Global Concept Guides: Understanding Numbers to 1,000, Thinking Flexibly about Numbers to 1,000, Skip Counting/Number Patterns, Comparing Numbers
Prior Learning:MAFS.1.NBT.2.2,MAFS.1.NBT.2.3
Progressions Document Link
Sample Show What You Know Task: Use the Go Math Ch. 2 Show What You Knowor the Diagnostic Interview Task TE p. 54.
Mathematics Florida Standards for Mathematical Content:
Understand place value
MAFS.2.NBT.1.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
- 100 can be thought of as a bundle of ten tens –called a “hundred.”
- The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
MAFS.2.NBT.1.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
MAFS.2.NBT.1.4Compare two-three digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
Use place value understanding and properties of operations to add and subtract.
MAFS.2.NBT.2.8Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900 / Comments:Using base-ten blocks to build three and four-digit numbers will help children understand how the value of a digit changes depending upon its place within a number. Students should be encouraged to represent base-ten models with pictorial representations. Click here for a video on pictorial representations on three and four-digit numbers.
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. (Spanish)
Notes on Assessment:
Assessment: Modified Unit 2
See common performance task link below. Please administer question 1 and 2 AFTER the second GCG and 3 and 4 AFTER the third GCG.
Unpacking the Standards for this Unit: “Second grade students extend their base-ten understanding as they view 10 tens as a unit called a ‘hundred’. They use manipulative materials and pictorial representations to help make a connection between the written three-digit numbers and hundreds, tens, and ones.” Click here for more info. It is vital during this unit to go through the steps of concrete, pictorial, abstract. Students who rushed through these steps are not building a true understanding and often struggle long term (e.g. addition and subtraction with regrouping). A strong foundation in this concept will help students skip count, compare, and order numbers.
Common Performance Task with Rubric for this Unit:
Ja’quan’s Problem– Students will be representing number in pictorial and standard form through problem solving. Students will create and compare 3-digit numbers and recognize patterns within numbers up to a 1,000. Click here for common performance task and rubric.
Future learning: Representing numbers flexibly prepares children to make sense of adding and subtracting multi-digit numbers where regrouping is required. Understanding the decimal (place value) system has been described as “the most difficult and important instructional task in mathematics in the early years” (Resnick, 1983, p. 126). “Essentially, it involves interpreting numbers, not just as individual units or as points in a sequence, but as parts of other numbers.” (Martinez & Martinez, 2007, p. 120)
2nd / Global Concept 1 of 4 for this Unit of Study: Understanding Numbers to 1,000 / Projected Time Allotment:
4 Days
Sample Essential Questions:
Day 1: How do you use groups of tens to make hundreds?
Day 2: How do you model a 3-digit number with base-ten blocks?
Day 3/4: How can you find the value of a digit in a number?
Related Unit 2 Modified Assessment:Go Math Ch. 2 # 1, 2, 5, 8, 9, 10, 11, 12, 14, 15, 18
Instructional Resources
Manipulatives:
- Counters to make groups of ten to make a hundred.
- Base-ten blocks for modeling place value.
- Place value mats (page 1 and page 2) to help student make the connection between base-ten manipulatives and place value.
- Large digit cardsfor students tomodel numbers in standard form.
- Go Math Lesson 2.1 Essentials: SE p. 60 # 9 & 10; TE p. 57B (Enrich activity can be used within core or reteach small group); Enrich p. E10
- Go Math Lesson 2.2 Essentials: SE p. 64 #8-10
- Go Math Lesson 2.3 Essentials: SE p. 65 (Math Talk)-Day 2; p. 68 #11
- Go Math Lesson 2. 5Essentials: SE p. 75 #10, 76 #11-12; Enrich p. E 14
- Voyages Anchors Lesson: Build the Numberp. 93 and p.94– building numbers with base-ten blocks
- iTools- Base-Ten Blocks- virtual manipulative
- Animated Math: Hundreds, Tens, and Ones – guided support for reteach.
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- How can you prove the value of a digit?
- How can you tell how many hundreds there are in _____(e.g. 15 tens)?
- Justify which value is greater ____ or _____ (e.g. 42 tens or 402)
- Explain why 17 tens, and 1 hundred and 7 tens have the same value.
- How does placing a zero in the beginning, middle, or end of a number change the value?
Our students are better able to…
- Use base-ten blocks to model grouping tens to make a hundred (SMP 5).
- Justify equivalent values of different models (e.g. 17 tens = 170) (SMP 3).
- Make connections between base-ten blocks, quick pictures, and standard form for place value (SMP 7).
- Communicate using precise Math vocabulary (SMP 6).
- Facilitate discussion on grouping tens within the place value system (SMP 3).
- Provide multiple opportunities for students to make connections between base-ten blocks, quick pictures, and the standard form of a number (SMP 7).
- Focus on student understanding of how tens and hundreds are related (SMP 7).
- Emphasize precise use of vocabulary: ones, tens, hundreds, thousand, equivalent, value, model, standard form, digit, unit, rod/long, flat (SMP 6).
