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Math Puzzles and Brain Teasers

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The document is a presentation on math puzzles and brain teasers by Kathleen Cotter Lawler. It covers topics such as patterns, squares, guided discovery, fractals, Asian cultures' relationship with math, math balancing, puzzle numbers, magic squares, and understanding place value. The presentation provides visual examples and explanations for each topic to illustrate different math concepts and puzzles in an engaging way.

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Math Puzzles and Brain Teasers Presented by Kathleen Cotter Lawler © Activities for Learning, Inc. 2012
Patterns © Activities for Learning, Inc. 2012
Patterns © Activities for Learning, Inc. 2012
Patterns © Activities for Learning, Inc. 2012
Patterns © Activities for Learning, Inc. 2012
Patterns © Activities for Learning, Inc. 2012
Patterns © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares 22 =4 © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares 32 =9 © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares 42 = 16 © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares 52 = 25 © Activities for Learning, Inc. 2012
Squares © Activities for Learning, Inc. 2012
Squares 62 = 36 © Activities for Learning, Inc. 2012
Guided Discovery © Activities for Learning, Inc. 2012
Guided Discovery To encourage and guide the child to discovery. © Activities for Learning, Inc. 2012
Guided Discovery To encourage and guide the child to discovery. Ask questions, encouraging the child to find the “trick” or “secret pattern”. © Activities for Learning, Inc. 2012
Guided Discovery It is vitally important that children think about what they are doing and not be satisfied with memorizing a rule. © Activities for Learning, Inc. 2012
Fractals © Activities for Learning, Inc. 2012
Fractals • Coined in 1975. © Activities for Learning, Inc. 2012
Fractals • Coined in 1975. • Derived from the Latin fractus meaning "broken" or "fractured." © Activities for Learning, Inc. 2012
Fractals © Activities for Learning, Inc. 2012
Fractals How many purple triangles? © Activities for Learning, Inc. 2012
Fractals Now how many purple triangles? © Activities for Learning, Inc. 2012
Fractals How about now? © Activities for Learning, Inc. 2012
Fractals Now how many purple triangles? © Activities for Learning, Inc. 2012
Fractals Now how many purple triangles? Cotter Tens Fractal © Activities for Learning, Inc. 2012
Fractals © Activities for Learning, Inc. 2012
Fractals © Activities for Learning, Inc. 2012
Fractals © Activities for Learning, Inc. 2012
Fractals © Activities for Learning, Inc. 2012
Fractals © Activities for Learning, Inc. 2012
Fractals © Activities for Learning, Inc. 2012
Fractals © Activities for Learning, Inc. 2012
Asian Cultures • In Asian cultures, families play with numbers the way Americans play with words. © Activities for Learning, Inc. 2012
Asian Cultures • In Asian cultures, families play with numbers the way Americans play with words. • This is one reason why Asians tend to succeed in math. © Activities for Learning, Inc. 2012
Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 © Activities for Learning, Inc. 2012
Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 10 = 3 + 7 © Activities for Learning, Inc. 2012
Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 6+2=8 © Activities for Learning, Inc. 2012
Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 three 4s = 10 + 2 © Activities for Learning, Inc. 2012
Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 three 4s = 10 + 2 3 x 4 = 12 © Activities for Learning, Inc. 2012
Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 three 4s = four 3s © Activities for Learning, Inc. 2012
Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 three 4s = four 3s 3x4=4x3 © Activities for Learning, Inc. 2012
Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 what + 5 = 3 + 9 © Activities for Learning, Inc. 2012
Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 a+5=3+9 7+5=3+9 © Activities for Learning, Inc. 2012
Puzzle Numbers © Activities for Learning, Inc. 2012
Puzzle Numbers Make an equation using 3 4 2 5 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
Puzzle Numbers Make an equation using 3 + 4 = 2+ 5 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
Puzzle Numbers Make an equation using 3 4 2 5 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
Puzzle Numbers Make an equation using 3+ 4– 2= 5 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
Puzzle Numbers Make an equation using 4 2 8 4 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
Puzzle Numbers Make an equation using 4 / 2= 8 / 4 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
Puzzle Numbers Make an equation using 4 2 8 4 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
Puzzle Numbers Make an equation using 4÷ 2 = 8÷ 4 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
Puzzle Numbers Make an equation using 4 2 8 4 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
Puzzle Numbers Make an equation using 4= 2 — ) 8=4 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
Magic Squares © Activities for Learning, Inc. 2012
Magic Squares Magic number is 15. © Activities for Learning, Inc. 2012
Magic Squares © Activities for Learning, Inc. 2012
Magic Squares © Activities for Learning, Inc. 2012
Magic Squares © Activities for Learning, Inc. 2012
Magic Squares © Activities for Learning, Inc. 2012
Magic Squares © Activities for Learning, Inc. 2012
Magic Squares © Activities for Learning, Inc. 2012
Magic Squares © Activities for Learning, Inc. 2012
Magic Squares © Activities for Learning, Inc. 2012
Magic Squares © Activities for Learning, Inc. 2012
Magic Squares © Activities for Learning, Inc. 2012
Magic Squares Magic number is 0. © Activities for Learning, Inc. 2012
Magic Squares © Activities for Learning, Inc. 2012
Asian Cultures • Asian language also plays a role with their success with math. © Activities for Learning, Inc. 2012
Asian Cultures • Asian language also plays a role with their success with math. • They use a “math way” to name numbers. © Activities for Learning, Inc. 2012
Math Way of Naming Numbers © Activities for Learning, Inc. 2012
Math Way of Naming Numbers Children often think of 14 as 14 ones, not ten and 4 ones. © Activities for Learning, Inc. 2012
Math Way of Naming Numbers Children often think of 14 as 14 ones, not ten and 4 ones. The pattern that is needed to make sense of tens and ones is hidden! © Activities for Learning, Inc. 2012
