1 to 15 cubes

It's not an everyday problem, but there will be times when you need to calculate the capacity of something. Instead of staring blankly into the trunk of your car, getting a tension headache trying to find the biggest bathtub, or weeping when confronted by the decision over buying a new fridge-freezer or oven, just take control! Advertisements There are only three measurements you need to take to work out the volume or capacity in cubic feet: length, width and height. It's worth being aware of the object you're measuring, however. Volume in cubic feet = Length (feet) x Width (feet) x Height (feet) Advertisement Calculating irregular shapes If the shape is irregular, mentally divide it into regular shapes and calculate the volume for each part separately, before adding them all together. For example, an L shaped cabinet designed to fit the corner of a room could be dealt with as two different rectangles, one longer, one shorter. Just work out the capacity of each one individually and then add them together for the total capacity of the cabinet. Converting from units other than feet If you're shopping online, the dimensions of something may only be given in inches. If you're looking at plans for a room, maybe the figures are given in meters or yards. But don't worry! To arrive at the cubic feet measurement, you only need to add one extra step into your calculations... • If you need to convert to cubic feet from inches: divide the final number (i.e. the total you get after mul...

A cube is a three-dimensional shape that has all edges of equal length. The volume of a cube is given by the product of its three dimensions. For example, if the edges of a cube measure "a" centimeters, the volume of the cube will be given by the product "a × a × a", which is equal the 3rd power. The Rubik's cube shown has its edges equal to 3 units. So, its volume is: a 3 = a × a × a = a 3 = 3 × 3 × 3 = 27 units or cubic centimeters (27 cm 3) (if we choose our volume unit as cubic centimeters). Um perfect number, also called a formula S n = n 2, where n is an integer. Cubed Numbers Table for Positive Numbers Cubed Positive Numbers 0 cubed equals 0 1 cubed equals 1 2 cubed equals 8 3 cubed equals 27 4 cubed equals 64 5 cubed equals 125 6 cubed equals 216 7 cubed equals 343 8 cubed equals 512 9 cubed equals 729 10 cubed equals 1000 11 cubed equals 1331 12 cubed equals 1728 13 cubed equals 2197 14 cubed equals 2744 15 cubed equals 3375 16 cubed equals 4096 17 cubed equals 4913 18 cubed equals 5832 19 cubed equals 6859 20 cubed equals 8000 Cubed Numbers Table for Negative Numbers Cubed Negative Numbers -0 cubed equals -0 -1 cubed equals -1 -2 cubed equals -8 -3 cubed equals -27 -4 cubed equals -64 -5 cubed equals -125 -6 cubed equals -216 -7 cubed equals -343 -8 cubed equals -512 -9 cubed equals -729 -10 cubed equals -1000 -11 cubed equals -1331 -12 cubed equals -1728 -13 cubed equals -2197 -14 cubed equals -2744 -15 cubed equals -3375 -16 cubed equals -4096 -17 cubed equals ...

Cards Term (1)^3 Definition 1 Term (2)^3 Definition 8 Term (3)^3 Definition 27 Term (4)^3 Definition 64 Term (5)^3 Definition 125 Term (6)^3 Definition 216 Term (7)^3 Definition 343 Term (8)^3 Definition 512 Term (9)^3 Definition 729 Term (10)^3 Definition 1000 Term (11)^3 Definition 1331 Term (12)^3 Definition 1728 Term (13)^3 Definition 2197 Term (14)^3 Definition 2744 Term (15)^3 Definition 3375

