# MEMORY WORK - MATH FACTS 1

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5 MEMORY WORK - MATH FACTS SUBTRACTION BOARD (aka Strip Board) Subtraction with Golden Bead materials Subtraction with Colored Beads To memorize Subtraction Tables. Linear structure of subtraction. Analysis of number PRESENTATION SUMMARY: Set up the materials with the blue strips on the right of the board and red strips on the left. The tan strips without numbers are placed vertically above the subtraction board, from left to right, longest to shortest, respectively above the numbers -. As with the Addition Board, the blue strips are still placed first, however they are placed from left to right now. Depending on the age and understanding of your child, the first few times you present the subtraction facts on this board you may choose to do the work of laying the blue strips only on the top row with the numbers. Later when working through and entire facts tables you will still place the blank strips directly over the numbers on the top row to mark the minuend, but you can lay the blue and red strips on the blank rows of squares below the numbers of the top row to do the work of each equation. Explain that the blank strips are to cover the numbers we do not need, and that the blue strips (the subtrahend) are used to take away. Again, the blue unsegmented strips indicate you are removing a *group* of to see how many units are left (red strip). Subtraction Board MATERIALS: Subtraction Board Traditionally made of wood, this board has a red grid with a blue line at the number. Across the top are the numbers - printed in blue and - in red. The blue line after the nine is to serve as a reminder that subtraction facts with a difference (answer) of more than nine need not be memorized. There is also another version of the Subtraction board, a simplified version of this one, consisting only of the top line of this board. Two sets of Numbered Strips The blue and red strips are marked exactly the same as those with the Addition Board. Blank Strips The Subtraction Board has an additional set of strips without any markings having lengths from one to seventeen. They are used to mark the subtrahend by covering up all subtrahends greater than the number needed. (The child may choose to use only the longest blank strip to mark the minuend.) Livable Learning by JMJ Publishing - Montessori Made Easy: The BIG BOOK - Math Album

6 MEMORY WORK - MATH FACTS SUBTRACTION BOARD Exercise : Present equations with minuends -. Starting with as the first minuend, first cover all numbers to the right of the minuend. Take the vertical blank strip immediately above the and use it to horizontally cover the numbers to. Then proceed through the subtraction facts tables for. For - take the blue strip marked and place it to the left of the blank strip covering the numbers to. If you are doing the work on the numbered row of the board, all the blue numerals on the board will now be covered except for the number - this is the answer. For the next equation - the blank strip will remain in place covering -, then place the blue strip marked and the board will show the blue number. When doing the work on only the top row of numbers it is not necessary to use the red strips, however to compare equations you will want to place the corresponding red strips on the board to the left of the blue strips to indicate the answer. Supplements: As with any of the math boards, the Equations slips can be used to draw random equations to work out on the board. The child s work can be recorded on Tables Cards, in Table Booklets or on blank paper with a squared grid. Extension: This work could be extended for older children working with negative numbers, using a second board placed to the left of the Subtraction Strip Board for the negative numbers on the number line. This second board would use grey strips (to correspond with the grey Snake Game beads.) Exercise : Present equations with minuends -. If the answer is a number in red at the top of the equation, it is not one that needs to be memorized or recorded. Set up with as the minuend, there is no need for a blank strip. You may want to start by saying something like: Let s see how many numbers we can take away from and have a remainder of less than. Place the first blue subtrahend over the numbers - resulting in the equation -=. If you place the blue strip numbered next, the result of - will equal and since is a red number in the top row it is not an equation that we will record or memorize. Continue on with this work, using the blank strips immediately above the minuend to cover unneeded numbers in the top row of numbers. Work through the math facts for the minuends -. The facts Table Cards will help familiarize you with the equations that are necessary to this work of subtraction. Variation: Choose a subtrahend and use it to subtract from each number on the board, e.g. if you choose as the subtrahend you may choose to work with -, -, -, -, -, -, -, -, -. The blank strip will be moved for each equation. The aim of this variation is to lead the child to the discovery of the patterns of results of certain combinations, e.g. when is subtracted from any number, the result is the next smallest number, or with as the subtrahend when is subtracted from an even number the result is even, and when subtracted from an odd number the result is odd. Livable Learning by JMJ Publishing - Montessori Made Easy: The BIG BOOK - Math Album