Math Way of Naming Numbers 11 = ten 1 20 = 2-ten 12 = ten 2 21 = 2-ten 1 13 = ten 3 22 = 2-ten 2 14 = ten 4 23 = 2-ten 3 .... .... 19 = ten 9 .... 99 = 9-ten 9 © Activities for Learning, Inc. 2012
Math Way of Naming Numbers • Just as reciting the alphabet doesn’t teach reading, counting doesn’t teach arithmetic. © Activities for Learning, Inc. 2012
Math Way of Naming Numbers • Just as reciting the alphabet doesn’t teach reading, counting doesn’t teach arithmetic. • Just as we first teach the sound of the letters, we first teach the name of the quantity (math way). © Activities for Learning, Inc. 2012
Math Way of Naming Numbers 11 = ten 1 20 = 2-ten 12 = ten 2 21 = 2-ten 1 13 = ten 3 22 = 2-ten 2 14 = ten 4 23 = 2-ten 3 .... .... 19 = ten 9 .... 99 = 9-ten 9 © Activities for Learning, Inc. 2012
Math Way of Naming Numbers • Only 11 words are needed to count to 100 the math way, 28 in English. (All Indo-European languages are non-standard in number naming.) © Activities for Learning, Inc. 2012
Math Way of Naming Numbers • Only 11 words are needed to count to 100 the math way, 28 in English. (All Indo-European languages are non-standard in number naming.) • Asian children learn mathematics using the math way of counting. © Activities for Learning, Inc. 2012
Math Way of Naming Numbers • Only 11 words are needed to count to 100 the math way, 28 in English. (All Indo-European languages are non-standard in number naming.) • Asian children learn mathematics using the math way of counting. • They understand place value in first grade; only half of U.S. children understand place value at the end of fourth grade. © Activities for Learning, Inc. 2012
Math Way of Naming Numbers • Only 11 words are needed to count to 100 the math way, 28 in English. (All Indo-European languages are non-standard in number naming.) • Asian children learn mathematics using the math way of counting. • They understand place value in first grade; only half of U.S. children understand place value at the end of fourth grade. • Mathematics is the science of patterns. The patterned math way of counting greatly helps children learn number sense. © Activities for Learning, Inc. 2012
Understanding Place Value 2-ten 2 0 © Activities for Learning, Inc. 2012
Understanding Place Value 2-ten 2 0 © Activities for Learning, Inc. 2012
Understanding Place Value 2-ten 2 0 © Activities for Learning, Inc. 2012
Understanding Place Value 3-ten 2 0 3 © Activities for Learning, Inc. 2012
Understanding Place Value 3-ten 2 0 3 © Activities for Learning, Inc. 2012
Understanding Place Value 3-ten 2 0 3 © Activities for Learning, Inc. 2012
Understanding Place Value 3-ten 7 2 0 3 7 © Activities for Learning, Inc. 2012
Understanding Place Value 3-ten 7 3 7 2 0 © Activities for Learning, Inc. 2012
Understanding Place Value 6-ten 2 0 6 © Activities for Learning, Inc. 2012
Understanding Place Value 6-ten 2 2 0 6 2 © Activities for Learning, Inc. 2012
Understanding Place Value 6-ten 2 6 2 2 0 © Activities for Learning, Inc. 2012
Understanding Place Value 10-ten 1 0 0 © Activities for Learning, Inc. 2012
Understanding Place Value 10-ten 1 0 0 © Activities for Learning, Inc. 2012
Understanding Place Value 10-ten 1 0 0 © Activities for Learning, Inc. 2012
Understanding Place Value 1 hundred 1 0 0 © Activities for Learning, Inc. 2012
Understanding Place Value 1 hundred 1 0 0 © Activities for Learning, Inc. 2012
Understanding Place Value 1 hundred 1 0 0 © Activities for Learning, Inc. 2012
Understanding Place Value 1 hundred 1 0 0 © Activities for Learning, Inc. 2012
Place Value Cards 3 0 3- ten 3 0 0 3 hun-dred 3 0 0 0 3 th- ou-sand © Activities for Learning, Inc. 2012
Place Value Cards 3 0 0 0 3 0 0 0 3 0 0 8 6 5 0 6 0 0 6 0 0 5 0 8 5 0 8 © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 Cleared © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 Thousands © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 Hundreds © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 Tens © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 Ones © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 8 + 6 © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 8 + 6 © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 8 + 6 © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 8 + 6 14 © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 8 + 6 14 © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 8 + 6 14 © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 8 + 6 14 © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 Why keep the two columns even? © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 Do we need to trade? © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 © Activities for Learning, Inc. 2012
AL Abacus - Side 2 1000 100 10 1 Do we need to trade? © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 3658 + 2738 6 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 3658 + 2738 6 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 3658 + 2738 6 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 3658 + 2738 6 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 3658 + 2738 396 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 396 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 396 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 396 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 6396 © Activities for Learning, Inc. 2012
Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 6396 © Activities for Learning, Inc. 2012
Short Division © Activities for Learning, Inc. 2012
Short Division 3) 4 7 1 © Activities for Learning, Inc. 2012
Short Division 3) 4 7 1 © Activities for Learning, Inc. 2012
Short Division 1 3) 4 7 1 © Activities for Learning, Inc. 2012
Short Division 1 3) 4 7 1 1 © Activities for Learning, Inc. 2012
Short Division 1 5 3) 4 7 1 1 © Activities for Learning, Inc. 2012
Short Division 1 5 3) 4 7 1 2 1 © Activities for Learning, Inc. 2012
Short Division 1 5 7 3) 4 7 1 2 1 © Activities for Learning, Inc. 2012
Short Division 1 5 7 3) 4 7 1 2 1 © Activities for Learning, Inc. 2012
Short Division 9) 8 0 5 3 © Activities for Learning, Inc. 2012
Short Division 9) 8 0 5 3 © Activities for Learning, Inc. 2012
Short Division 8 9) 8 0 5 3 © Activities for Learning, Inc. 2012
Short Division 8 9) 8 0 5 3 8 © Activities for Learning, Inc. 2012
Short Division 8 9 9) 8 0 5 3 8 © Activities for Learning, Inc. 2012
Short Division 8 9 9) 8 0 5 3 8 4 © Activities for Learning, Inc. 2012
Short Division 8 94 9) 8 0 5 3 8 4 © Activities for Learning, Inc. 2012
Short Division 8 9 4 r7 9) 8 0 5 3 8 4 © Activities for Learning, Inc. 2012
