In a 6-week course focusing on multi-digit numbers with decimals to the thousandths, students will develop a strong understanding of various ways to represent and manipulate these numbers. They will learn to read and write multi-digit numbers with decimals in standard form, word form, and expanded form. For example, they will be able to express the number 3.542 in standard form as 3.542, in word form as "three and five hundred forty-two thousandths," and in expanded form as 3 + 0.5 + 0.04 + 0.002.

Additionally, students will learn how to compose and decompose multi-digit numbers with decimals to the thousandths using the values of the digits in each place. For instance, they will be able to break down the number 4.726 into its component parts as 4 + 0.7 + 0.02 + 0.006. They will practice demonstrating these compositions or decompositions using objects, drawings, and expressions or equations to reinforce their understanding.

Furthermore, students will explore the plotting, ordering, and comparing of multi-digit numbers with decimals up to the thousandths. They will learn techniques for accurately plotting these numbers on number lines and using comparison symbols (<, >, =) to compare their values. They will also develop skills in ordering numbers from least to greatest and vice versa.

Lastly, students will study rounding multi-digit numbers with decimals to the thousandths. They will learn different rounding methods, such as rounding to the nearest hundredth, tenth, or whole number, depending on the given context. Through practice and application, students will develop the ability to accurately round numbers to the appropriate place value.