Global Concept Guides: Understanding Numbers to 1,000, Thinking Flexibly about Numbers to 1,000, Skip Counting/Number Patterns, Comparing Numbers
Prior Learning: MACC.1.NBT.2.2.a, MACC.1.NBT.2.2.b, MACC.1.NBT.2.2.b, MACC.1.NBT.2.3
Progressions Document Link
Sample Show What You Know Task: Use the Go Math Ch. 2 Show What You Know or the Diagnostic Interview Task TE p. 54
Common Core State Standards for Mathematical Content :
Understand place value
MACC.2.NBT.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).
MACC.2.NBT.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.
MACC.2.NBT.8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900 / Comments:
Notes on Assessment:
Unit 3 Assessment: Go Math Ch. 2
See common performance task link below.
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
This GCG focuses on representing 3-digit numbers with base ten blocks and finding the value of each digit. / 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 given 3-digit number with base ten blocks?
Day 3: How do you use base ten blocks to help find the value of a digit?
Day 4:How can you find the value of a digit in a number?
Related Unit 3 Assessment:Go Math Ch. 2 #1, 2, 9, 10, 13, 14, 23, 24
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)
- Large digit cardsfor students touse for students modeling numbers in standard form.
- Go Math Lesson 2.1 Essentials:SE p. 60 # 9 & 10; TE 57B (use Enrich activity as engage); Enrichp. 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
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 7 tens have the same value.
- How does placing a zero in the (beginning, middle, 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 )
- 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.
- Focus on student understanding of how tens and hundreds are related. (SMP 7)
- Emphasize precise use of vocabulary: ones, tens, hundreds, equivalent, value, model, standard form, digit. (SMP 6)
2nd / Global Concept 2 of 4 for this Unit of Study: Thinking Flexibly about Numbers to 1,000
This GCG focuses on making models, pictures, and values of 3-digit numbers in multiple ways. / Projected Time Allotment:
4 days
Sample Essential Questions:
Day 1: How do you write a 3-digit number that is shown by a set of base ten blocks?
Day 2: What are three ways to write a 3-digit number?
Day 3: How can you use base ten blocks or quick pictures to show the value of a number in different ways?
Day 4: How can an organized list help me represent the value of a number in multiple ways?
Related Unit 3 Assessment: Go Math Ch. 2# 6, 11, 12, 15, 16, 19, 20
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 2.4 Essentials: Engage TE p. 69, SE p. 71-72.
- Go Math Lesson 2.6 Essentials: select problems from SE p. 79 & 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 & 88
- 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 number in the hundreds digit?
- What is a number where the hundreds digit is two more than the tens digit?
- How can you prove that 1 hundred, 4 tens, and 3 ones is equal to 13 tens and 13 ones?
- How does the value of the number ___ 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?
Our students are better able to…
- Use base ten blocks to represent three digit numbers different ways which could include any of the following: quick pictures, base ten blocks, standard form, word form and expanded form. (SMP 2, 5)
- Explain how the value of a digit changes based on its position within a number. (SMP 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 3 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)
- Facilitate the use of an organized list when representing
- 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, digit. (SMP 6)
2nd / Global Concept 3 of 4 for this Unit of Study: Skip Counting/Number Patterns
This GCG focuses on patterns in place value and skip counting up to 1,000. / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1: How do you use patterns in place value to find 10 more, 10 less, 100 more, or 100 less than a 3-digit number?
Day 2: How do you use patterns to skip count forwards and backwards by 2s and 5s up to 1,000?
Day 3: How does place value help you identify and extend counting patterns?
Related Unit 3 Assessment:Go Math Ch. 2# 3, 4, 17, 18
Instructional Resources
Manipulatives:
- Place Value Chart with 10 frames- page 1 and page 2.
- Base Ten Blocks to represent numbers to identify patterns of digits in each place value.
- Hundred Chartto show patterns when counting forward and backwards by 2s, 5s, 10s, and 100s.
- Open Number Line which allows students to count by 2s, 5s, 10s, and 100s and identify patterns.
- Go Math Lesson 1.9 Essentials: Problem Solving TE p. 48
- Go Math Lesson 2.9 Essentials: Model and Draw TE p. 90; Problem Solving #20-23 TE p. 92; 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. Questions #9-10 TE p. 95;Problem Solving#11-13 TE p. 96
- iTools Base-Ten Blocks –virtual manipulative
- iTools Hundreds Chart (1-100) – virtual manipulative
- - Studentswill 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 2s, 5s, 10s, or 100s and why is this a useful skill to have?
- Your teacher has asked you to count and make sure that she has 1,000 crayons in her bin. Should you count by 2s, 5s, 10s, or 100s? Explain your thinking.
- Use skip counting to solve this problem. Miguel has 256 cookies. He gives 6 cookies to each of his 10 friends. Three more friends walk in and Miguel gives each of them 5 cookies. Six friends walk in and he gives each of them 2 cookies. How many cookies does he have now?
Our students are betterable to…
- Model counting strategies on a hundred chart, an open number line, and a place value chart with base ten blocks. (SMP 4)
- Discover patterns that occur when skip counting by 2s, 5s, 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 2s, 5s, 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, skip counting, groups, forward, backward, extend (SMP 6)
2nd / Global Concept 4 of 4 for this Unit of Study: Comparing Numbers
This GCG focuses on comparing 3-digit numbers using place value. / 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 without drawing a picture?
Day 3: How do the comparison symbols help you compare numbers efficiently?
Related Unit 3 Assessment:Go Math Ch. 3 # 7, 8, 21, 22
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 which can help student 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
- iTools Base-Ten Blocks– virtual manipulative - Select “Compare” under the Activities tab.
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- Why would you need to compare numbers in real life?
- The Thomas siblings have been saving their allowance to go shopping. Janae has saved $143, Edmond has saved $234, Harold saved $158 and La’quitta saved $243. Compare all the numbers using the comparison symbols.
- Sachelle sees more than 317 black ants but fewer than 346 black ants. How many black ants might she have seen? Explain your thinking.
Our students are better able to…
- Use models (base tens, place value charts, number lines, etc…) to compare numbers.
- Select the most efficient tools/strategies to compare numbers. (SMP 5)
- Solve real world word problems that involve number comparison. (SMP 1)
- Provide opportunities for students to model numbers to compare values. (SMP 4 , 5)
- Facilitate conversations amongst students about what the most efficient strategies are. (SMP 3)
- Provide students with word problems and probe their thinking. (SMP 1, 3)
- Emphasize precise use of vocabulary: ones, tens, hundreds, place value, compare, efficient, digit, value, number lines, comparison symbols. (SMP 6)