Global Concept Guides:Counting By Ones and Tens, Understanding Tens and Ones, Thinking About Numbers Flexibly, andNumbers to 120
Prior Learning:MAFS.K.OA.1.1, MAFS.K.OA.1.2, MAFS.K.CC.2.4,MAFS.K.CC.2.5, MAFS.K.NBT.1.1
Progressions Document Link
Show What You Know Task:Use the Go Math Chapter 6 Show What You Know (p. 238). Informally assess your students’ ability to count by ones from/to any given number up to 100 and their ability to count by ten to 100.
Common Core State Standards for Mathematical Content:
Extend the counting sequence.
MAFS.1.NBT.1.1Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
Understand place value.
MAFS.1.NBT.2.2Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
a. 10 can be thought of as a bundle of ten ones — called a “ten.”
b. The numbers from 11 to 19 are composed of ten and one, two, three, four, five, six, seven, eight, or nine ones.
c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
d. Decompose two-digit numbers in multiple ways (e.g., 64 can be decomposed into 6 tens and 4 ones or into 5 tens and 14 ones).
MAFS.1.NBT.2.3Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. / Comments:
PLEASE WATCH:
Go Math Grade 1: Big Idea 2 Video
This video explains the entire progression of Unit 7. Although the NGSSS are mentioned in this video, the concepts addressed are still relevant to the Common Core State Standards.
This parent flyer and included video can be utilized by both you and parents to build content knowledge and understanding of the strategies highlighted in this unit.
Notes on Assessment:
Go Math Chapter 6 Form B Assessment
The performance task should be given after of GCG 2.
See common performance task link below.
Unpacking the Standards for this Unit:
When counting, students should have ample experiences with the hundreds chart to see patterns between numbers, such as all of the numbers in a column on the hundreds chart have the same digit in the ones place, and all the digits in the same row have the same number in the tens place. Students should be able to rote count forward to 120 from any number less than 120. When given a two-digit number, students will mentally find 10 more or 10 less without counting.
The idea that 2 tens can replace 20 ones is a monumental shift in thinking for 1st graders. It can be challenging for young children to consider a group of something as “one” when all previous experiences have been counting single objects.
Teachers can build a deeper understanding of numbers and their relationships through providing interesting and engaging tasks. Students need ample opportunities to group proportional objects (e.g., cubes, beans, beads, ten frames) to make groups of ten prior to using pre-grouped materials like base ten blocks. Through experiences such as these, the teacher is able to identify students’ misconceptions, such as interpreting 2 tens and the 3 ones as 5 objects, rather than as 23 ones, or 1 ten and 13 ones, or 2 tens and 3 ones.
Common Performance Task with Rubric for this Unit:
Students will represent a 2-digit number in standard and expanded form as well as with a quick pic. Students will fill in missing numbers on part of a 100 chart. Students will analyze AND explain whether a student’s quick pic of a number is correct or incorrect. Click herefor performance task and rubric.
Future learning:
“At Grade 2, students extend their base-ten understanding to hundreds. They now add and subtract within 1000, with composing and decomposing, and they understand and explain the reasoning of the processes they use. They become fluent with addition and subtraction within 100.” (K-5 Number and Operations in Base Ten Progressions Document, pg. 8)
1st / Global Concept 1 of 4 for this Unit of Study (Click to view PowerPoint in slide show mode):Counting By Ones and Tens
Counting by ones and tens from any given number up to 120 / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1:How can you count from any number?
Day 2: How do numbers change as you count by tens?
Day 3: How can knowing a counting pattern help you count to 120?
Related Unit 6 Assessment:Go Math Ch. 6 #2, 4, 15, 17
Instructional Resources
Manipulatives:
- Pentominoes:used on day 3 as independent practice for counting by 1’s and 10’s by any number
- 120 Chart: will be used in addition to the Hundred Chart to understand larger numbers
- Go Math Essentials: Lesson 6.1 Listen and Drawp. 243 can be used as an informal pre-assessment on Day 1. Math Talk in Action p. 243 includes some questions that can be used to start to promote higher-level thinking and understanding. Problem Solving p. 244 is word problems that can be used with core or small groups.
- Modified 120 chart: can be used on Day 1 to have students determine the missing numbers. This should be done as a whole group, because the students have not yet learned how to write numbers greater than 20.
- Numeral Cards: As independent practice on Day 1, students can flip over a card and write that number and the next five numbers in their journal.
- Go Math Essentials:Lesson 6.2 Listen and Drawp. 245can be used as an engage on Day 2. The questions provided can be used to facilitate a discussion about the patterns that are seen on a hundreds chart when counting by tens. Use On Your Own p. 247 #4-8 for independent practice on Day 2 to count forward by tens from a given number. Problem solving component will be used on a different day.
