It is a race against the clock to answer 30 mental arithmetic questions. A game involving mental arithmetic and strategy for two players or one player against the computer. The programme covers Mental Arithmetic in addition, subtraction, multiplication and. It is created and designed based on children’s visualisation capacity through 55 specially-designed number bonds cards with association of 2 sets of Secrets. IBrainMath is a revolutionary way for children to learn Mental Arithmetic.
The app will appeal to most elementary-aged students, and will motivate many to practice critical addition, subtraction, multiplication, division, and number sequencing skills.This section gives the meaning of multiplication by presenting some images of it, and some of the kinds of problems it solves.Math Cards. MeaningMathLand: Mental Arithmetic is a fun, arcade-style math practice game that offers a heavy dose of play sprinkled with math problems. Bidmaze.This article deals with the meaning of multiplication, how it is introduced in Think Math!, and the early acquisition of facts.
Multiplication can be used as a “shortcut” for repeated addition — just as it can be used for solving many other problems — but that’s not what it is. The two operations behave differently and answer different questions.Multiplication is not repeated addition In most curricula, multiplication is introduced as repeated addition, or adding like groups. These usually include 2 unhelpful practices memorization.Multiplication and addition are the two basic arithmetic operations (division and subtraction are the names of operations that “undo,” or are the inverses of, multiplication and addition).Presented with two distinct sets — like the set of two red letters (vowels) and three blue letters (consonants) shown here — addition tells how many letters there are in all, and multiplication tells how many two-letter combinations can be made starting with a vowel and ending with a consonant.
Even if we have a preference for how we label the first two pictures below (insisting, for example, that one is 4 × 3 and the other is 3 × 4, which mathematicians do not do), we have no way of making such an assignment for the last tray. Children can, of course, rearrange objects grouped as 3 + 3 + 3 + 3 to show the equivalence to 4 + 4 + 4, but it takes rearranging, and is not “obvious.”But if the same cookies are arranged on a tray in rows and columns, it’s perfectly obvious that any way we hold the tray, the number of cookies is the same. Thinking only about repeated addition, we might compute the total cookies in these two pictures as 3 + 3 + 3 + 3 and 4 + 4 + 4With either the picture or the expressions, it is nothing short of a miracle that 4 × 3 = 3 × 4. (What does it mean to “add” something two-thirds of a time, or even to “add” it zero times?!) Moreover, some facts about multiplication — like commutativity, the fact that 4 × 3 = 3 × 4 — are hard to understand using repeated addition.The expressions 3 × 4 and 4 × 3 might be interpreted as plates with cookies.
This image works perfectly even for fractions and explains the algorithm for multiplication of fractions.If the three-by-four rectangle is placed “level” one way, it has 3 rows and 4 columns if we rotate it 90 degrees, rows become columns and columns become rows, so it will have 4 rows and 3 columns. When the elements in the rows and columns happen to be squares aligned side-to-side, multiplication counts those squares, and therefore tells us the area of the rectangle. The repeated addition idea is presented, too, but later, as an example of another kind of problem that multiplication solves.Given the number of rows and columns in a rectangular array, multiplication tells us how many elements are in the array without making us count them one by one or repeatedly add (or skip count) the elements in each row or column. Of course it is also useful to see how multiplication can simplify a computation that would otherwise require repeated addition, but that should not be multiplication’s primary image and, for that reason, preferably not its first image.In Think Math! multiplication is associated primarily with arrays and intersections, and connected quite early with “combinations” (including simple pairings) of things: streets and avenues, vowels and consonants in two-letter words, and so on. But if we describe that picture with a multiplication expression, 3 × 4 and 4 × 3 are equally correct there is no mathematically preferred order for writing the multiplication expressions.It is useful and possible for young students to develop an idea of multiplication that does survive the transition from whole numbers to fractions and decimals.
How many others can you make?Children can perform the experiments, creating the actual combinations, and they can invent their own system for recording these combinations. How many two-letter words can you make beginning with a red letter and ending with a blue letter?How many two-block towers, exactly this shape , can you make with these blocks?Here are two examples. Arrays and the multiplication tableEarly in second grade, children can solve and enjoy problems like these.Here are two red letters and three blue letters: A, I, S, N, T. This can be a fascinating cultural side topic for students who have learned to multiply multi-digit numbers.
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But we can see where this leads: the intersections, themselves, itemize the combinations that the children are looking for and help them see how to organize those lists the number of intersections can be found by multiplication, and children are getting a preview of those multiplication ideas. Intersections as a model for making an organized listWhen the number of possibilities is greater, as it is with the block-tower problem, children tend to miss combinations, or double-list them, unless they are systematic.Here is one way to visualize the pairings in these two experiments.Each intersection represents a combination.The × symbol itself is connected to the intersection imagery, the crossing of lines.Children can “drive” their finger along “A street” and “N avenue” and label the stoplight at that intersection “an.”They can check that they have a tower for each intersection: the intersection of blue-bottom and red-top for example.When second graders first perform these experiments, they are learning how to make systematic lists, not about multiplication. When the number of possibilities is small enough, as it is with the two-letter words, second graders quickly find all the possibilities. With the towers, children might draw them, or might indicate the color combinations in some more abstract way.
In fact, the focused, deliberate effort that seems to be needed for some triples (like 7, 8, 56) may be precisely because there are so few natural contexts in which those triples otherwise appear. The former are visually more like the insides of tables the latter are visually more like intersections.Anchor Building the basic factsWhen we see the same triples of numbers — 3, 5, 15 4, 3, 12 2, 5, 10 6, 4, 24 — popping up in different contexts, they begin to feel familiar even before any conscious effort to memorize them. The cells inside the table (and carefully avoiding getting confused with the “header” cells above each column and to the left of each row) again show how multiplication answers the question “how many pairings can be made?”Mathematics uses both structures — tables and intersecting lines — extensively.Multiplication is often represented by arrays of adjacent squares — the “area model” of multiplication — or by arrays of dots or other small objects.
Doubling and halvingIn first grade, children learn to double () all whole numbers up through 12. The following ideas present several contexts for the same basic facts to vary the practice (to keep it interesting and build a rich variety of imagery) so that by the time children are trying to memorize multiplication facts, they are already so familiar with the most common ones that they know them “cold,” and the number of remaining facts that require rote memorization is quite small (only fifteen!).
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