Global Concept Guides: Modeling Addition and Subtraction,Open Number Lines, Hundreds Charts
Prior Learning: Developing strategies for adding and subtracting as well as place value are both critical learning area for Grade 1.
Progressions Document Link
Show What You Know Task:Results of Unit 9 Assessment and Performance Task as well as Unit 14 Performance Task
Common Core State Standards for Mathematical Content :
Use place value understanding and properties of operations to add and subtract.
1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
Use place value understanding and properties of operations to add and subtract.
1.NBT.5Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
1.NBT.6 Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), 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 and explain the reasoning used. / Comments:
Notes on Assessment:
Students apply multiple strategies to add and subtract two-digit numbers. Preview performance task before beginning this unit of study to ensure coverage of content that will lead to student success.
See Common Performance Task link below
Unpacking the Standards for this Unit:
First Grade students use concrete materials, models, drawings and place value strategies to add within 100. They do so by being flexible with numbers as they use the base-ten system to solve problems. The standard algorithm of carrying or borrowing is neither an expectation nor a focus in First Grade. Students use strategies for addition and subtraction in Grades K-3. By the end of Third Grade students use a range of algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction to fluently add and subtract within 1000. Students are expected to fluently add and subtract multi-digit whole numbers using the standard algorithm by the end of Grade 4. (NCPDI, p. 21).
Common Performance Task with Rubric for this Unit:
Use part of a hundreds chart to show 10 and 1 more than a given number, write a number sentence to represent that problem, show thinking on an open number line and write a story to match the equation.
Click here for performance task and rubric.
Future learning:
“Understanding the value of the digits is more than telling the number of tens and hundreds. Second grade students who truly understand the position and place value of the digits are also able to confidently model the number with some type of visual representation. Others who seem like they know, because they can state which number is in the tens place, may not truly know what each digit represents.” Click here for more info
Second graders apply their understanding of place value concepts from first grade to help them represent numbers flexibly with base ten blocks. Having a deep understanding of this concept will help lay the groundwork for using operations with numbers.
1st / Global Concept (1 of 3)for this Unit of Study: Modeling Addition and SubtractionRevisit the concept of modeling through manipulative use, base ten blocks or quick pictures depending on the level of support needed / Projected Time Allotment:
4 days
Essential Questions:
Day 1:How does building a model help me think about addition or subtraction?
Day 2:How can I use tools to add or subtract with tens and ones?
Day 3:How did you decide when to exchange units for rods?
Day 4:How did you decide when to exchange rods for units?
Related Go Math Chapter Test Questions: N/A
Instructional
Manipulatives:
- Snap cubes –for student that need to physically build a group of ten
- Hundreds chart – to practice adding and subtracting ten more, ten less, one more, and one less
- Ten Frames – to help transition from a grouped models to a pre-grouped tool
- Base ten blocks – to make connections to place value
- The Game of Tens and Ones – Use dice to add or subtract on a Hundreds chart
- Race for a Flat–players take turns rolling number cubes and finding the sums of the numbers rolled. Base Ten Blocks are used to represent the sums in an effort to be the first to accumulate blocks with a total value of 100.
- Race to Clear the Mat –children take turns rolling two number cubes to determine the value of the Base Ten Blocks to remove from their place-value mat in an effort to be the first to clear all the blocks off their mat.
- Who’s Got the Most – Students use Base Ten Blocks to model two 2-digit numbers.
- Game options in PowerPoint
- Fair Bear Share–Students are arranging items into groups of tens and left over ones to relate physical models to the pictorial representation
Sample HOT Questions:
- How many groups of 10 can be made from __? How many ones would be left over?
- What things in our classroom can we add together by making groups of tens?
- How do your tools represent what is happening in the problem?
- Are 5 tens and 11 ones the same as 6 tens and 1 one? Justify your thinking.
- After you rolled the number cubes, how did you know how many units to put on your mat?
- After you rolled the number cubes, how did you find the number of units to clearoff your mat?
What are the students doing?
- Directly model the actions within a word problem using base ten blocks and other tools (SMP 1, 2, 4)
- Regroup 2-digit numbers within addition/subtraction problems. (SMP 1)
- Articulate when and why they need to regroup when seeing an addition/subtraction problem. (SMP 1, 3)
- Provide opportunities for students to directly model the actions with a word problem using base ten blocks.
