Student Actions

Teacher Actions

• Develop accurate and appropriate procedural fluency through practice with 0.1, 0.01, and 0.001 students will efficiently be able to increase or decrease their number by the required amount.

• Develop the ability to make conjectures, model, and generalize by representing mathematical ideas using concrete materials, pictures, and symbols to internalize the concept that these are amounts within whole numbers.

• Develop the ability to communicate mathematically when solving problems and finding 0.1, 0.01, 0.001 more and less students justify their thinking and explain their solutions.

• Develop a deep and flexible conceptual understanding when using their understanding of operations with whole numbers, decimals, and fractions to choose strategies and procedures to access and solve real-world math problems involving finding  0.1, 0.01, 0.001 more and less than a number.

• Develop a productive mathematical disposition by looking for patterns in place value when finding  0.1, 0.01, 0.001 more or less of a number.

• Build procedural fluency from conceptual understanding by connecting prior knowledge of place value to find 0.1, 0.01, 0.001 more or less of a number. 

• Facilitate meaningful mathematical discourse by having students compare and contrast strategies and identify effective and efficient methods. 

• Pose purposeful questions which illustrate student thinking such as, “How did you get that?”  “Can anyone add to this thinking?”

• Assist students create or apply models to explain thinking, e.g. using multiple tenths charts, hundredths charts, and thousandths charts while clarifying their thinking and then using these charts to explain their thinking.

Key Understandings

Misconceptions 

• Find 0.1, 0.01, and 0.001 more or less than a number.

• Find 0.1, 0.01, and 0.001 more or less than a number with less decimal digits

• EX:  What is 0.001 less than 5.67?

• Order a set of numbers that includes decimal fractions in both fraction or decimal form.

• Using concrete models, such as charts, to find 0.1 more/less, 0.01 more/less, and 0.001 more/less than a number.

• They connect their prior experiences with using decimal notation for fractions and the addition of fractions with denominators of 10 and 100. They use concrete models and number lines to extend this understanding to decimals to the thousandths.

• Utilize base-ten blocks or bundled objects to represent decimal numbers in multiple ways

• Discuss the importance of lining up place values

• Use pictures, diagrams, tables, and models to compare decimal fractions in either a fraction or decimal form

• Use appropriate mathematics vocabulary

• Reading decimals correctly such as 0.26 as "twenty-six hundredths" instead of  "point two six"

• Use number lines to determine the appropriate placement of decimals such as .9, .09, .19, etc.

• Whole-number relationships can be applied to fractions or decimals. For example, believing 0.26 is greater than 0.8 because 26 is greater than 8.

• Decimals are just like whole numbers; everything you do with whole numbers you do with decimals.

• The more digits to the right of the decimal point the bigger the number.

• All numbers are lined up on the left or right, rather than by their place value. 

  Knowledge Connections

Prior Knowledge

Leads to 

• Represent tenths and hundredths with concrete models (4.N.3.6).
• Use place value to describe decimals; compare and order them (5.N.1.2, 5.N.1.3).

• Accurately estimating decimals (6.N.4.1).

• Illustrate or model decimals to solve problems with decimals (6.N.4.2, 6.N.4.4).