers. Duplex is available for the horizontal sets only. Horizontal Addition - Duplex Printįollowing are the "duplex" versions (2-sided printing) of the addition flash card sets. Vertical addition fold-and-glue flash cards: There is also one set of commutative property 0-12 addition facts. Some sets include a few cards defining basic addition termology. ![]() These printable math flash cards include all addition facts from 0 through 20. (Basically, try changing the scale setting in your PDF Print window to "Fit" or "Fit to page".) 1) Printable ADDITION Flash Cards If the flash cards are cut off when you print them, see below for PDF print margin troubleshooting. Also consider printing on thicker card stock paper so your flash cards last longer. ![]() Printers vary, so it's a good idea to print a "test page" before printing a full flash card set. Horizontal cards need Portrait orientation. Vertical flash cards need Landscape orientation. IMPORTANT: Be sure to check your printer's orientation before printing. However, two-sided printing requires a duplex-enabled printer or a special printing technique (see below for how to do the technique). No folding or gluing needed for either of these.ĭuplex printing allows you to print on both sides of the paper, with or without answers. I'm fairly sure that you need to be careful to use them (and memorisation) as a tool for thought, and not get sucked into memorising as a substitute for thinking.In addition to fold-and-glue, the horizontal sets are available in "no answers" format (one-sided only) as well as duplex (prints on both sides). It helped because it is necessary to think hard, and it is easier to think hard if the stuff you are thinking about is safely stored in long term memory and not taking up space in short term memory, reducing the scratch space available for use while thinking. Wouldn't it be lovely if we had some kind of super-pair so that this always works? I've fought my way back to understanding Mac Lane's definition. Perhaps we have a D-arrow and maybe instead of using f to get from c to Sd we can go a round about route g to get from c to Se and then Sh to complete the journey from Se to Sd. Can we relate the pair and the pair ? (Where did I get the idea of asking that question? From my rote memorisation!) Since that is the only way to relate objects in D to objects in C I guess we will use it a lot. Now you can use S to go from d to Sd and with any luck their will be a morphism. Indeed it occurs to me that given two categories C and D one would like to be able to relate an object in D to an object in C but morphisms only go between objects in the same category so one is stuck. Some time later the explanation starts making sense. If I don't know what he means I can still know what he says. Unfortunately the explanation makes less sense to me than the definition.Īh well. Fortunately he explains it on the next page. I've no idea what this weird gibberish is all about. Universals and Limits, Mac Lane writesĭefinition: If is a functor and and object of, a universal arrow from to is a pair consisting of an object of and an arrow of, such that to every pair with an object of and an arrow of, there is a unique arrow of with I guess you do your study of mathematics quite a lot of damage.įor an example from last week, I'm fighting Cats for Mats. there exists n such that and are close together" Turn it over. there exist m and n such that and are close together." What Alan's brain is willing to accept and able to see is "its Cauchy if. What strikes me about the Cauchy example, and remembering my own struggles with learning analysis, is that the text says "its Cauchy if. I use rote memorisation in my study of mathematics, but I'm not clear where flashcards fit in. ![]()
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