MA.5.NSO.1 Number Sense and Operations
Understand the place value of multi-digit numbers with decimals to the thousandths place.
Read and write multi-digit numbers with decimals to the thousandths using standard form, word form and expanded form. Example: The number sixty-seven and three hundredths written in standard form is 67.03 and in expanded form is 60 + 7 + 0.03 or (6 × 10) + (7 × 1) + (3 × 1/100).
Purpose and Instructional Strategies
The purpose of this benchmark is for students to read numbers appropriately and to write numbers in all forms. Utilizing place value, students are expected to understand the value of tenths, hundredths, and thousandths, extending from their work to read and write whole numbers in any form in Grade 4 (MA.4.NSO.1.2). Writing numbers in expanded form can help students see the relationship between decimals and fractions. (MTR.5.1). Translating from written form to symbolic form builds the foundation for moving from written to algebraic form in Grade 6 (MA.6.AR.1.1).
Representing numbers in flexible ways will help students name, order, compare and operate with decimals. (MTR.3.1)
During instruction, teachers should relate all three forms using place value charts and base ten manipulatives (e.g., blocks). (MTR.3.1, MTR.4.1, MTR.5.1)
Common Misconceptions or Errors
Students may incorrectly read and write from expanded form if one of the digits is 0, like in the number 67.03 as used in the benchmark example. A common mistake that students make is to name the number as 67.3 because they do not see that 3 is the value of hundredths.
Instructional Task 1
Use the number cards below to write a number in standard, word and expanded forms. You can use the cards in any order to make your number, but it must have a digit other than zero in the thousandths place.
Instructional Item 1
Which shows the number below in word form? (7 × 100) + (2 × 1) + (5 ×1/10) + (9 ×1/1000)
a. 𝑆𝑒𝑣𝑒𝑛𝑡𝑦 − 𝑡𝑤𝑜 𝑎𝑛𝑑 𝑓𝑖𝑓𝑡𝑦 − 𝑛𝑖𝑛𝑒 𝑡ℎ𝑜𝑢𝑠𝑎𝑛𝑑𝑡ℎ𝑠
b. 𝑆𝑒𝑣𝑒𝑛 ℎ𝑢𝑛𝑑𝑟𝑒𝑑 𝑡𝑤𝑜 𝑎𝑛𝑑 𝑓𝑖𝑓𝑡𝑦 − 𝑛𝑖𝑛𝑒 ℎ𝑢𝑛𝑑𝑟𝑒𝑑𝑡ℎ𝑠
c. 𝑆𝑒𝑣𝑒𝑛 ℎ𝑢𝑛𝑑𝑟𝑒𝑑 𝑡𝑤𝑜 𝑎𝑛𝑑 𝑓𝑖𝑣𝑒 ℎ𝑢𝑛𝑑𝑟𝑒𝑑 𝑛𝑖𝑛𝑒 𝑡ℎ𝑜𝑢𝑠𝑎𝑛𝑑𝑡ℎ𝑠
d. 𝑆𝑒𝑣𝑒𝑛𝑡𝑦 − 𝑡𝑤𝑜 𝑎𝑛𝑑 𝑓𝑖𝑣𝑒 ℎ𝑢𝑛𝑑𝑟𝑒𝑑 𝑛𝑖𝑛𝑒 𝑡ℎ𝑜𝑢𝑠𝑎𝑛𝑑𝑡ℎ𝑠
Instructional Item 2
Write 𝑒𝑖𝑔ℎ𝑡 𝑡ℎ𝑜𝑢𝑠𝑎𝑛𝑑 𝑎𝑛𝑑 2 ℎ𝑢𝑛𝑑𝑟𝑒𝑑𝑡ℎ𝑠 in standard form.