- Count 10: Use for independent practice for Day 2 to count backward by tens.
- Hundreds Chart Patterns: These can be used to build conceptual knowledge of the patterns seen when
- Missing Numbers: This can be used as independent practice on Day 3. Students will count forward and backwards by 10’s and 1’s.
- Go Math Essentials: Lesson 6.2: Problem Solving p. 248 to complete missing numbers.
- Pentominoes Activity:Use a dry erase marker to write a number in one of the squares and have students continue the counting sequence. See PowerPoint for more details.
- Animated Math Model- Skill 27: Counting Patterns (Counting by Tens From Any Number)
- Give the Dog a Bone - students find where a number would be on a blank 100 chart
Sample HOT Questions: Select or create appropriate questions to facilitate student discussion.
- How is counting from 101 to 120 similar to counting from 1 to 20?
- What do you notice about each number in a row/column as you count? (Using the 120 chart)
- What is the number after 21? Is it less than or greater than 21? How do you know?
- Without counting, how can you tell me what number is ten more than 33?
- Is 33 greater or less than 43? How do you know?
Our students arebetter able to…
- Explain how they can tell you what one or ten more/less than a number is without having to count. (SMP 7)
- Use precise vocabulary when explaining the patterns they find. (SMP 6)
- Provide opportunities for students to find counting patterns when using tools such as the hundred chart, 120 chart and number lines. (SMP 7)
- Emphasize use of correct vocabulary: Column, row, greater than, less than, unit and digit. (SMP 6)
1st / Global Concept 2 of 4 for this Unit of Study (Click to view PowerPoint in slide show mode):Understanding Tens and Ones
Making groups of tens and ones using manipulatives / Projected Time Allotment:
4 days
Sample Essential Questions:
Day 1: How can you group ones to make counting quicker?
Day 2: How can you show a number as tens and ones?
Day 3: How can you represent a number using base ten blocks?
Day 4: What are four different ways you can represent a number?
Related Unit 6 Assessment: Go Math Ch. 6 #1,3,7,8,10-14, 16, 21, 23, 24
Instructional Resources
Manipulatives:
- Proportional Objects (Snap Cubes/Counters/Chain Links/Beads/Beans): These objects should be used prior to the pre-grouped base ten blocks to explore the idea that ten ones make one ten.
- Ten frames: Utilize when modeling numbers to help students understand and unitize ten ones into one ten.
- Base Ten Blocks: (Wait until day 3) Students will use base ten blocks to explore different representations of a number.
- Go Math Essentials: Lesson 6.3Listen and Draw p. 249 along with the teacher questions in the Teach and Talk can be used as an engage to get students thinking about counting a group of ten as one ten rather than having to count every object in the group.Share and Show p. 250 can be used as after the engage as an informal assessmentof the concept. Problem Solving p. 252 has real world scenarios that can be used as independent practice. On your Own p. 251 can be used with a small group that needs a reteach opportunity. These students should physically be placing the snap cubes in ten frames.
- Representing Numbers Game: This can be used for partner practice or whole group on Day 2. Students will choose a card and then represent the number 3 other ways. For example, if the student turns over 1 ten 4 ones, they will record: 14, 10+4, and a quick pic on their recording sheet.
- Go Math Essentials: Lesson 6.6 Share and Show p. 262 can be used after the first part of building conceptual knowledge as an informal assessment of the concept. Problem Solving p. 264 and Problem Solving p.268 can be used as independent practice while the teacher pulls a small group. Closure: Students should select who represented the number correctly and why.
- Differentiation activities for Day 4 can be found on the PowerPoint.
Sample HOT Questions: Select or create appropriate questions to facilitate student discussion.
- What is the difference between 2 and 20?
- What is the difference between 13 and 31?
- When you look at the number 19, how do you know if the 9 tells the number of tens or the number of ones?
- When writing the number 32, why does it matter in which order you write the 3 and the 2?
Our students are better able to…
- Choose appropriate tools and be open to moving to more efficient tools as their understanding progresses. (SMP 5)
- Use precision while explaining the concept of place value when counting and representing numbers. (SMP 6)
- Represent numbers flexibly. (SMP 5)
- Provide opportunities to see the natural connections between student-produced groups of ten (like the snap cube rods and ten frames) to the pre-grouped base ten rod. (SMP 5)
- Emphasize use of correct vocabulary: digit, ones, tens, hundred, order and place value. (SMP 6)
- Provide opportunities to see and represent numbers flexibly. (SMP 5)
1st / Global Concept 3 of 4 for this Unit of Study (Click to view PowerPoint in slide show mode):Thinking About Numbers Flexibly
Showing numbers in different ways / Projected Time Allotment:
4 days
Sample Essential Questions:
Day 1: How can two different base ten models represent the same number?