Short Division 8 9 4 r7 9) 8 0 5 3 8 4 © Activities for Learning, Inc. 2012
Short Division 4) 9 3 6 2 © Activities for Learning, Inc. 2012
Short Division 4) 9 3 6 2 © Activities for Learning, Inc. 2012
Short Division 4) 9 3 6 2 2 © Activities for Learning, Inc. 2012
Short Division 4) 9 3 6 2 1 2 © Activities for Learning, Inc. 2012
Short Division 4) 9 3 6 2 1 23 © Activities for Learning, Inc. 2012
Short Division 4) 9 3 6 2 1 1 23 © Activities for Learning, Inc. 2012
Short Division 4) 9 3 6 2 1 1 234 © Activities for Learning, Inc. 2012
Short Division 4) 9 3 6 2 1 1 2340 © Activities for Learning, Inc. 2012
Short Division 4) 9 3 6 2 1 1 2 3 4 0 r2 © Activities for Learning, Inc. 2012
Short Division 4) 9 3 6 2 1 1 2 3 4 0 r2 © Activities for Learning, Inc. 2012
Multivides © Activities for Learning, Inc. 2012
Multivides • Self-checking multiplication and division exercise. © Activities for Learning, Inc. 2012
Multivides • Self-checking multiplication and division exercise. • Any remainder means a mistake was made somewhere. © Activities for Learning, Inc. 2012
Multivides 7 Start with any number. Multiply it by 2… © Activities for Learning, Inc. 2012
Multivides 7 x2 14 Start with any number. Multiply it by 2… © Activities for Learning, Inc. 2012
Multivides 7 x2 14 Start with any x3 number. 42 Multiply it by 2, then 3. . . © Activities for Learning, Inc. 2012
Multivides 7 x2 14 Start with any x3 number. 42 x4 Multiply it by 168 2, then 3, then 4. . . © Activities for Learning, Inc. 2012
Multivides 7 x2 14 Start with any x3 number. 42 x4 Multiply it by 168 x5 2, then 3, 840 then 4, and x6 on up 5 040 to 9. x7 35 280 x8 282 240 x9 2 540 160 © Activities for Learning, Inc. 2012
Multivides 7 x2 14 Next divide the x3 total by 2. . . 42 x4 168 x5 840 x6 5 040 x7 35 280 x8 282 240 x9 2 540 160 © Activities for Learning, Inc. 2012
Multivides 7 x2 14 Next divide the x3 2)2 540 160 total by 2. . . 42 1 270 080 x4 168 x5 840 x6 5 040 x7 35 280 x8 282 240 x9 2 540 160 © Activities for Learning, Inc. 2012
Multivides 7 x2 14 Next divide by x3 2)2 540 160 2, then 3. . . 42 3)1 270 080 x4 423 360 168 x5 840 x6 5 040 x7 35 280 x8 282 240 x9 2 540 160 © Activities for Learning, Inc. 2012
Multivides 7 x2 14 Next divide by x3 2)2 540 160 2, then 3, then 42 3)1 270 080 4. . . x4 4)423 360 168 105 840 x5 840 x6 5 040 x7 35 280 x8 282 240 x9 2 540 160 © Activities for Learning, Inc. 2012
Multivides 7 x2 14 Next divide by x3 2)2 540 160 2, then 3, then 42 3)1 270 080 4, on up to 9. x4 4)423 360 168 5)105 840 x5 6)21 168 840 7)3 528 x6 8)504 5 040 x7 9)63 35 280 7 x8 282 240 x9 2 540 160 © Activities for Learning, Inc. 2012
Multivides 7 x2 14 Final quotient x3 2)2 540 160 must equal 42 3)1 270 080 starting x4 4)423 360 number. 168 5)105 840 x5 6)21 168 840 7)3 528 x6 8)504 5 040 x7 9)63 35 280 7 x8 282 240 x9 2 540 160 © Activities for Learning, Inc. 2012
Multivides A multivide a day keeps the flashcards away! © Activities for Learning, Inc. 2012
Check Numbers © Activities for Learning, Inc. 2012
Check Numbers • Method to check answers. © Activities for Learning, Inc. 2012
Check Numbers • Method to check answers. • Each number has a check number. © Activities for Learning, Inc. 2012
Check Numbers 34 © Activities for Learning, Inc. 2012
Check Numbers 34 3+4=7 © Activities for Learning, Inc. 2012
Check Numbers 34 (7) 3+4=7 © Activities for Learning, Inc. 2012
Check Numbers 28 © Activities for Learning, Inc. 2012
Check Numbers 28 2 + 8 = 10 © Activities for Learning, Inc. 2012
Check Numbers 28 2 + 8 = 10; 1+0=1 © Activities for Learning, Inc. 2012
Check Numbers 28 (1) 2 + 8 = 10; 1+0=1 © Activities for Learning, Inc. 2012
Check Numbers 5635 © Activities for Learning, Inc. 2012
Check Numbers 5635 5 + 6 = 11 and 3 + 5 = 8 © Activities for Learning, Inc. 2012
Check Numbers 5635 5 + 6 = 11 and 3 + 5 = 8 1 + 1 = 2 + 8 = 10 © Activities for Learning, Inc. 2012
Check Numbers 5635 5 + 6 = 11 and 3 + 5 = 8 1 + 1 = 2 + 8 = 10 1+0=1 © Activities for Learning, Inc. 2012
Check Numbers 5635 (1) 5 + 6 = 11 and 3 + 5 = 8 1 + 1 = 2 + 8 = 10 1+0=1 © Activities for Learning, Inc. 2012
Check Numbers 5635 6 + 3 = 9 = 0 and 5 + 5 = 10 = 1 © Activities for Learning, Inc. 2012
Check Numbers 5635 (1) 6 + 3 = 9 = 0 and 5 + 5 = 10 = 1 © Activities for Learning, Inc. 2012
Check Numbers 5635 (1) 6 + 3 = 9 = 0 and 5 + 5 = 10 = 1 © Activities for Learning, Inc. 2012
Check Numbers 7146 © Activities for Learning, Inc. 2012
Check Numbers 7146 7 + 1 = 8 and 4 + 6 = 10 © Activities for Learning, Inc. 2012
Check Numbers 7146 7 + 1 = 8 and 4 + 6 = 10 8+1+0=9=0 © Activities for Learning, Inc. 2012
Check Numbers 7146 (0) 7 + 1 = 8 and 4 + 6 = 10 8+1+0=9=0 © Activities for Learning, Inc. 2012
Check Numbers • Method to check answers. • Each number has a check number. • When you calculate equations, the check numbers of the numbers will be the same as the check number of the answer. © Activities for Learning, Inc. 2012
Check Numbers 5635 + 28 © Activities for Learning, Inc. 2012
Check Numbers 5635 + 28 5663 © Activities for Learning, Inc. 2012
Check Numbers 5635 (1) + 28 5663 © Activities for Learning, Inc. 2012
Check Numbers 5635 (1) + 28 (1) 5663 © Activities for Learning, Inc. 2012
Check Numbers 5635 (1) + 28 (1) 5663 (2) © Activities for Learning, Inc. 2012
Check Numbers 5635 (1) + 28 (1) 5663 (2) © Activities for Learning, Inc. 2012
Check Numbers 8863 + 687 © Activities for Learning, Inc. 2012
Check Numbers 8863 + 687 9550 © Activities for Learning, Inc. 2012
Check Numbers 8863 (7) + 687 9550 © Activities for Learning, Inc. 2012
Check Numbers 8863 (7) + 687 (3) 9550 © Activities for Learning, Inc. 2012
Check Numbers 8863 (7) + 687 (3) 9550 (1) © Activities for Learning, Inc. 2012
Check Numbers 8863 (7) + 687 (3) 9550 (1) © Activities for Learning, Inc. 2012
Check Numbers 7146 x 7 © Activities for Learning, Inc. 2012
Check Numbers 7146 x 7 50,022 © Activities for Learning, Inc. 2012
Check Numbers 7146 (0) x 7 50,022 © Activities for Learning, Inc. 2012
Check Numbers 7146 (0) x 7 (7) 50,022 © Activities for Learning, Inc. 2012
Check Numbers 7146 (0) x 7 (7) 50,022 (0) © Activities for Learning, Inc. 2012
Check Numbers 7146 (0) x 7 (7) 50,022 (0) © Activities for Learning, Inc. 2012
Check Numbers ) 9 805 3 © Activities for Learning, Inc. 2012
Check Numbers 89r7 ) 9 805 4 3 © Activities for Learning, Inc. 2012
Check Numbers 89r7 (0) ) 9 805 4 3 © Activities for Learning, Inc. 2012
Check Numbers 89r7 (0) ) 9 8 0 5 (7) 4 3 © Activities for Learning, Inc. 2012
Check Numbers (3) (7) 89r7 (0) ) 9 8 0 5 (7) 4 3 © Activities for Learning, Inc. 2012
Check Numbers (3) (7) 89r7 (0) ) 9 8 0 5 (7) 4 3 (3) x © Activities for Learning, Inc. 2012