(1) The The plots above show the first 255 (top figure) and 511 (bottom figure) cubic numbers represented in binary. Pollock (1843-1850) conjectured that every number is the sum of at most 9 cubic numbers (Dickson 2005, p.23). As a part of the study of positive cubes ( , proved by Dickson, Pillai, and Niven in the early twentieth century), that every "sufficiently large" integer is a sum of no more than 7 positive cubes ( ). However, it is not known if 7 can be reduced (Wells 1986, p.70). The number of positive cubes needed to represent the numbers 1, 2, 3, ... are 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 2, ...(OEIS In 1939, Dickson proved that the only in , and the largest number known requiring seven cubes is 8042. Deshouillers et al. (2000) conjectured that 7373170279850 is the largest integer that cannot be expressed as the sum of four nonnegative cubes. The following table gives the first few numbers which require at least , 2, 3, ..., 9 (i.e., or more) positive cubes to represent them as a sum. OEIS numbers 1 1, 8, 27, 64, 125, 216, 343, 512, ... 2 2, 9, 16, 28, 35, 54, 65, 72, 91, ... 3 3, 10, 17, 24, 29, 36, 43, 55, 62, ... 4 4, 11, 18, 25, 30, 32, 37, 44, 51, ... 5 5, 12, 19, 26, 31, 33, 38, 40, 45, ... 6 6, 13, 20, 34, 39, 41, 46, 48, 53, ... 7 7, 14, 21, 42, 47, 49, 61, 77, ... 8 15, 22, 50, 114, 167, 175, 186, ... 9 23, 239 There is a finite set of numbers which cannot be expressed as the sum of distinct positive cubes: 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14...

School Supply Unifix Cubes Counting Activity Mats This unifix cubes activity is great for morning work, math centers, or small group practice in any Pre-K or Kindergarten classroom. All of the counting mats include numbers 1-10. The numbers are displayed in random order to help solidify student practice with number recognition and counting. It also supports one-to-one correspondence and even comparing. How to Use the Counting Mats Kids need a lot of practice with counting to truly understand the relationship between numbers and quantities. When students are using these counting mats, I have them read a number on the mat and count that number of cubes out as they form a tower. When students finish all of the towers on the mat, they count each cube back off of the mat, one tower at a time. RELATED RESOURCE: Teacher Tips For students who need support with number identification, have a For students who need more support with counting, you could have them count out the number of cubes onto a Grab Your Free Copy Ready to start counting and building? Grab these School Supply Unifix Cubes Counting Activity Mats by clicking the large, yellow download button below! Then, be sure you request your invitation to let us help you plan all year long inside the

(1) The The plots above show the first 255 (top figure) and 511 (bottom figure) cubic numbers represented in binary. Pollock (1843-1850) conjectured that every number is the sum of at most 9 cubic numbers (Dickson 2005, p.23). As a part of the study of positive cubes ( , proved by Dickson, Pillai, and Niven in the early twentieth century), that every "sufficiently large" integer is a sum of no more than 7 positive cubes ( ). However, it is not known if 7 can be reduced (Wells 1986, p.70). The number of positive cubes needed to represent the numbers 1, 2, 3, ... are 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 2, ...(OEIS In 1939, Dickson proved that the only in , and the largest number known requiring seven cubes is 8042. Deshouillers et al. (2000) conjectured that 7373170279850 is the largest integer that cannot be expressed as the sum of four nonnegative cubes. The following table gives the first few numbers which require at least , 2, 3, ..., 9 (i.e., or more) positive cubes to represent them as a sum. OEIS numbers 1 1, 8, 27, 64, 125, 216, 343, 512, ... 2 2, 9, 16, 28, 35, 54, 65, 72, 91, ... 3 3, 10, 17, 24, 29, 36, 43, 55, 62, ... 4 4, 11, 18, 25, 30, 32, 37, 44, 51, ... 5 5, 12, 19, 26, 31, 33, 38, 40, 45, ... 6 6, 13, 20, 34, 39, 41, 46, 48, 53, ... 7 7, 14, 21, 42, 47, 49, 61, 77, ... 8 15, 22, 50, 114, 167, 175, 186, ... 9 23, 239 There is a finite set of numbers which cannot be expressed as the sum of distinct positive cubes: 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14...

