Four Operations with Decimals
Students will deepen their understanding of decimals as they work with decimals to the thousandths place. Students will extend their strategies for computing with whole numbers to add, subtract, multiply, and divide decimals.
Note: Lessons will vary in length, depending on the amount of time you have with students, the resources that you choose to accompany the unit, the level of rigor within each learning target, and any other factors that may contribute to the pacing of your learning progressions. It is recommended that you adjust the pace and length of each learning progression(s) accordingly in response to these factors.
These learning progressions were developed using Next Generation Learning Standards and were crosswalked with the Common Core Standards.
Download the complete Grade 5 Math Unit 2 framework to customize for your own planning.
Essential Outcomes
Numbers in Base Ten
- NY-5.NBT.7 – Using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations:
- add and subtract decimals to hundredths;
- multiply and divide decimals to hundredths.
- Relate the strategy to a written method and explain the reasoning used.
- NY-5.NBT.3 Read, write, and compare decimals to thousandths.
- NY-5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
- NY-5.NBT.4 – Use place value understanding to round decimals to any place.
Other Standards Addressed in this Unit
Numbers in Base Ten
- NY-5.NBT.1 – Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
- NY-5.NBT.2 – Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.
Essential Questions and Big Ideas
- How do numbers with decimals relate to the base ten number system?
- Decimals maintain the relationships between digits that are based on powers of ten.
- A digit in one place is ten times the value of the same digit in the place to the right.
- A digit in one place is 1/10 the value of the same digit in the place to the left.
- The patterns in place values continue in the decimal places (tenths, hundredths, thousandths).
- Numbers with decimals can be written in expanded form and word form.
- How do I add and subtract with decimals?
- Addition and subtraction is based on the base ten number system.
- Like place values are added together.
- If there is not a digit in a certain place value, a zero can be used as a placeholder.
- How do I multiply with decimals?
- Numbers with decimals can be multiplied in a similar way to whole numbers.
- When multiplying tenths by tenths, hundredths are created.
- Multiplying decimal places create smaller decimal places.
- How do I divide with decimals?
- Numbers with decimals can be divided in a similar way to whole numbers.
- When dividing by an amount with a decimal, multiply by a power of ten to create a whole number. Multiply the dividend by the same power of ten to keep the relationship between amounts the same.
- When dividing a decimal by a whole number, maintain the location of the decimal place.
- How do I solve multi-step problems?
- When solving multi-step problems, identify the unknowns.
- After identifying the unknowns, identify the actions and relationships within the problem.
- Write number sentences to represent the actions and relationships within a problem.
Download the complete Grade 5 Math Unit 2 framework to customize for your own planning.