Check Numbers (3) (7) 89r7 (0) ) 9 8 0 5 (7) 4 3 (3) x © Activities for Learning, Inc. 2012
Simplifying Fractions © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions 21 28 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions 21 28 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions 21 28 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions 45 72 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions 45 72 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions 45 72 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions 12 16 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions 12 16 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions 12 16 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions 12 16 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions 12 16 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Simplifying Fractions 12 16 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
Problem Solving © Activities for Learning, Inc. 2012
Problem Solving A problem is not a problem if the solution is obvious. © Activities for Learning, Inc. 2012
Problem Solving A problem is not a problem if the solution is obvious. Japanese teachers discuss one problem in depth rather than four problems superficially. © Activities for Learning, Inc. 2012
Problem Solving A problem is not a problem if the solution is obvious. Japanese teachers discuss one problem in depth rather than four problems superficially. They encourage multiple solutions. © Activities for Learning, Inc. 2012
Problem Solving A problem is not a problem if the solution is obvious. Japanese teachers discuss one problem in depth rather than four problems superficially. They encourage multiple solutions. Wrong solutions are discussed. © Activities for Learning, Inc. 2012
Problem Solving A problem is not a problem if the solution is obvious. Japanese teachers discuss one problem in depth rather than four problems superficially. They encourage multiple solutions. Wrong solutions are discussed. The students do not look for “key” words. © Activities for Learning, Inc. 2012
Critical Thinkers Ellis, D. Becoming a Master Student, 1997. © Activities for Learning, Inc. 2012
Critical Thinkers Critical Thinkers: distinguish between fact and opinion; Ellis, D. Becoming a Master Student, 1997. © Activities for Learning, Inc. 2012
Critical Thinkers Critical Thinkers: distinguish between fact and opinion; ask questions; Ellis, D. Becoming a Master Student, 1997. © Activities for Learning, Inc. 2012
Critical Thinkers Critical Thinkers: distinguish between fact and opinion; ask questions; make detailed observations; Ellis, D. Becoming a Master Student, 1997. © Activities for Learning, Inc. 2012
Critical Thinkers Critical Thinkers: distinguish between fact and opinion; ask questions; make detailed observations; uncover assumptions and define their terms; and Ellis, D. Becoming a Master Student, 1997. © Activities for Learning, Inc. 2012
Critical Thinkers Critical Thinkers: distinguish between fact and opinion; ask questions; make detailed observations; uncover assumptions and define their terms; and assertions based on sound logic and solid evidence. Ellis, D. Becoming a Master Student, 1997. © Activities for Learning, Inc. 2012
How to Assist Critical Thinking © Activities for Learning, Inc. 2012
How to Assist Critical Thinking How did you get your answer? © Activities for Learning, Inc. 2012
How to Assist Critical Thinking How did you get your answer? Why did that work? © Activities for Learning, Inc. 2012
How to Assist Critical Thinking How did you get your answer? Why did that work? Will that work every time? © Activities for Learning, Inc. 2012
How to Assist Critical Thinking How did you get your answer? Why did that work? Will that work every time? Be quiet! Allow processing and thinking time. © Activities for Learning, Inc. 2012
Math Puzzles and Brain Teasers Presented by Kathleen Cotter Lawler © Activities for Learning, Inc. 2012

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Math Puzzles and Brain Teasers

  • 1. Math Puzzles and Brain Teasers Presented by Kathleen Cotter Lawler © Activities for Learning, Inc. 2012
  • 2. Patterns © Activities for Learning, Inc. 2012
  • 3. Patterns © Activities for Learning, Inc. 2012
  • 4. Patterns © Activities for Learning, Inc. 2012
  • 5. Patterns © Activities for Learning, Inc. 2012
  • 6. Patterns © Activities for Learning, Inc. 2012
  • 7. Patterns © Activities for Learning, Inc. 2012
  • 8. Squares © Activities for Learning, Inc. 2012
  • 9. Squares © Activities for Learning, Inc. 2012
  • 10. Squares © Activities for Learning, Inc. 2012
  • 11. Squares © Activities for Learning, Inc. 2012
  • 12. Squares © Activities for Learning, Inc. 2012
  • 13. Squares 22 =4 © Activities for Learning, Inc. 2012
  • 14. Squares © Activities for Learning, Inc. 2012
  • 15. Squares © Activities for Learning, Inc. 2012
  • 16. Squares © Activities for Learning, Inc. 2012
  • 17. Squares © Activities for Learning, Inc. 2012
  • 18. Squares © Activities for Learning, Inc. 2012
  • 19. Squares 32 =9 © Activities for Learning, Inc. 2012
  • 20. Squares © Activities for Learning, Inc. 2012
  • 21. Squares © Activities for Learning, Inc. 2012
  • 22. Squares © Activities for Learning, Inc. 2012
  • 23. Squares © Activities for Learning, Inc. 2012
  • 24. Squares © Activities for Learning, Inc. 2012
  • 25. Squares © Activities for Learning, Inc. 2012
  • 26. Squares © Activities for Learning, Inc. 2012
  • 27. Squares 42 = 16 © Activities for Learning, Inc. 2012
  • 28. Squares © Activities for Learning, Inc. 2012
  • 29. Squares 52 = 25 © Activities for Learning, Inc. 2012
  • 30. Squares © Activities for Learning, Inc. 2012
  • 31. Squares 62 = 36 © Activities for Learning, Inc. 2012
  • 32. Guided Discovery © Activities for Learning, Inc. 2012
  • 33. Guided Discovery To encourage and guide the child to discovery. © Activities for Learning, Inc. 2012
  • 34. Guided Discovery To encourage and guide the child to discovery. Ask questions, encouraging the child to find the “trick” or “secret pattern”. © Activities for Learning, Inc. 2012
  • 35. Guided Discovery It is vitally important that children think about what they are doing and not be satisfied with memorizing a rule. © Activities for Learning, Inc. 2012
  • 36. Fractals © Activities for Learning, Inc. 2012
  • 37. Fractals • Coined in 1975. © Activities for Learning, Inc. 2012
  • 38. Fractals • Coined in 1975. • Derived from the Latin fractus meaning "broken" or "fractured." © Activities for Learning, Inc. 2012
