Mathematics Lesson: Comparing Decimals to Solve Real-World Situations 5.NBT.3 Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Essential Question How does the placement of the decimal impact the value of a number?

Model Airplane Monte is building a model airplane with his grandfather. The instructions tell them they need wheels with a diameter between 1.45 and 1.475. Will a wheel with a diameter of 1.463 work? Solve the problem using the following steps:  Reread the problem and determine what the problem is asking you to find. Predict/Estimate the solution. Determine the solution to the problem and write an explanation of your thinking in words. Support your answer to the problem using the 2 different representations of a number line and a place value chart. Review your solution and determine if it is reasonable.

Explanation in Words In order for a wheel with a diameter of 1.463 to work in the model, I know that 1.463 needs to be greater than 1.45 and less than 1.475.   First, I compared 1.463 to 1.45. I compared each digit, starting with the numbers to the left, since they are the largest. Since both numbers have 1 in the ones place, I moved to the tenths place. Since both numbers have 4 in the tenths place, I moved to the hundredths place. I know that 6 hundredths is larger than 5 hundredths, so I know that 1.463 is greater than 1.45. Next, I compared 1.463 to 1.475. Again, I compared each digit, starting with the numbers to the left. Since both numbers have 1 in the ones place, I moved to the tenths place. Since both numbers have 4 in the tenths place, I moved to the hundredths place. I know that 7 hundredths is larger than 6 hundredths, so I know that 1.475 is greater than 1.463. Since 1.463 is greater than 1.45 and less than 1.475, the wheel will work in the model.

Number Line:

Place Value Chart: Ones . Tenths Hundredths Thousandths 1 4 5   6 3 7 Students can use the place value chart to compare the digits from left to right to determine that 6 hundredths is between 5 hundredths and 7 hundredths.

Comparing Decimals to Solve Real-World Situations-Practice Laura compared 0.37 and 0.327 in the following way: 0.37 > 0.327. Explain how Laura knew this to be true. Use the UPSE format in your Math Notebook.