7 MEMORY WORK - MATH FACTS SUBTRACTION CHARTS Subtraction Strip Board To memorize Subtraction Tables Recognition of number patterns Transfer from concrete to abstract addition PRESENTATION SUMMARIES: Charts provide the child with immediate feedback by allowing the child to look up answers quickly while acquiring the ability to working out problems in the head. The following terminology need only to be introduced to an older child: The minuend is the first number in a subtraction equation. It is the number to be made smaller. The subtrahend is the second number in a subtraction equation, it is the number to be subtracted. The answer to a subtraction equation is called the difference. Chart # Finger Chart The minuends are the numbers in red squares along the top of this chart and down the right diagonal. The subtrahends are in blue along the left diagonal. Place the right finger on the red minuend (the number to be subtracted from) and the left finger on the blue subtrahend (the number to be taken away). Moving first down and then across, where the two fingers meet is the answer. In this chart, differences have been eliminated which would result in a negative number, or with an answer of more than. Subtraction Chart - Blank Chart - = - = - = - = - = Subtraction Chart - Control Chart - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = Chart # Control Chart Chart # contains all basic subtraction facts for the tables -. - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = Chart # Blank Chart As with the other blank charts, this chart serves as a self test to the child as he fills in the differences with the Bingo tiles. On any of the blank charts you may use the Equation Cards as calling slips, and using extra photocopied or laminated copies of this chart for playing cards, more than one child can play Subtraction Bingo. Livable Learning by JMJ Publishing - Montessori Made Easy: The BIG BOOK - Math Album

9 MEMORY WORK - MATH FACTS MULTIPLICATION CHARTS Multiplication Board To memorize Multiplication Tables Recognition of number patterns Transfer from concrete to abstract multiplication PRESENTATION SUMMARIES: Multiplication is also known as fast addition, e.g. x is the same as ++. The multiplicand is simply an addend that is repeated. The multiplier of a multiplication equation is the number of times the multiplicand should be repeated. With x, the is the multiplier (the number of sets) and the is the multiplicand (the number in each set). The result of multiplying is known as the product. x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = Multiplication Chart - Control Chart x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = Chart # Control Chart Chart # contains all basic multiplication tables and their products up to x. This chart can be used to verbally quiz the child. x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = With Chart # as a control, you may also try a patterned chant of the math facts, reciting and clapping twice on the legs and once with the hands: One (hands clap on legs) times Two (hands clap on legs) is Two (hands clap together) Practice this chant with rhythm until the child can recite all of the facts tables without missing a beat one times one is one, (breath) one times two is two, (breath) one times three is three (breath)... x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = Multiplication Chart - Control Chart x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = Chart # Commutative Control Chart This control chart avoids repetition by eliminating all the commutative factors so there is only one combination of numbers on the board. As with addition, the order of the numbers in the multiplication equation has no effect on the result. To understand this chart, start with Chart #. The equation x remains, however the equation x is a commutative equation, so it is removed by covering it with a small slip of paper. Continue as you did with the Addition Commutative Control Chart, until what remains of Chart # is the same as Chart #. Now, you will see, with this simplification, instead of memorizing multiplication equations the child has only to memorize - since there is also no need to memorize the duplicates, or the table of TEN (now a repetition of the ONE table with a zero). Livable Learning by JMJ Publishing - Montessori Made Easy: The BIG BOOK - Math Album