  • 39. Fractals © Activities for Learning, Inc. 2012
  • 40. Fractals How many purple triangles? © Activities for Learning, Inc. 2012
  • 41. Fractals Now how many purple triangles? © Activities for Learning, Inc. 2012
  • 42. Fractals How about now? © Activities for Learning, Inc. 2012
  • 43. Fractals Now how many purple triangles? © Activities for Learning, Inc. 2012
  • 44. Fractals Now how many purple triangles? Cotter Tens Fractal © Activities for Learning, Inc. 2012
  • 45. Fractals © Activities for Learning, Inc. 2012
  • 46. Fractals © Activities for Learning, Inc. 2012
  • 47. Fractals © Activities for Learning, Inc. 2012
  • 48. Fractals © Activities for Learning, Inc. 2012
  • 49. Fractals © Activities for Learning, Inc. 2012
  • 50. Fractals © Activities for Learning, Inc. 2012
  • 51. Fractals © Activities for Learning, Inc. 2012
  • 52. Asian Cultures • In Asian cultures, families play with numbers the way Americans play with words. © Activities for Learning, Inc. 2012
  • 53. Asian Cultures • In Asian cultures, families play with numbers the way Americans play with words. • This is one reason why Asians tend to succeed in math. © Activities for Learning, Inc. 2012
  • 54. Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 © Activities for Learning, Inc. 2012
  • 55. Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 10 = 3 + 7 © Activities for Learning, Inc. 2012
  • 56. Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 6+2=8 © Activities for Learning, Inc. 2012
  • 57. Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 three 4s = 10 + 2 © Activities for Learning, Inc. 2012
  • 58. Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 three 4s = 10 + 2 3 x 4 = 12 © Activities for Learning, Inc. 2012
  • 59. Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 three 4s = four 3s © Activities for Learning, Inc. 2012
  • 60. Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 three 4s = four 3s 3x4=4x3 © Activities for Learning, Inc. 2012
  • 61. Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 what + 5 = 3 + 9 © Activities for Learning, Inc. 2012
  • 62. Math Balance 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 a+5=3+9 7+5=3+9 © Activities for Learning, Inc. 2012
  • 63. Puzzle Numbers © Activities for Learning, Inc. 2012
  • 64. Puzzle Numbers Make an equation using 3 4 2 5 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
  • 65. Puzzle Numbers Make an equation using 3 + 4 = 2+ 5 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
  • 66. Puzzle Numbers Make an equation using 3 4 2 5 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
  • 67. Puzzle Numbers Make an equation using 3+ 4– 2= 5 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
  • 68. Puzzle Numbers Make an equation using 4 2 8 4 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
  • 69. Puzzle Numbers Make an equation using 4 / 2= 8 / 4 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
  • 70. Puzzle Numbers Make an equation using 4 2 8 4 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
  • 71. Puzzle Numbers Make an equation using 4÷ 2 = 8÷ 4 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
  • 72. Puzzle Numbers Make an equation using 4 2 8 4 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
  • 73. Puzzle Numbers Make an equation using 4= 2 — ) 8=4 with mathematics symbols, = + – x ÷ ) /, keeping the numbers in the same order. © Activities for Learning, Inc. 2012
  • 74. Magic Squares © Activities for Learning, Inc. 2012
  • 75. Magic Squares Magic number is 15. © Activities for Learning, Inc. 2012
  • 76. Magic Squares © Activities for Learning, Inc. 2012
  • 77. Magic Squares © Activities for Learning, Inc. 2012
  • 78. Magic Squares © Activities for Learning, Inc. 2012
  • 79. Magic Squares © Activities for Learning, Inc. 2012
  • 80. Magic Squares © Activities for Learning, Inc. 2012
  • 81. Magic Squares © Activities for Learning, Inc. 2012
  • 82. Magic Squares © Activities for Learning, Inc. 2012
  • 83. Magic Squares © Activities for Learning, Inc. 2012
  • 84. Magic Squares © Activities for Learning, Inc. 2012
  • 85. Magic Squares © Activities for Learning, Inc. 2012
  • 86. Magic Squares Magic number is 0. © Activities for Learning, Inc. 2012
  • 87. Magic Squares © Activities for Learning, Inc. 2012
  • 88. Asian Cultures • Asian language also plays a role with their success with math. © Activities for Learning, Inc. 2012
  • 89. Asian Cultures • Asian language also plays a role with their success with math. • They use a “math way” to name numbers. © Activities for Learning, Inc. 2012
  • 90. Math Way of Naming Numbers © Activities for Learning, Inc. 2012
  • 91. Math Way of Naming Numbers Children often think of 14 as 14 ones, not ten and 4 ones. © Activities for Learning, Inc. 2012
  • 92. Math Way of Naming Numbers Children often think of 14 as 14 ones, not ten and 4 ones. The pattern that is needed to make sense of tens and ones is hidden! © Activities for Learning, Inc. 2012
  • 93. Math Way of Naming Numbers 11 = ten 1 20 = 2-ten 12 = ten 2 21 = 2-ten 1 13 = ten 3 22 = 2-ten 2 14 = ten 4 23 = 2-ten 3 .... .... 19 = ten 9 .... 99 = 9-ten 9 © Activities for Learning, Inc. 2012
  • 94. Math Way of Naming Numbers • Just as reciting the alphabet doesn’t teach reading, counting doesn’t teach arithmetic. © Activities for Learning, Inc. 2012
  • 95. Math Way of Naming Numbers • Just as reciting the alphabet doesn’t teach reading, counting doesn’t teach arithmetic. • Just as we first teach the sound of the letters, we first teach the name of the quantity (math way). © Activities for Learning, Inc. 2012
  • 96. Math Way of Naming Numbers 11 = ten 1 20 = 2-ten 12 = ten 2 21 = 2-ten 1 13 = ten 3 22 = 2-ten 2 14 = ten 4 23 = 2-ten 3 .... .... 19 = ten 9 .... 99 = 9-ten 9 © Activities for Learning, Inc. 2012
  • 97. Math Way of Naming Numbers • Only 11 words are needed to count to 100 the math way, 28 in English. (All Indo-European languages are non-standard in number naming.) © Activities for Learning, Inc. 2012
  • 98. Math Way of Naming Numbers • Only 11 words are needed to count to 100 the math way, 28 in English. (All Indo-European languages are non-standard in number naming.) • Asian children learn mathematics using the math way of counting. © Activities for Learning, Inc. 2012
  • 99. Math Way of Naming Numbers • Only 11 words are needed to count to 100 the math way, 28 in English. (All Indo-European languages are non-standard in number naming.) • Asian children learn mathematics using the math way of counting. • They understand place value in first grade; only half of U.S. children understand place value at the end of fourth grade. © Activities for Learning, Inc. 2012