2nd / Global Concept 2 of 4 for this Unit of Study: Thinking Flexibly about Numbers to 1,000 / Projected Time Allotment:4 days
Sample Essential Questions:
Day 1: How do you record a 3-digit number that is shown by a set of base-ten blocks?
Day 2: How can you use base-ten blocks or quick pictures to show the value of a number in different ways?
Day 3: How can you represent 3-digit numbers in multiple ways?
Day 4: What strategy can you use to organize the different ways to represent a number?
Related Unit 2 Modified Assessment: Go Math Ch. 2# 1, 2, 5, 8, 9, 10, 12, 14, 15, 18
Instructional Resources
Manipulatives:
- Base-ten blocks for students to build and represent numbers
- Place value mats to organize representations with base-ten blocks (part 1 and part 2).
- Secret code cardsto represent numbers in expanded form and standard form (for more information,see the PowerPoint)
- Go Math Lesson 2.4Essentials: Engage TE p. 69, SE p. 70 or 71 and Problem Solving on p. 72.
- Number Representation-Graphic Organizer to represent numbers multiple ways.
- Animated Math Model- Animated model to show the different representations of numbers.
- Go Math Lesson 2.6 Essentials: select problems from SE p. 79 & Problem Solving on p. 80
- Go Math Lesson 2.7 Essentials: quick pictures and SE p. 83
- Go Math Lesson 2.8 Essentials: Listen and Draw SE p. 85, select items from p. 86-87Problem Solving p. 88.
- What Am I Riddle Cards
- Real World Number Scavenger Hunt- Challenges students to identify numbers in the real world
- Expanded Form Memory Game
- Journal Prompts for extending Place Value
- Voyages Place Value Lessons: Find The Missing Number , Different forms of numbers
- ETA Center Idea: Build a Bug House
- NCTM Illuminations: Create A House
- iTools: Base-Ten Blocks- Select “Other Forms” tab towards the bottom of the screen.
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- How can you represent the number _____ three different ways?
- What is the value of the digit in the (hundreds/tens/ones)place?
- Name a number where the digit in the (hundreds/tens/ones)place is two more than the digit in the (hundreds/tens/ones) place?
- How can you prove that 1 hundred, 4 tens, and 3 ones is equal to 14 tens and 3 ones?
- How does the value of the digit ___ change in each of these numbers? (e.g. How does the value of the number 4 change in 426, 342, 174?)
- How are 874 and 784 alike and different?
- What does the zero in ___ represent? (e.g. 206, 508, 120, 630).
- Why can’t we write the number ___ without the zero? (e.g. 206, 508, 120, 630).
- How would the value of ___ if we re-wrote it without the zero? (e.g. 206, 508, 120, 630).
Our students are better able to…
- Use base-ten models to represent three-digit numbers flexibly includingconcrete models with base-ten blocks and quick pictures (SMP 2, 5).
- Represent three-digit numbers in standard form, expanded form, and word form (SMP 2, 6).
- Explain how the value of a digit changes based on its position within a number (SMP 3, 7).
- Use an organized list to flexibly represent a number multiple ways (SMP 7, 8).
- Can increase/decrease the value of a number by adding and taking away base-ten blocks (SMP 2).
- Help students make connections between the different forms of a number (e.g. 1 hundred, 2 tens, and3 ones is the same as 100+20+3) (SMP 2, 5).
- Encourage students to flexibly move through the steps of concrete, pictorial, abstract when representing numbers different ways (SMP 2, 7).
- Facilitatediscussions to develop student understandingof how to flexibly represent three-digit numbers (e.g. 123 can be created using 1 hundred, 2 tens, and 3 ones; 0 hundreds, 12 tens, and 3 ones; 0 hundreds, 0 tens, and 123 ones, etc.). (SMP 7).
- Provide real-world scenarios when increasing/decreasing the value of a number (SMP 2).
- Emphasize precise use of vocabulary: ones, tens, hundreds, equivalent, value, model, standard form, expanded form, word form, and digit (SMP 6).
2nd / Global Concept 3 of 4 for this Unit of Study: Skip Counting/Number Patterns / Projected Time Allotment: 3 days
Sample Essential Questions:
Day 1: How do you use patterns in place value to find 10 more or 10 less within 100?
Day 2: How do you use patterns in place value to find 10 more or 10 less within 1,000?
Day 3: How do you use patterns in place value to find 100 more or 100 within 1,000?
Related Unit 2 Modified Assessment:Go Math Ch. 2# 3, 4, 13, 17
Instructional Resources
Manipulatives:
- Place Value Chart with 10 frames- page 1 and page 2.
- Place Value Mat without 10 frames.
- Base-ten Blocks- to represent numbers to identify patterns of digits in each place value.
- Hundred Chart is intended to print and tape together vertically to show patterns when counting by 10s and 100s. ~ 100 chart, 200 chart, 300 chart, 400 chart
- Open Number Line- allows students to count by 10 and 100s and identify patterns.