Day 2:How can you show different ways to represent a two-digit number using base ten?
Day 3:How can you show all the ways to represent a two-digit number using base ten?
Day 4:How can you use tens and ones to represent a number in more than one way?
Related Unit 6 Assessment: Go Math Ch. 6 #5, 18
Instructional Resources
Manipulatives:
- Base Ten Blocks - Students will use base ten blocks to explore different representations of a given number.
- I Have, Who Has: This activity can be used as an engage on Day 1. It will get students thinking about the base ten representations of numbers.
- Tens and Ones Match-Up Task: Cooperative task for exploring multiple representations of the same number. This task is a great way to introduce the topic of flexible representation on Day 1; it allows the students to “discover” the concept on their own.
- Go Math Essentials: Lesson 6.8 Share and Show p. 271 #4-6 can be used on Day 2 as independent practice. Students will create multiple representations of a given number. Unlock the Problem p. 269 can be used as an engage on Day 3. The problem relates flexible thinking to the real world.
- Different Ways Task: This task can be used as independent practice on Day 3. Students will try to show all the ways to represent a two-digit number.
- Virtual Manipulatives- Base Ten Blocks
- Animated Math Model- Skill 31: Different Ways to Show Numbers
- Flexible Representations: This website poses students with a 2-digit number and asks the students to select which representation matches the number.
- Expanded Form: This website asks students to represent numbers in an expanded base ten form.
Sample HOT Questions: Select or create appropriate questions to facilitate student discussion.
- Jose says that there is only one way that he can use base ten blocks to represent the number 65. Is this reasonable?
- Juan represented a number using 4 tens and 3 ones. Kim represented a number with 3 tens and 13 ones. Kim says that even though they look different their numbers are the same. Do you agree with her? Explain your thinking.
- Jack’s teacher asked him to represent the number 57 with base ten blocks. He said that he cannot, because he only has 4 tens and some ones in the bottom of his bin. Do you think he is correct? Explain.
Our students are better able to…
- Compose (create through different combinations) and decompose (break apart in different ways) two digit numbers flexibly. Example: 25 can be made up of 1 ten and 15 ones or 2 tens and 5 ones or 25 ones. (SMP 5)
- Communicate clearly about their representations of numbers. (SMP 6)
- Give students opportunities to explore different representations of the same number. (SMP 5)
- Emphasize use of correct vocabulary: decompose, compose, similar, different, reasonable and representation. (SMP 6)
1st / Global Concept 4 of 4 for this Unit of Study (Click to view PowerPoint in slide show mode):Numbers 100 to 120
Model, read, and write numbers from 100 to 120 / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1: How can you model, read, and write numbers from 100 to 110?
Day 2: How can you model, read, and write numbers from 110 to 120?
Day 3: How can you represent the numbers 100 to 120 in more than one way?
Related Unit 6 Assessment: Go Math Ch. 6 #6, 9, 19, 20, 22
Instructional Resources
Manipulatives:
- Base Ten Blocks - Students will use base ten blocks to explore different representations of a given number.
- Go Math Essentials: Lesson 6.9 On Your Ownp.275 and Problem Solving p. 276 can be used for independent or partner practice for Day 1.
- Go Math Essentials: Lesson 6.10 Listen and Draw p. 277 can be used with Teach and Talk questions to as an engage on Day 2. This will be a review of the fact that 10 tens is the same as (equals) 100 from the previous day. On Your Own p. 279 and Problem Solving p. 280 can be used as independent practice on Day 2. Math Talk in Action p. 279 can be used to help facilitate a discussion problem 11 during closure on Day 2.
- Flexible Representations 100-120 Students will flip a card, record what is there, and then draw at least two more quick pics to represent the number.
- See PowerPoint for tasks that can be used to differentiate on Day 3.
- iTools: Number Chart - Virtual Hundred Chart (Select numbers 1-100 or the chart will include 0)
- Virtual Manipulatives - Base Ten Blocks
Sample HOT Questions: Select or create appropriate questions to facilitate student discussion.
- What number is the same as 11 tens? Explain your thinking.
- How many ones are in the number 110? Explain your thinking.
- Jacqueline represented the number 115 with 10 tens and 15 ones. Do you agree with her representation? Explain your thinking.
Our students are better able to…
- Represent numbers 101 to 120 in more than one way; compare and contrast these different models. (SMP 3, 5)
- Communicate effectively about their models as well as peers’ models. (SMP 6)
- Facilitate student discussion on the similarities and differences in various representations of the same number. (SMP 3)
- Use precise language when discussing models of numbers: tens, ones, exchange, trade, regroup (SMP 6)