Cards Term (1)^3 Definition 1 Term (2)^3 Definition 8 Term (3)^3 Definition 27 Term (4)^3 Definition 64 Term (5)^3 Definition 125 Term (6)^3 Definition 216 Term (7)^3 Definition 343 Term (8)^3 Definition 512 Term (9)^3 Definition 729 Term (10)^3 Definition 1000 Term (11)^3 Definition 1331 Term (12)^3 Definition 1728 Term (13)^3 Definition 2197 Term (14)^3 Definition 2744 Term (15)^3 Definition 3375

It's not an everyday problem, but there will be times when you need to calculate the capacity of something. Instead of staring blankly into the trunk of your car, getting a tension headache trying to find the biggest bathtub, or weeping when confronted by the decision over buying a new fridge-freezer or oven, just take control! Advertisements There are only three measurements you need to take to work out the volume or capacity in cubic feet: length, width and height. It's worth being aware of the object you're measuring, however. Volume in cubic feet = Length (feet) x Width (feet) x Height (feet) Advertisement Calculating irregular shapes If the shape is irregular, mentally divide it into regular shapes and calculate the volume for each part separately, before adding them all together. For example, an L shaped cabinet designed to fit the corner of a room could be dealt with as two different rectangles, one longer, one shorter. Just work out the capacity of each one individually and then add them together for the total capacity of the cabinet. Converting from units other than feet If you're shopping online, the dimensions of something may only be given in inches. If you're looking at plans for a room, maybe the figures are given in meters or yards. But don't worry! To arrive at the cubic feet measurement, you only need to add one extra step into your calculations... • If you need to convert to cubic feet from inches: divide the final number (i.e. the total you get after mul...

A cube is a three-dimensional shape that has all edges of equal length. The volume of a cube is given by the product of its three dimensions. For example, if the edges of a cube measure "a" centimeters, the volume of the cube will be given by the product "a × a × a", which is equal the 3rd power. The Rubik's cube shown has its edges equal to 3 units. So, its volume is: a 3 = a × a × a = a 3 = 3 × 3 × 3 = 27 units or cubic centimeters (27 cm 3) (if we choose our volume unit as cubic centimeters). Um perfect number, also called a formula S n = n 2, where n is an integer. Cubed Numbers Table for Positive Numbers Cubed Positive Numbers 0 cubed equals 0 1 cubed equals 1 2 cubed equals 8 3 cubed equals 27 4 cubed equals 64 5 cubed equals 125 6 cubed equals 216 7 cubed equals 343 8 cubed equals 512 9 cubed equals 729 10 cubed equals 1000 11 cubed equals 1331 12 cubed equals 1728 13 cubed equals 2197 14 cubed equals 2744 15 cubed equals 3375 16 cubed equals 4096 17 cubed equals 4913 18 cubed equals 5832 19 cubed equals 6859 20 cubed equals 8000 Cubed Numbers Table for Negative Numbers Cubed Negative Numbers -0 cubed equals -0 -1 cubed equals -1 -2 cubed equals -8 -3 cubed equals -27 -4 cubed equals -64 -5 cubed equals -125 -6 cubed equals -216 -7 cubed equals -343 -8 cubed equals -512 -9 cubed equals -729 -10 cubed equals -1000 -11 cubed equals -1331 -12 cubed equals -1728 -13 cubed equals -2197 -14 cubed equals -2744 -15 cubed equals -3375 -16 cubed equals -4096 -17 cubed equals ...

School Supply Unifix Cubes Counting Activity Mats This unifix cubes activity is great for morning work, math centers, or small group practice in any Pre-K or Kindergarten classroom. All of the counting mats include numbers 1-10. The numbers are displayed in random order to help solidify student practice with number recognition and counting. It also supports one-to-one correspondence and even comparing. How to Use the Counting Mats Kids need a lot of practice with counting to truly understand the relationship between numbers and quantities. When students are using these counting mats, I have them read a number on the mat and count that number of cubes out as they form a tower. When students finish all of the towers on the mat, they count each cube back off of the mat, one tower at a time. RELATED RESOURCE: Teacher Tips For students who need support with number identification, have a For students who need more support with counting, you could have them count out the number of cubes onto a Grab Your Free Copy Ready to start counting and building? Grab these School Supply Unifix Cubes Counting Activity Mats by clicking the large, yellow download button below! Then, be sure you request your invitation to let us help you plan all year long inside the