Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three- digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Measurement Topic
This standard is reported on the report card in these quarters as follows:
2nd Grade Students Learning 2nd Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic: Demonstrates understanding of addition
Report Card Measurement Topic: Demonstrates understanding of subtraction
Report Card Measurement Topic: Demonstrates understanding of addition
Report Card Measurement Topic: Demonstrates understanding of subtraction
1st Grade Students Learning 2nd Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic: Demonstrates understanding of addition
Report Card Measurement Topic: Demonstrates understanding of subtraction
Report Card Measurement Topic: Demonstrates understanding of addition
Report Card Measurement Topic: Demonstrates understanding of subtraction
About the Math
Skills and concepts below are learning goals for this standard.
Explain addition and subtraction within 1,000 using physical tools, drawings and number lines.
Students can use a myriad of tools to represent addition and subtraction. Base ten blocks are one tool for students to use. Place value chips are another. Students should also have ample opportunities to work with number lines to represent their thinking and computation. Work with phsyical models should be connected to number lines and equations. Computation should be supported with representations, especially number lines.
Count on to find the sum.
Teaching of the counting on strategy begins in Kindergarten with one-digit addends. Counting on extends to larger numbers by breaking apart one addend and adding it to the other addend in chunks. Given 124+245, a student might start with 245+120 to get 365 and then add 365+4=369. A student might break apart 245=200+40+5 and start with 124+200=324, 324+40=364, 364+5=369.
Count back to subtract.
We can count back to find the difference. One can count back starting with the minuend and counting back the amount of the subtrahend. On the number line, we see 536 - 357 where 357 has been decomposed and counted back from 536. One could also find the difference between 536 and 357 on the number line if desired.
Use partial sums to add.
We can decompose addends and add the parts. Those partial sums can then be added to find the final sum.
The partial sums algorithm for adding 3-digit numbers breaks the addition problem into a series of easier problems based on place value. Answers to the simpler problems are added together to determine the final sum.
When adding 378 + 254 we can decompose each addend and add place values. For example,
300 + 70 + 8 + 200 + 50 + 4 500 + 120 + 12 = 632
Then partial sums are added together. 500 + 120 + 12 = 632
Students can represent partial sums with physical tools and number lines. As students develop understanding, their focus should be shifted to decomposing one of the addends as it is usually more efficient.
Use think addition to find the difference.
Another option is to count up from the subtrahend. Here to find the difference of 536 - 179. One started with 179 and counted up to 536. The size of the jumps between these numbers can vary. Here, a jump of 21 was followed by 300, and then 36. Adding
those jumps together identifies the difference as 357.
Use compensation/adjusting to add or subtract more efficiently.
Numbers can be adjusted to compute more efficiently, This can be helpful in many situations. Consider 289 + 457. It can be thought of as 300 + 446 instead. The sums are the same. The latter is a more efficient computation because students can count on by 300. When adjusting addition expressions, an amount is given from one addend to the other. Adjusting subtraction functions differently. It is built on the notion of constant or same difference. Simply, 5 - 4 is the same as 4 - 3. Both are adjusted by 1. It can be used to solve something like 702 - 329. Instead, we can think of 699 - 326 finding a friendlier computation that requires no regrouping. When adjusting subtraction problems, BOTH numbers are adjusted in the same way.
Addition: When the parts of a set are known, addition is used to name the whole in terms of its parts.
Subtraction: In a part-part whole model when the whole is known and one of the parts, subtraction names the other part. This is called the "take away" model. Subtraction can also find the difference between two whole values. To find the difference, you can count up from the smaller or down from the larger value, whichever is easier or makes sense. We sometimes overlook subtraction as the difference between two whole values and focus on the take away model.
Both situations need to be part of instruction.
Essential vocabulary for this standard includes: place value, commutative property, associative property, identity property, compose, and decompose .Visit the online dictionaryLinks to an external site. for vocabulary support.
Progression of Standard within Grade 2
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
Progression Throughout Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Explain addition and subtraction within 1,000 using physical tools, drawings and number lines.
Count on to find the sum.
Count back to subtract.
Use partial sums to add.
Use think addition to find the difference.
Use compensation/adjusting to add or subtract more efficiently.