  • 100. Math Way of Naming Numbers • Only 11 words are needed to count to 100 the math way, 28 in English. (All Indo-European languages are non-standard in number naming.) • Asian children learn mathematics using the math way of counting. • They understand place value in first grade; only half of U.S. children understand place value at the end of fourth grade. • Mathematics is the science of patterns. The patterned math way of counting greatly helps children learn number sense. © Activities for Learning, Inc. 2012
  • 101. Understanding Place Value 2-ten 2 0 © Activities for Learning, Inc. 2012
  • 102. Understanding Place Value 2-ten 2 0 © Activities for Learning, Inc. 2012
  • 103. Understanding Place Value 2-ten 2 0 © Activities for Learning, Inc. 2012
  • 104. Understanding Place Value 3-ten 2 0 3 © Activities for Learning, Inc. 2012
  • 105. Understanding Place Value 3-ten 2 0 3 © Activities for Learning, Inc. 2012
  • 106. Understanding Place Value 3-ten 2 0 3 © Activities for Learning, Inc. 2012
  • 107. Understanding Place Value 3-ten 7 2 0 3 7 © Activities for Learning, Inc. 2012
  • 108. Understanding Place Value 3-ten 7 3 7 2 0 © Activities for Learning, Inc. 2012
  • 109. Understanding Place Value 6-ten 2 0 6 © Activities for Learning, Inc. 2012
  • 110. Understanding Place Value 6-ten 2 2 0 6 2 © Activities for Learning, Inc. 2012
  • 111. Understanding Place Value 6-ten 2 6 2 2 0 © Activities for Learning, Inc. 2012
  • 112. Understanding Place Value 10-ten 1 0 0 © Activities for Learning, Inc. 2012
  • 113. Understanding Place Value 10-ten 1 0 0 © Activities for Learning, Inc. 2012
  • 114. Understanding Place Value 10-ten 1 0 0 © Activities for Learning, Inc. 2012
  • 115. Understanding Place Value 1 hundred 1 0 0 © Activities for Learning, Inc. 2012
  • 116. Understanding Place Value 1 hundred 1 0 0 © Activities for Learning, Inc. 2012
  • 117. Understanding Place Value 1 hundred 1 0 0 © Activities for Learning, Inc. 2012
  • 118. Understanding Place Value 1 hundred 1 0 0 © Activities for Learning, Inc. 2012
  • 119. Place Value Cards 3 0 3- ten 3 0 0 3 hun-dred 3 0 0 0 3 th- ou-sand © Activities for Learning, Inc. 2012
  • 120. Place Value Cards 3 0 0 0 3 0 0 0 3 0 0 8 6 5 0 6 0 0 6 0 0 5 0 8 5 0 8 © Activities for Learning, Inc. 2012
  • 121. AL Abacus - Side 2 1000 100 10 1 Cleared © Activities for Learning, Inc. 2012
  • 122. AL Abacus - Side 2 1000 100 10 1 Thousands © Activities for Learning, Inc. 2012
  • 123. AL Abacus - Side 2 1000 100 10 1 Hundreds © Activities for Learning, Inc. 2012
  • 124. AL Abacus - Side 2 1000 100 10 1 Tens © Activities for Learning, Inc. 2012
  • 125. AL Abacus - Side 2 1000 100 10 1 Ones © Activities for Learning, Inc. 2012
  • 126. AL Abacus - Side 2 1000 100 10 1 8 + 6 © Activities for Learning, Inc. 2012
  • 127. AL Abacus - Side 2 1000 100 10 1 8 + 6 © Activities for Learning, Inc. 2012
  • 128. AL Abacus - Side 2 1000 100 10 1 8 + 6 © Activities for Learning, Inc. 2012
  • 129. AL Abacus - Side 2 1000 100 10 1 8 + 6 14 © Activities for Learning, Inc. 2012
  • 130. AL Abacus - Side 2 1000 100 10 1 8 + 6 14 © Activities for Learning, Inc. 2012
  • 131. AL Abacus - Side 2 1000 100 10 1 8 + 6 14 © Activities for Learning, Inc. 2012
  • 132. AL Abacus - Side 2 1000 100 10 1 8 + 6 14 © Activities for Learning, Inc. 2012
  • 133. AL Abacus - Side 2 1000 100 10 1 Why keep the two columns even? © Activities for Learning, Inc. 2012
  • 134. AL Abacus - Side 2 1000 100 10 1 © Activities for Learning, Inc. 2012
  • 135. AL Abacus - Side 2 1000 100 10 1 Do we need to trade? © Activities for Learning, Inc. 2012
  • 136. AL Abacus - Side 2 1000 100 10 1 © Activities for Learning, Inc. 2012
  • 137. AL Abacus - Side 2 1000 100 10 1 © Activities for Learning, Inc. 2012
  • 138. AL Abacus - Side 2 1000 100 10 1 Do we need to trade? © Activities for Learning, Inc. 2012
  • 139. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
  • 140. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
  • 141. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
  • 142. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
  • 143. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
  • 144. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
  • 145. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
  • 146. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
  • 147. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
  • 148. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc. 2012
  • 149. Four Digit Addition 1000 100 10 1 3658 + 2738 6 © Activities for Learning, Inc. 2012
  • 150. Four Digit Addition 1000 100 10 1 1 3658 + 2738 6 © Activities for Learning, Inc. 2012
  • 151. Four Digit Addition 1000 100 10 1 1 3658 + 2738 6 © Activities for Learning, Inc. 2012
  • 152. Four Digit Addition 1000 100 10 1 1 3658 + 2738 6 © Activities for Learning, Inc. 2012
  • 153. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc. 2012
  • 154. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc. 2012
  • 155. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc. 2012
  • 156. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc. 2012
  • 157. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc. 2012
  • 158. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc. 2012
  • 159. Four Digit Addition 1000 100 10 1 1 3658 + 2738 396 © Activities for Learning, Inc. 2012
  • 160. Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 396 © Activities for Learning, Inc. 2012
  • 161. Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 396 © Activities for Learning, Inc. 2012
  • 162. Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 396 © Activities for Learning, Inc. 2012
  • 163. Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 6396 © Activities for Learning, Inc. 2012
  • 164. Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 6396 © Activities for Learning, Inc. 2012
  • 165. Short Division © Activities for Learning, Inc. 2012
  • 166. Short Division 3) 4 7 1 © Activities for Learning, Inc. 2012
  • 167. Short Division 3) 4 7 1 © Activities for Learning, Inc. 2012
  • 168. Short Division 1 3) 4 7 1 © Activities for Learning, Inc. 2012
  • 169. Short Division 1 3) 4 7 1 1 © Activities for Learning, Inc. 2012
  • 170. Short Division 1 5 3) 4 7 1 1 © Activities for Learning, Inc. 2012
  • 171. Short Division 1 5 3) 4 7 1 2 1 © Activities for Learning, Inc. 2012
  • 172. Short Division 1 5 7 3) 4 7 1 2 1 © Activities for Learning, Inc. 2012
