In the Common Core math standards, students’ knowledge and understanding of base ten is essential. “Base ten” simply means that any number can be created with exactly 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Starting in kindergarten, students begin to develop an understanding of the number 10. K.OA.4 states that “For any number from 1 to 9, [students will be able to] find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.” K.OA.3 also states that students will be able to “Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation.” K.NBT.1 also states that students will be able to “Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
In 1st grade, students build on their knowledge of composing 10 and decomposing numbers leading to 10. 1.OA.4 states that students will be able to “Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.” 1.OA.6 also states that students will be able to “ Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9).”
Students really need to learn all of the combinations that make 10 before they leave Kindergarten to help them understand mathematics. If they do not, they will really struggle later on when adding 3 addends; adding a string of numbers; adding and subtracting with regrouping; counting coins, telling time, and doing mental math.
This “Best Friends that Make 10 Rainbow” is a great visual to help students learn all the ways to make 10! You can print this out to glue into students’ math books or send the flyer home with students to hang in their rooms. Additionally, you can copy the rainbow onto chart paper and create a great anchor poster to hang in your classroom.
Later in life, this rainbow will help students solve much harder math problems. Here is a fun and popular critical thinking problem: “What is the sum of all numbers 0-100?” By finding the sum of all digits 0-10, a strategy known as “solving a simpler problem,” students will be able to solve this harder problem easily.
When finding the sum of the digits 0-10, there are 5 sets of number pairs that make 10, totaling 50, and then the number 5 is left over. The sum of the numbers 0-10 is 55 since 50 + 5 = 55.
When adding numbers 0-100, students can pair numbers by making a rainbow and use the same thinking. 0 + 100 = 100; 1 + 99 = 100; 2 + 98 = 100; etc. There are 50 sets of number pairs that make 100, totaling 5,000, and then the number 50 is left over. The sum of the numbers 0-100 is 5,050 since 5,000 + 50 = 5,050.