10 MEMORY WORK - MATH FACTS ` ` Multiplication Chart - Finger Chart / Pythagoras Board Multiplication Chart - Half Chart Chart # Finger Chart This chart is a summary of the multiplication tables. It may also be called the Pythagorean table. The multipliers - are in the top horizontal blue border. (Multipliers are the first part of the multiplication equation). The multiplicands - are located in the left vertical border in red. The rest of the white squares are the products. Just as with the Addition Finger Chart #, the child moves one finger at a time to find the answer, starting with the right finger on the multiplier in the blue row and moving down to the row of the multiplicand, next moving the left finger across from the red column to meet the right finger. Note that with a multiplier or multiplicand of the operation of multiplication gives a number which will be found among the border squares. Practice on this chart may be done by picking random numbers and following the fingering to the answer. This chart can also be used in combination with the Tables Cards, Tables Booklets, or Equations Cards. Check the work of this chart with Control Chart #. Chart # Half Chart Horizontally this chart is half of the Multiplication Chart #. Just as with the Addition Half Chart the child finds both numbers, the multiplier and multiplicand, in the red column. The finger that is higher moves to the end of the row and then vertically down to same row as the other finger. The second finger moves right to meet the first finger to find the answer. Note that the answers on the outer diagonal are the squares of numbers. Check with Multiplication Control Chart #. Multiplication Chart - Blank Chart Chart # Blank Chart Here are some variations for blank charts: - Choose an equation card and place the answer tile on board. - Choose an answer tile first, then write down the equation on squared grid paper, then place the tile on the board. - Choose a number, think of all equations with that product. For example if is chosen then tiles would be placed at x, x, x, and x Livable Learning by JMJ Publishing - Montessori Made Easy: The BIG BOOK - Math Album

12 MEMORY WORK - MATH FACTS DIVISION CHARTS Division Board To memorize Division Tables Preparation for Long Division PRESENTATION SUMMARIES: The memorization of division is the synthesis of all four operations. Thus the reason for division being introduced last. With the basic division math facts the quotient should never be greater than and the remainder may not be equal to or greater than the divisor. Division Chart - Blank Chart Chart # Blank Chart This is the same chart as # except that it is blank. The fingering is the same and the answers are either written on the laminated chart with wipe-off markers, or numbered Bingo tiles are placed in the appropriate places on the chart. Use Chart # as a control. R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R Division Chart - Control Chart R R R R R Division Chart - Finger Chart Chart # Finger Chart Note the two colors for dividend numbers on the top row of the chart - the blue squares with white numbers are numbers that are equally divisible. The red numbers in white boxes are prime numbers (having only themselves and the number one as factors). Note the blue (divisor) numbers and the division signs are on the far left along the outer diagonal. Use this chart as a finger chart, e.g. to find start with right finger on at the top row and left finger on blue on the left diagonal, moving right finger down, then left finger across until they meet at the answer (quotient). Chart # Master Chart with Remainders This control chart is my original design and includes the remainders which will be found when working with the Division Board, Tables Cards or Booklets. This chart can be used as a control when working with Chart #. If the quotient box is empty the equation has a remainder. From the empty box on Chart # move the right finger to the right until you reach a box with a number (quotient). To find the remainder subtract the dividend directly above the quotient from the original dividend, e.g. move the right finger to for the quotient, then subtract from for the remainder of. Try another: first do the fingering for, then move the right finger from the empty square on Chart # to the right, stopping at the quotient then subtract from resulting in as a remainder resulting in the answer of Remainder or R. Livable Learning by JMJ Publishing - Montessori Made Easy: The BIG BOOK - Math Album

13 MEMORY WORK - MATERIALS MATH FACTS FOLDERS - charts, math tables cards, and equation cards. Use a Plano tackle box to store the equation cards ADDITION SUBTRACTION Tables Booklets MULTIPLICATION Multiplication and Division Boards DIVISION Addition and Subtraction Boards Livable Learning by JMJ Publishing - Montessori Made Easy: The BIG BOOK - Math Album

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