  • 173. Short Division 1 5 7 3) 4 7 1 2 1 © Activities for Learning, Inc. 2012
  • 174. Short Division 9) 8 0 5 3 © Activities for Learning, Inc. 2012
  • 175. Short Division 9) 8 0 5 3 © Activities for Learning, Inc. 2012
  • 176. Short Division 8 9) 8 0 5 3 © Activities for Learning, Inc. 2012
  • 177. Short Division 8 9) 8 0 5 3 8 © Activities for Learning, Inc. 2012
  • 178. Short Division 8 9 9) 8 0 5 3 8 © Activities for Learning, Inc. 2012
  • 179. Short Division 8 9 9) 8 0 5 3 8 4 © Activities for Learning, Inc. 2012
  • 180. Short Division 8 94 9) 8 0 5 3 8 4 © Activities for Learning, Inc. 2012
  • 181. Short Division 8 9 4 r7 9) 8 0 5 3 8 4 © Activities for Learning, Inc. 2012
  • 182. Short Division 8 9 4 r7 9) 8 0 5 3 8 4 © Activities for Learning, Inc. 2012
  • 183. Short Division 4) 9 3 6 2 © Activities for Learning, Inc. 2012
  • 184. Short Division 4) 9 3 6 2 © Activities for Learning, Inc. 2012
  • 185. Short Division 4) 9 3 6 2 2 © Activities for Learning, Inc. 2012
  • 186. Short Division 4) 9 3 6 2 1 2 © Activities for Learning, Inc. 2012
  • 187. Short Division 4) 9 3 6 2 1 23 © Activities for Learning, Inc. 2012
  • 188. Short Division 4) 9 3 6 2 1 1 23 © Activities for Learning, Inc. 2012
  • 189. Short Division 4) 9 3 6 2 1 1 234 © Activities for Learning, Inc. 2012
  • 190. Short Division 4) 9 3 6 2 1 1 2340 © Activities for Learning, Inc. 2012
  • 191. Short Division 4) 9 3 6 2 1 1 2 3 4 0 r2 © Activities for Learning, Inc. 2012
  • 192. Short Division 4) 9 3 6 2 1 1 2 3 4 0 r2 © Activities for Learning, Inc. 2012
  • 193. Multivides © Activities for Learning, Inc. 2012
  • 194. Multivides • Self-checking multiplication and division exercise. © Activities for Learning, Inc. 2012
  • 195. Multivides • Self-checking multiplication and division exercise. • Any remainder means a mistake was made somewhere. © Activities for Learning, Inc. 2012
  • 196. Multivides 7 Start with any number. Multiply it by 2… © Activities for Learning, Inc. 2012
  • 197. Multivides 7 x2 14 Start with any number. Multiply it by 2… © Activities for Learning, Inc. 2012
  • 198. Multivides 7 x2 14 Start with any x3 number. 42 Multiply it by 2, then 3. . . © Activities for Learning, Inc. 2012
  • 199. Multivides 7 x2 14 Start with any x3 number. 42 x4 Multiply it by 168 2, then 3, then 4. . . © Activities for Learning, Inc. 2012
  • 200. Multivides 7 x2 14 Start with any x3 number. 42 x4 Multiply it by 168 x5 2, then 3, 840 then 4, and x6 on up 5 040 to 9. x7 35 280 x8 282 240 x9 2 540 160 © Activities for Learning, Inc. 2012
  • 201. Multivides 7 x2 14 Next divide the x3 total by 2. . . 42 x4 168 x5 840 x6 5 040 x7 35 280 x8 282 240 x9 2 540 160 © Activities for Learning, Inc. 2012
  • 202. Multivides 7 x2 14 Next divide the x3 2)2 540 160 total by 2. . . 42 1 270 080 x4 168 x5 840 x6 5 040 x7 35 280 x8 282 240 x9 2 540 160 © Activities for Learning, Inc. 2012
  • 203. Multivides 7 x2 14 Next divide by x3 2)2 540 160 2, then 3. . . 42 3)1 270 080 x4 423 360 168 x5 840 x6 5 040 x7 35 280 x8 282 240 x9 2 540 160 © Activities for Learning, Inc. 2012
  • 204. Multivides 7 x2 14 Next divide by x3 2)2 540 160 2, then 3, then 42 3)1 270 080 4. . . x4 4)423 360 168 105 840 x5 840 x6 5 040 x7 35 280 x8 282 240 x9 2 540 160 © Activities for Learning, Inc. 2012
  • 205. Multivides 7 x2 14 Next divide by x3 2)2 540 160 2, then 3, then 42 3)1 270 080 4, on up to 9. x4 4)423 360 168 5)105 840 x5 6)21 168 840 7)3 528 x6 8)504 5 040 x7 9)63 35 280 7 x8 282 240 x9 2 540 160 © Activities for Learning, Inc. 2012
  • 206. Multivides 7 x2 14 Final quotient x3 2)2 540 160 must equal 42 3)1 270 080 starting x4 4)423 360 number. 168 5)105 840 x5 6)21 168 840 7)3 528 x6 8)504 5 040 x7 9)63 35 280 7 x8 282 240 x9 2 540 160 © Activities for Learning, Inc. 2012
  • 207. Multivides A multivide a day keeps the flashcards away! © Activities for Learning, Inc. 2012
  • 208. Check Numbers © Activities for Learning, Inc. 2012
  • 209. Check Numbers • Method to check answers. © Activities for Learning, Inc. 2012
  • 210. Check Numbers • Method to check answers. • Each number has a check number. © Activities for Learning, Inc. 2012
  • 211. Check Numbers 34 © Activities for Learning, Inc. 2012
  • 212. Check Numbers 34 3+4=7 © Activities for Learning, Inc. 2012
  • 213. Check Numbers 34 (7) 3+4=7 © Activities for Learning, Inc. 2012
  • 214. Check Numbers 28 © Activities for Learning, Inc. 2012
  • 215. Check Numbers 28 2 + 8 = 10 © Activities for Learning, Inc. 2012
  • 216. Check Numbers 28 2 + 8 = 10; 1+0=1 © Activities for Learning, Inc. 2012
  • 217. Check Numbers 28 (1) 2 + 8 = 10; 1+0=1 © Activities for Learning, Inc. 2012
  • 218. Check Numbers 5635 © Activities for Learning, Inc. 2012
  • 219. Check Numbers 5635 5 + 6 = 11 and 3 + 5 = 8 © Activities for Learning, Inc. 2012
  • 220. Check Numbers 5635 5 + 6 = 11 and 3 + 5 = 8 1 + 1 = 2 + 8 = 10 © Activities for Learning, Inc. 2012
  • 221. Check Numbers 5635 5 + 6 = 11 and 3 + 5 = 8 1 + 1 = 2 + 8 = 10 1+0=1 © Activities for Learning, Inc. 2012
  • 222. Check Numbers 5635 (1) 5 + 6 = 11 and 3 + 5 = 8 1 + 1 = 2 + 8 = 10 1+0=1 © Activities for Learning, Inc. 2012
  • 223. Check Numbers 5635 6 + 3 = 9 = 0 and 5 + 5 = 10 = 1 © Activities for Learning, Inc. 2012
  • 224. Check Numbers 5635 (1) 6 + 3 = 9 = 0 and 5 + 5 = 10 = 1 © Activities for Learning, Inc. 2012
  • 225. Check Numbers 5635 (1) 6 + 3 = 9 = 0 and 5 + 5 = 10 = 1 © Activities for Learning, Inc. 2012
  • 226. Check Numbers 7146 © Activities for Learning, Inc. 2012
  • 227. Check Numbers 7146 7 + 1 = 8 and 4 + 6 = 10 © Activities for Learning, Inc. 2012
  • 228. Check Numbers 7146 7 + 1 = 8 and 4 + 6 = 10 8+1+0=9=0 © Activities for Learning, Inc. 2012
  • 229. Check Numbers 7146 (0) 7 + 1 = 8 and 4 + 6 = 10 8+1+0=9=0 © Activities for Learning, Inc. 2012
  • 230. Check Numbers • Method to check answers. • Each number has a check number. • When you calculate equations, the check numbers of the numbers will be the same as the check number of the answer. © Activities for Learning, Inc. 2012
  • 231. Check Numbers 5635 + 28 © Activities for Learning, Inc. 2012
  • 232. Check Numbers 5635 + 28 5663 © Activities for Learning, Inc. 2012
  • 233. Check Numbers 5635 (1) + 28 5663 © Activities for Learning, Inc. 2012
  • 234. Check Numbers 5635 (1) + 28 (1) 5663 © Activities for Learning, Inc. 2012
  • 235. Check Numbers 5635 (1) + 28 (1) 5663 (2) © Activities for Learning, Inc. 2012
  • 236. Check Numbers 5635 (1) + 28 (1) 5663 (2) © Activities for Learning, Inc. 2012
  • 237. Check Numbers 8863 + 687 © Activities for Learning, Inc. 2012
  • 238. Check Numbers 8863 + 687 9550 © Activities for Learning, Inc. 2012