- Let’s Have Fun with 10 more and 10 less – CPALMS lesson using a hundred board with 10 more/10 less.
- Go Math Lesson 1.8 p. 41 and Go Math Lesson 1.9 p.45. Encourage students to find the missing numbers using 10 more or 10 less.
- Go Math Lesson 2.9 Essentials: Model and Draw TE p. 90; Problem SolvingTE p. 92 #20-23; Response to Intervention TEp. 89B.
- Go Math Lesson 2.10Essentials: ELL Language Support TE p. 93B; Enrich T.E. 93B; Listen and Draw TE p. 93; H.O.T. QuestionsTE p. 95 #9-10;Problem SolvingTE p. 96#11-13.
- iTools Base-Ten Blocks –virtual manipulative
- iTools Hundreds Chart (1-100) – virtual manipulative
- Give the Dog a Bone- - Students find a given number on a blank hundred chart.
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1,3)
- In what real world situation world you need to count by 10s or 100s and why is this skill useful?
- Nathan had 513 pages to read in his book. He read 10 pages and thinks he has 413 pages left. Do you agree with Nathan? Why or why not?
- Miguel has 256 cookies. He gives 10 cookies to each of his friends. Now he has 196 cookies. How many friends did he share cookies with?
- Savannah had 156 hair ribbons. She got 30 more. How many does she have?
Our students are better able to…
- Model counting strategies on a hundreds chart, an open number line, and a place value chart with base-ten blocks (SMP 4).
- Discover patterns that occur when counting by 10s, and 100s (SMP 7).
- Participate in conversations with their peers to justify their reasoning (SMP 2, 3).
- Provide opportunities for students to use manipulatives to count by 10s and 100s and discover patterns (SMP 4, 5).
- Probe students to help them make connections and discover patterns (SMP 7).
- Facilitate conversations between students to explain and justify their reasoning (SMP 2, 3).
- Emphasize precise use of vocabulary: patterns, groups, forward, backward, extend (SMP 6).
2nd / Global Concept 4 of 4 for this Unit of Study: Comparing Numbers / Projected Time Allotment:3 days
Sample Essential Questions:
Day 1: How can base-ten models help you compare numbers?
Day 2: How do you compare 3-digit numbers?
Day 3: How do the comparison symbols help you compare numbers efficiently?
Related Unit 2 Modified Assessment:Go Math Ch. 2# 4, 6, 7, 16, 18
Instructional Resources
Manipulatives:
- Base-ten Blocks for students to build models of numbers to compare the value of the numbers.
- Number lines for students to mark numbers on a number line to help compare the values of numbers.
- Secret code cards (found in Go Math manipulative kit) for students to build 3-digit numbers to compare.
- Place value mats-helps students organize base-ten blocks and numbers as they compare values.
- Grid paperto help organize their digits to efficiently use place value to compare their numbers.
- Go Math Lesson 2.11 Essentials: Unlock the Problem TE p. 97; Try Another Problem TE p. 98;Share and Show TE p. 99; On Your Own TE p. 100
- Go Math Lesson 2.12 Essentials: Listen and Draw TE p. 101; Problem Solving TE p. 104
- Max Mumm’s Number-Voyages Excursions activity
- Can I Put You in Your Place? – CPalms – game for ordering and comparing numbers
- Tornadoes: Which months had the most in 2009?– Lesson for comparing and ordering numbers
- Comparing Numbers Game- Students will apply their understanding of comparing numbers in a war type game.
- What’s Your Size- Students will solve problems by comparing and ordering numbers
- iTools Base-Ten Blocks– virtual manipulative - Select “Compare” under the Activities tab.
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- In what real world situations do you need to compare numbers?
- The Thomas siblings have been saving their allowance to go shopping. Janae has saved $342, Edmond has saved $234, and La’quitta saved $243. Order the siblings from the least amount saved to the greatest amount saved. Explain the process of comparing the amount of money Edmond and La’quitta saved.
- Sachelle sees more than 317 black ants but fewer than 346 black ants. How many black ants might she have seen? Explain your thinking.
- Adam has 12 tens, and 4 ones. Lesley has 1 hundred 1 ten and 14 ones. Who has the greater amount?
- How can you tell if two numbers are equal?
- The digit 9 is greater than the digit 1 so why is 98 less than 104?
Our students are better able to…
- Use models (base-tens, place value charts, number lines, etc.) to compare numbers(SMP 4, 5).
- Solve real world word problems that involve number comparison (SMP 1, 4).
- Compare or determine equality when numbers are represented flexibly (SMP 2, 7).
- Explain the process of comparing values of three-digit numbers (SMP 3).
- Provide opportunities for students to model numbers to compare values (SMP 4,5).
- Facilitate conversations amongst students about efficiency when comparing numbers (SMP 3).
- Provide students with word problems where numbers are represented flexibly(SMP 1, 3).
- Emphasize precise use of vocabulary: ones, tens, hundreds, place value, compare, efficient, digit, value, number lines, and comparison symbols(SMP 6).