+ Exploring Math: Breaking Numbers Apart in a Base-Ten System Created by Patrice Covino and Megan Stein, 2013 + Solve. 27 + 42= + Solving Strategies, Mathematical Thinking 27dffffffhhffffxxxxxxxxxxxxxxxwwwwwwwwwwwwwwwww+ 42 (20+40)+ (7+2) 30 + 42 – 3 Goal: To provide children with a strong foundation in number sense so they can work with numbers fluently. + What is Base-Ten? Base-Ten is a “place value” system where any single digit can represent a different value depending on it’s placement in a number. Example: Note the value of the digit 5 in each number below. 325 152 578 5 vs. 50 vs. 500 + Decomposing Numbers Children need a strong sense of numbers to be able compose and decompose them comfortably. Decomposition/ Composition of Numbers: 325 300 + 20 + 5 Understanding 325 the place value of 325 entails knowing that: is closer to 300 than 400 It is 100 more than 225 It is 25 more than 300 It is 5 less than 330 It is composed of 32 groups of ten and 5 ones + How might this look in Kindergarten? 16 = 10 + 6 1 group of tens and 6 ones ★★★★★★★★★★ ★★★★★★ + Why learn about it as early as Kindergarten? Common Core Kindergarten Math Standards Work with numbers 11–19 to gain foundations for place value. 1. Compose and decompose numbers from 11 to 19 into a group of ten 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. Becoming comfortable with Base 10 in Kindergarten allows children to build a solid number sense foundation, which they can later rely on as they approach more challenging work. + Kindergarten Base-Ten Goals Across the Year Number and Operation in Base Ten January • • • • June March • • • • • • • • • • • • Explain that counting tells how many items there are altogether—when counting, the last number tells the total number of items; it is a cumulative count Understand that numbers exist in a specific order (number line) Understand that a number corresponds with a group of objects and the marching numeral Create an equivalent set for a given number up to 10 Understand that the distance between any two consecutive counting numbers on a given number line is one Understand that we begin counting a set of objects with the number one Understand that numbers can also be used to tell the position of objects in a sequence and numbers represent a quantity Count to 100 by ones and tens Count on from a given number within 100 Count backwards from 20 Write numbers 30 Skip count by fives to 100 Skip count by twos to 20 Compare two written numbers between up to 10 using language such as greater than, less than, or equal to Compose and decompose numbers 11-19 into groups of 10s and 1s Understand that zero is a number that represents a group with no object + What does Base-Ten look like in the classroom? Repeated counting practice and developing mental images for quantities up to 10 Days in School Count (by 1s, 2s, 5s, and 10s) Morning Meeting choral counting Ten Frames (games on Ten Frames- memory, build a number) Base-10 Blocks Connecting cube towers (one more, one less, ordering) Drawings organized for Base-Ten + How can I support my child at home? Provide FUN opportunities for your child to compose and decompose numbers in the form of tactile or visual supports. Consider using the following materials: Play-doh or Clay Dried Pasta Cereal, Pretzels, etc. Markers, crayons, paper Base 10 Flash Cards Sponges cut into longs and cubes Rekenrek- home-made or store-bought!