  • 239. Check Numbers 8863 (7) + 687 9550 © Activities for Learning, Inc. 2012
  • 240. Check Numbers 8863 (7) + 687 (3) 9550 © Activities for Learning, Inc. 2012
  • 241. Check Numbers 8863 (7) + 687 (3) 9550 (1) © Activities for Learning, Inc. 2012
  • 242. Check Numbers 8863 (7) + 687 (3) 9550 (1) © Activities for Learning, Inc. 2012
  • 243. Check Numbers 7146 x 7 © Activities for Learning, Inc. 2012
  • 244. Check Numbers 7146 x 7 50,022 © Activities for Learning, Inc. 2012
  • 245. Check Numbers 7146 (0) x 7 50,022 © Activities for Learning, Inc. 2012
  • 246. Check Numbers 7146 (0) x 7 (7) 50,022 © Activities for Learning, Inc. 2012
  • 247. Check Numbers 7146 (0) x 7 (7) 50,022 (0) © Activities for Learning, Inc. 2012
  • 248. Check Numbers 7146 (0) x 7 (7) 50,022 (0) © Activities for Learning, Inc. 2012
  • 249. Check Numbers ) 9 805 3 © Activities for Learning, Inc. 2012
  • 250. Check Numbers 89r7 ) 9 805 4 3 © Activities for Learning, Inc. 2012
  • 251. Check Numbers 89r7 (0) ) 9 805 4 3 © Activities for Learning, Inc. 2012
  • 252. Check Numbers 89r7 (0) ) 9 8 0 5 (7) 4 3 © Activities for Learning, Inc. 2012
  • 253. Check Numbers (3) (7) 89r7 (0) ) 9 8 0 5 (7) 4 3 © Activities for Learning, Inc. 2012
  • 254. Check Numbers (3) (7) 89r7 (0) ) 9 8 0 5 (7) 4 3 (3) x © Activities for Learning, Inc. 2012
  • 255. Check Numbers (3) (7) 89r7 (0) ) 9 8 0 5 (7) 4 3 (3) x © Activities for Learning, Inc. 2012
  • 256. Simplifying Fractions © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
  • 257. Simplifying Fractions © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
  • 258. Simplifying Fractions © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
  • 259. Simplifying Fractions © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
  • 260. Simplifying Fractions 21 28 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
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  • 262. Simplifying Fractions 21 28 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
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  • 265. Simplifying Fractions 45 72 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
  • 266. Simplifying Fractions 12 16 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
  • 267. Simplifying Fractions 12 16 © Activitiesfor Learning, Inc. 2012 © Activities for Learning, Inc. 2012
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  • 273. Problem Solving A problem is not a problem if the solution is obvious. © Activities for Learning, Inc. 2012
  • 274. Problem Solving A problem is not a problem if the solution is obvious. Japanese teachers discuss one problem in depth rather than four problems superficially. © Activities for Learning, Inc. 2012
  • 275. Problem Solving A problem is not a problem if the solution is obvious. Japanese teachers discuss one problem in depth rather than four problems superficially. They encourage multiple solutions. © Activities for Learning, Inc. 2012
  • 276. Problem Solving A problem is not a problem if the solution is obvious. Japanese teachers discuss one problem in depth rather than four problems superficially. They encourage multiple solutions. Wrong solutions are discussed. © Activities for Learning, Inc. 2012
  • 277. Problem Solving A problem is not a problem if the solution is obvious. Japanese teachers discuss one problem in depth rather than four problems superficially. They encourage multiple solutions. Wrong solutions are discussed. The students do not look for “key” words. © Activities for Learning, Inc. 2012
  • 278. Critical Thinkers Ellis, D. Becoming a Master Student, 1997. © Activities for Learning, Inc. 2012
  • 279. Critical Thinkers Critical Thinkers: distinguish between fact and opinion; Ellis, D. Becoming a Master Student, 1997. © Activities for Learning, Inc. 2012
  • 280. Critical Thinkers Critical Thinkers: distinguish between fact and opinion; ask questions; Ellis, D. Becoming a Master Student, 1997. © Activities for Learning, Inc. 2012
  • 281. Critical Thinkers Critical Thinkers: distinguish between fact and opinion; ask questions; make detailed observations; Ellis, D. Becoming a Master Student, 1997. © Activities for Learning, Inc. 2012
  • 282. Critical Thinkers Critical Thinkers: distinguish between fact and opinion; ask questions; make detailed observations; uncover assumptions and define their terms; and Ellis, D. Becoming a Master Student, 1997. © Activities for Learning, Inc. 2012
  • 283. Critical Thinkers Critical Thinkers: distinguish between fact and opinion; ask questions; make detailed observations; uncover assumptions and define their terms; and assertions based on sound logic and solid evidence. Ellis, D. Becoming a Master Student, 1997. © Activities for Learning, Inc. 2012
  • 284. How to Assist Critical Thinking © Activities for Learning, Inc. 2012
  • 285. How to Assist Critical Thinking How did you get your answer? © Activities for Learning, Inc. 2012
  • 286. How to Assist Critical Thinking How did you get your answer? Why did that work? © Activities for Learning, Inc. 2012
  • 287. How to Assist Critical Thinking How did you get your answer? Why did that work? Will that work every time? © Activities for Learning, Inc. 2012
  • 288. How to Assist Critical Thinking How did you get your answer? Why did that work? Will that work every time? Be quiet! Allow processing and thinking time. © Activities for Learning, Inc. 2012
  • 289. Math Puzzles and Brain Teasers Presented by Kathleen Cotter Lawler © Activities for Learning, Inc. 2012

Notes de l'éditeur

  1. All the rows, columns, and diagonals sum to the same number.1. It includes all the numbers from 1 to 9.2. Even numbers in the corners; other numbers are odd.3. Each row adds to 15.4. Each column adds to 15.5. Both diagonals add to 15.6. The overall figure is a square.7. Opposite corners (and sides) equal 10.
  2. All the rows, columns, and diagonals sum to the same number.1. It includes all the numbers from 1 to 9.2. Even numbers in the corners; other numbers are odd.3. Each row adds to 15.4. Each column adds to 15.5. Both diagonals add to 15.6. The overall figure is a square.7. Opposite corners (and sides) equal 10.
  3. Tell the child she can build herown magic square. Demonstrate as follows.
  4. Let’s put 5 in the middle and our magic number will still be 15.Now let’s put an odd number, say 7, in the corner.
  5. What other number can we fill in? [3 in the lower right, 7 + 5 = 12, so 3 is needed to make 15]
  6. What other number can we fill in? [none] So we can choose again.Let’s write a 1 next to the 7.