- Help make connections with regrouping and representing numbers flexibly. (SMP 3)
- Emphasize precise use of vocabulary: ones, tens, digits, values, regroup, regrouping, trading, addend, sum, difference, represent, model (SMP 6)
1st / Global Concept (2 of 3)for this Unit of Study: Open Number Lines
Utilize open number lines to track student thinking and record the jumps that make sense to them / Projected Time Allotment:
4 days
Essential Questions:
Day 1:How can I record my thinking on an open number line?
Day 2:How can using an open number line help me to solve addition or subtraction problems?
Day 3:How can I strategically break apart a number to help me add and subtract 2-digit numbers?
Related Go Math Chapter Test Questions: N/A
Instructional
Manipulatives:
- Open number lines- Students will use open number lines to decompose numbers to help add and subtract.
- Hundreds chart- Students may use this tool to help decompose numbers for addition and subtraction.
- Snap cubes- Students may use this tool to show how to decompose a number.
- Ten frames- Students may use this tool to help understand a group of ten and ways to decompose a number.
- Base ten blocks-The use of base ten blocks will help students build their understanding of place value.
- Adding on an Open Number Line–This is a lesson that can be used to introduce the tool, open number line, using addition.
- More Practice Add on Open Number Line–Use the open number lines to record your strategies for adding each pair of numbers.
- Open Number Line Lesson
- Problem Solving Scenarios– Examples of word problems to use for building strategy use
- Addition with Tens on the Number Line–Using an open number line, students jump by tens to decompose addition problems into friendly steps
Sample HOT Questions:
- How can skip counting by tens on a hundreds chart help me use an open number line to add or subtract?
- How can I use a number line to help me model how I combine and compare numbers?
- How can decomposing a number help you subtract? Add?
- What is another way to break apart these numbers to add? Subtract?
What are the students doing?
- Use an open number as a tool for applying the break-apart strategy to efficiently solve 2-digit addition and subtraction problems. (SMP 5, 7)
- Compare their number line solution with another students’ solution and discuss similarities and differences (SMP6)
- Provide opportunities for students to use open number lines and base ten blocks to model strategies based on place value. (SMP 5, 7)
- Facilitate a conversation with students about various ways to decompose numbers for addition and subtraction and use of the open number line (SMP 3, 6)
1st / Global Concept (3 of 3)for this Unit of Study: Hundreds Chart
Visualize number relationships based on structure of hundreds chart / Projected Time Allotment:
2 days
Essential Questions:
Day 1:How does a hundreds chart help you compose and decompose numbers?
Day 2:How does visualizing the structure of a hundreds chart help you add or subtract?
Related Go Math Chapter Test Questions: N/A
Instructional
Manipulatives:
- Blank Hundreds Chart- students visualize locations of numbers based on given numbers
- Hundreds Chart-Students may use this tool to help decompose numbers for addition and subtraction.
- Base ten blocks-The use of base ten blocks will help students build their understanding of place value.
- Pentominoes-Student finds the missing numbers to apply strategies of adding by tens and ones.
- Adding on a Hundred Chart-see PowerPoint for detailed lesson information
- Build a Wacky Hundreds Chart
- Problem Solving Scenarios – Examples of word problems to use for building strategy use
- Interactive Number Grid Games
- Interactive Number Grid
Sample HOT Questions:
- How can skip counting by tens or ones on a hundreds chart help you add or subtract?
- How can you use a hundreds chart to model how todecompose numbers to add?
- How can decomposing a number help you subtract? Add?
- What is another way to break apart these numbers to add? Subtract?
What are the students doing?
- Use a hundreds chart as a tool for applying the break-apart strategy to efficiently solve 2-digit addition and subtraction problems. (SMP 5, 7)
- Compare their hundreds chart strategies with another students’ solution and discuss similarities and differences (SMP 6)
- Provide opportunities for students to use open hundreds charts and base ten blocks to model strategies based on place value. (SMP 5, 7)
- Facilitate a conversation with students about various ways to decompose numbers for addition and subtraction and the structure of a hundreds chart (SMP 3, 6)