Explain addition and subtraction within 1,000 using physical tools, drawings and number lines.
Count on to find the sum.
Count back to subtract.
Use partial sums to add.
Use think addition to find the difference.
Use compensation/adjusting to add or subtract more efficiently.
Understand that the two digits of a two-digit number represent amounts of tens and ones (1.NBT.2)
Add/subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction (3.NBT.2)
These tasks can be used with small group or whole group instruction.
Instructional Materials for the various computation strategies can be found in Figuring Out Fluency Addition and Subtraction with Whole Numbers (this book has been provided to schools) as follows: Book Cover for Figuring Out Fluency Addition and Subtraction with Whole Numbers
Count On (Addition)/Count Back (Subtraction)-- pages 20-37
Partial Sums (Addition)-- pages 58-78
Think Addition (Subtraction)-- pages 102-119
Make Tens/Hundreds (Addition)-- pages 38-56
Compensation (Addition and Subtraction)-- pages 80-100
Provide base ten blocks or place value disks, a thousands chart (made by gluing multiple charts together and place value mats with hundreds, tens, and ones. Have students add two three-digit numbers. Pose problems in context such as in the fishing tournament there was a 237 pound blue marlin caught and a 438 pound blue marlin caught. How much did the two fish weigh altogether? Provide time for students to work with a partner to solve the problem with whatever tool they would like. They could use a number line as a tool as well as the blocks, disks, or hundreds chart. Invite students to share their model and their solution path. Pose questions such as what did you do first to solve the problem? How did you count your blocks/disks? How did you solve the problem using a number line? Provide time for other students to share and make connections between how students solved the problem. How is your thinking the same and different from the way another student solved the problem?
Draw a number line such as the one below and ask students to identify the equation it represents.
Show the students a number bond and have them identify the equations it represents. For example, 355 + 317 = 672, 317 + 355 = 672, 672 - 355 = 317 and 672 - 317 = 355. Create additional number bonds and have students identify the equations. Students can also create their own number bonds.
Display a representation such as the one below and ask students to identify the equation it represents.
One way to add 284 + 379 is to add 200 + 300 = 500 80 + 70 = 150 4 + 9 = 13 500 + 150 + 13 = 663 What is another way to solve 284 + 379?
What is the standard form for 3 hundreds, 17 tens, and 5 ones?
You add two three-digit numbers together and the sum is about 500. What could the addends be? What are two other numbers that would work?
Using the digits 2, 4, 0, 1, 3, and 8 only once, make two 3-digit numbers that will result in the smallest sum. Now make two 3-digit numbers that will result in the largest difference.
Asha creates two 3-digit numbers with a difference of 284. She then creates two 3-digit numbers with a sum of 284. What could be Asha’s two number sentences? Compare your number sentences with your neighbor’s number sentences.
Two families are renting a beach house together. Because the families have a different number of children, they will each pay a different amount. Family A is paying $425 and family B is paying $475. Does it cost more than $1,000 to rent the beach house? How do you know?
Use two different strategies to solve 614 + 295 = and 432 - 118 =
Sorting Estimates - Students work to sort expressions based on their estimated sums. They should have the opportunity to justify their thinking and reasoning behind the placement of each expression. Teachers can create their own expressions using index cards or use the options provided in theworksheetLinks to an external site..
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
Print Resources
Book Thumbnail
Book Title
Grade
Pages
Teaching Student-Centered Mathematics
K-3
146 (Numbers, Squares, Sticks, and Dots, Activity 5.21) 165 (Ten-Frame Adding and Subtraction,Activity 6.1) 184-185 (Expanded Lesson: Exploring Subtraction Strategies)
Hands-On Standards
1-2
40-41 (Exploring Place Value) 44-45 (Adding Without Regrouping) 46-47 (Adding With Regrouping) 48-49 (Subtracting Without Regrouping) 50-51 (Subtracting With Regrouping)
Hands On Standards
3-4
20-21 (Adding and Subtracting) 22-23 (Estimating the Sum or Difference)
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three- digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Measurement Topic
The standard is reported on the report card through these measurement topics. Expand the measurement topic for a description of what students who meet expectation are able to do.
2nd Grade Students Learning 2nd Grade Standards by Measurement Topic