Global Concept Guides: Recognizing the Counting Sequence,Whole Numbers Between 10-100 as Tens and Ones, Compare Numbers to 120
Prior Learning: “Developing understanding of whole number relationships and place value, including grouping in tens and ones” has been listed as a critical learning area for Grade 1. These concepts have been weaved throughout multiple units throughout the year and were explicitly addressed during Units 6 and 7. Students in grade 1 are expected to show mastery on the critical area concepts by the end of the year.
Progressions Document Link
Show What You Know Task:Results of Units 6 and 7 Assessments and Performance Tasks
Common Core State Standards for Mathematical Content :
MAFS.1.NBT.1.1Count to 120 (99), starting at any number less than 120 (99). In this range, read and write numerals and represent a number of objects with a written numeral.
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 a 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).
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:
The Critical Areas are not in addition to the standards; rather, they help by grouping and summarizing the most critical skills at each grade level, those around which teachers should plan much of their instructional time throughout the year. The instruction of these areas should form a firm foundation on which to build concepts and procedures in later years.
Notes on Assessment:
See common performance task link below
Unpacking the Standards for this Unit:
Students develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples of10. They compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they understand the order of the counting numbers and their relative magnitudes.
Common Performance Task with Rubric for this Unit:
Students show their understanding through use of a hundreds chart, problem solving and comparison of numbers.
Click herefor performance task and rubric.
Future learning:
At Grade 2, students extend their base-ten understanding to hundreds by viewing 10 tens as forming a new unit called a “hundred”. This lays the groundwork for understanding the structure of the base-ten system. They will 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. (Progressions Document)
1st / Global Concept 1 of 3 for this Unit of Study (Click to view PowerPoint in slide show mode):Recognizing the Counting Sequence
Students will fluently find 10 more or 10 less without manipulatives or counting / Projected Time Allotment:
2 days
Essential Questions:
Day 1:How can I use a hundreds chart to solve 10 more/10 less?
Day 2: How can I mentally find ten more or ten less?
Related Go Math Chapter Test Questions: NA
Instructional
Manipulatives:
- Hundreds Chart- students will use the hundreds chart to complete various activities listed in the PowerPoint
- Hundreds Board Pictures Activity: Riddle for creating the letter H on a hundreds chart. The teacher can create additional riddles for the hundreds chart.
- Scrambled Hundreds Board: Students fill in missing numbers on hundreds charts.
- 100 chart activities-Activity 10: Students will use a hundreds chart to find 10 more/10 less
- Ten More or Less Game: Students will choose a numeral card then spin a spinner. The spinner will determine whether the student needs to mentally find 10 more or 10 less than the number. The partner will use a hundreds chart to check the answer.
- Piggly Wiggly: The students will connect the concept of mentally finding 10 more and ten less to money. There are 4 sample problems. The teacher can create similar problems to use in the classroom.
- TenGame: Students will roll dice to create a 2 digit number to use as a starting number. They will then spin a spinner to determine whether they need to find 10 more/10 less. They should solve and then write the equation to match.
- See PowerPoint for some ideas to informally assess students ability to mentally find 10 more/10 less than a given number.
- iTools- Number Chart- Virtual Hundred Chart. (Select numbers 1-100 or the chart will include 0)
Sample HOT Questions: Select or create appropriate questions to facilitate student discussion.
- Start at ___ and count up to ___. (By ones or tens)
- 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 hundred or 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 __? Explain your thinking
- Is 33 greater or less than 43? How do you know?
Our students are better able to…
- Mentally find ten more or ten less than any given number up to 100. (SMP 1 & 8)
- Describe a pattern for finding ten more or ten less than a number using appropriate vocabulary. (SMP 6)
- Count from any given number to 120 by ones and tens by recognizing counting patterns. (SMP 7)
We give the students ample opportunities to determine ten more or ten less than any given number up to 100. (SMP 1 & 8)
Emphasize the use of correct vocabulary: Column, row, greater than, less than, unit, digit. (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)
1st / Global Concept 2 of 3 for this Unit ofStudy (Click to view PowerPoint in slide show mode):Whole Numbers Between 10-100 as Tens and Ones
Students will show mastery of flexibly representing numbers through 100 / Projected Time Allotment:
3 days
Essential Questions:
Day 1:What are different ways I can represent the same number?
Day 2:How can you model numbers using tens and ones?
Day 3: How can I show multiple ways to represent a number using tens and ones?
