![]() ![]() Eventually, many elements (not the Elements of Euclid!) were discovered. Physicists and chemists found this approach very productive-to understand water or salt it was realized that common table salt was sodium chloride, a compound made of two elements, sodium and chlorine and that water was created from hydrogen and oxygen. One way to get insights into something one is trying to understand better is to break the thing down into its component parts, something simpler. *The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.Mathematics too has profited from the idea that sometimes things of interest might have a structure which allowed them to be decomposed into simpler parts. 8 thousands + 6 hundreds + 10 tens + 9 ones Select all the ways that express the number 8,709.Express the number 5,783 using only tens and ones.Express the number 5,783 using only thousands and hundreds.Express the number 5,783 using only hundreds and ones.For example, students decompose 34 in multiple ways using tens and ones.For example, students decompose 362 in multiple ways using hundreds, tens, and ones. ![]() Teacher provides opportunities to decompose numbers in multiple ways using manipulatives and a chart to organize their thinking and asks students to name/identify the different ways to name the values (regrouping the hundreds into tens and the tens into the ones, e.g., 36 tens and 2 ones or 3 hundreds and 62 ones, etc.).To reinforce this concept, students count by units based on the place value. Students group 10 ones as a group of ten and focus on the value of each digit based on its place value. For example, represent 34 using counters and explain the value of each digit.For example, decompose 362 using base ten blocks and explain the value of each digit.To reinforce this concept, students may count by units based on the place value. When decomposing a number, students focus on the value of each digit based on its place value. Instruction includes decomposing numbers using manipulatives that group (base ten blocks) and those that do not group such as counters.Students can misunderstand that when decomposing a number in multiple ways, the value of the number does not change.Students need practice with representing two and three-digit numbers with manipulatives that group (base ten blocks) and those that do NOT group, such as counters, etc. Students can misunderstand that the 5 in 57 represents 5, not 50 or 5 tens.Flexibility of place value is a prerequisite for conceptual understanding of a standard algorithm for addition and subtraction with regrouping.Students should see examples of numbers within 10,000 where zero is a digit and make sense of its value. ![]() Have students compare and contrast the representations shared ( MTR.4.1). Allow students to decompose numbers in as many ways as possible.For example, use base ten blocks to show how in the number 5,783, 1 hundred can be regrouped as 10 tens to express it as 5 thousands + 6 hundreds + 18 tens + 3 ones, while asking students how they are the same ( MTR.2.1). Model to show how multiple representations relate to the original number. Students should use objects (e.g., base ten blocks), drawings, and expressions or equations side-by-side to see compare and contrast the representations.For example, when subtracting 5,783 – 892, we can represent 5,783 as 5 thousands + 6 hundreds +ġ8 tens + 3 ones by regrouping 1 hundred as 10 tens, allowing us to subtract 9 tens ( MTR.2.1, MTR.3.1). ![]()
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