Related Go Math Chapter Test Questions: NA
Instructional
Manipulatives:
- Base Ten Blocks: can be used to represent numbers using place value
- Tens and Ones Mat: can be used to organize student thinking when using base ten blocks or to record quick pictures
- Ten Frames: can be used to reteach students who are struggling with ten ones making a ten
- Counters/Snap Cubes: can be used to model and flexibly represent numbers
- Base Ten Block Cards: This can be used as a partner game on Day 1. Students can flip over a card and record the number as many ways as they can. (ex. Standard form, base ten language, expanded form, number sentence, etc). Students can compare their number buildto their partner’s number build.
- I Have/Who Has: This activity can be used as an engage on Day 2 to review representing numbers using tens and ones.
- Concentration: Students will play a concentration game where they try to match a base ten model to the standard form. To extend the game, students can record another base ten representation of the number.
- Model and Show More than One Way: The students are given a number and have to draw 2 quick pics to represent the number.
- What Number am I?: Students will be given a clue and have to determine the number. The teacher can also have students create their own “What Number am I?” clues and trade with a partner.
- Multiple Ways: The students will choose a numeral card and show as many ways to represent the number with base ten blocks as many ways as we can.
- iTools- Base Ten Blocks
- Virtual Manipulatives- Base ten blocks
Sample HOT Questions: Select or create appropriate questions to facilitate student discussion.
- What is the value of the 1 in the number 14? Explain your thinking
- Alana thinks you can only model the number 24 with 2 tens and 4 ones. Do you agree with Alana’s thinking? Why or why not?
- Robby thinks that you can only model the number 60 with ten rods. Do you agree with Robby’s thinking? Why or why not?
- How can you prove that 6 tens and 4 ones is the same as 4 tens and 24 ones?
Our students are better able to…
- Flexibly compose and decompose two digit numbers. Example: 25 can be made up of 1 ten and 15 ones or 2 tens and 5 ones or 25 ones. (SMP 5)
- Use precise language when explaining how numbers can be represented in more than one way using tens and ones. (SMP 6)
- Give students opportunities to explore different representations of the same number. (SMP 5)
- Require students to use the correct vocabulary: decompose, compose, similar, different, reasonable, representation (SMP 6)
1st / Global Concept 3 of 3 for this Unit of Study (Click to view PowerPoint in slide show mode):Compare Numbers to 120
Students will compare numbers using comparison symbols as well as understanding the relative magnitude of numbers / Projected Time Allotment:
3 days
Essential Questions:
Day 1: How can place value help you compare numbers?
Day 2:How can we use symbols to compare numbers?
Day 3:What strategies can you use to compare numbers?
Related Go Math Chapter Test Questions: NA
Instructional
Manipulatives:
- Base Ten Blocks: can be used to build models of numbers to compare the value of the numbers
- Number Lines: Students can mark numbers on a number line to help compare the values of numbers.
- Place Value Mats: can be used to help students organize base ten blocks and numbers to help them compare values
- Balance of Values Lesson: This lesson can be used to begin Day 1. Students will actually use pan balances or balance scales to compare numbers. It is important to use the guiding questions under the section “The Bigger Picture.”
- Take Off/Touchdown: can be played on Day 1 to facilitate a discussion about using place value to compare numbers (see PowerPoint for details)
- Animal Top It: This task can be used on Day 2. Students compare length and weights of animals. They should record the comparisons with symbols in their journals.
- Roll and Compare: This task can be used on Day 2. Students will roll dice and then draw a quick pic and use symbols to compare their numbers.
- Four Corners: This can be used as a whole group activity at the beginning of Day 3. Students will be given a card that represents a number. The students will then decide which corner would be true for their number. The teacher should probe students about their thinking.
- So Sweet: Students will compare the sugar in popular cereals. This can be used as partner work on Day 3.
- iTools- Base Ten Blocks
- Virtual Manipulatives- Base ten blocks
Sample HOT Questions: Select or create appropriate questions to facilitate student discussion.
- Why would you need to compare numbers in real life?
- Amaya has more than 23 stickers but less than 31 stickers. How many stickers could she have? Explain your thinking
- What are 3 numbers greater than 65? How can you use place value to justify your answer?
Our students are better able to…
Use models such as base tens, place value charts, number lines and quick pics to compare numbers. (SMP 4)
Select the most efficient tools/strategies to compare numbers. (SMP 5)
Use the correct vocabulary: Place Value, Digit, Greater Than, Less Than, Equal to and symbols: >, <, and = to compare numbers. (SMP 6)
For more info on SMP’s click here. / Because as teachers we…
- Provide opportunities for students to model numbers to compare values. (SMP 4)
- Facilitate conversations amongst students about what the most efficient strategies are to compare numbers. (SMP 5)
- Emphasize the use of correct vocabulary: Place Value, Digit, Greater Than, Less Than, Equal to and symbols: >, <, and = to compare numbers. (SMP 6)