Thank You - Corwin

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Thank youFOR YOURINTEREST INCORWINPlease enjoy this complimentary excerpt from TheCommon Core Mathematics Companion: TheStandards Decoded, Grades K-2. Students extend theirunderstanding of place value by bundling tens with thislesson.LEARN MORE about this title, includingFeatures, Table of Contents, and Reviews.

Number and Operations in Base Ten2.NBT.A*Cluster AUnderstand place value.STANDARD 12.NBT.A.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:a. 100 can be thought of as a bundle of ten tens—called a “hundred.”b. 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).STANDARD 22.NBT.A.2: Count within 1000; skip-count by 5s, 10s, and 100s.STANDARD 32.NBT.A.3: Read and write numbers to 1000 using base-ten numerals, number names, and expandedform.STANDARD 42.NBT.A.4: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits,using , , and symbols to record the results of comparisons.*Major clusterNumber and Operations in Base Ten 2.NBT.ACluster A: Understand place value.Grade 2 OverviewStudents extend their understanding of place value to hundreds and to thousands by bundling 10 tens to make a hundred andlater extend that understanding to bundling 10 hundreds to make 1 thousand. It is important to scaffold the work of this clusterso that students understand the concept of 1 hundred and then multiple hundreds. Conceptual understandings and skills builtin previous grades should be explicitly connected to the new ideas in Grade 2 including place value, counting, and comparingnumerals to 1,000.Standard for Mathematical PracticeSFMP 2. Reason abstractly and quantitatively.SFMP 3. Construct viable arguments and critique the reasoning of others.SFMP 4. Model with mathematics.SFMP 5. Use appropriate tools strategically.SFMP 6. Attend to precision.SFMP 7. Look for and make use of structure.SFMP 8. Look for and express regularity in repeated reasoning.In second grade, students continue to develop a deep understanding of place value and use that understanding to add andsubtract within 1,000. This cluster focuses on the development of place value up to and beyond 100. Students should use thestructure of building tens out of 10 ones, building hundreds out of 10 tens, and building a thousand out of 10 hundreds. This isthe structure of our base-ten place value system. It is built on repeated reasoning that every time you have 10 of a particular item,you group it to make the next place value unit. Students use precision in describing their work with appropriate vocabulary andreading numbers accurately. They explain their reasoning to classmates throughout the cluster and compare their thinking withthat of their peers.Related Content ��1.NBT. B.2  1.NBT.B.398 The Common Core Mathematics Companion: The Standards Decoded, Grades K–2

STANDARD 1 (2.NBT.A.1)Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:a. 100 can be thought of as a bundle of ten tens—called a “hundred.”Students begin to unitize or consider 10 tens as a group or unit called 1 hundred.What the STUDENTS do: Review earlier place value experiences using concretematerials. Ask students to model and describe what happenswhen they have 10 ones. Reinforce the concept that 10ones can be bundled into 1 ten. Introduce the next place on the place value chart(Reproducible 11). Develop student vocabulary to see a hundred as a unitcomposed of 10 tens. Give students bundles of 10 straws or linking cubes andhave them make groups of 100. Given bundles of tens, students group them into bundles of100 and place them in the appropriate place on the placevalue chart. Understand the vocabulary that 1 hundred is made up of 10tens.GRADE 2What the TEACHER does:Addressing Student Misconceptions and Common ErrorsAlthough students may correctly place concrete representations on the hundreds chart and be able to read the numberrepresented accurately, they may become confused when writing the numeral since there are no objects in the tens or ones place,as in the number 405 or 450. Provide students with numeral cards that include the digit 0 so that students can put the 0 in thetens place and ones place to represent that there are no objects in those places. This should help them transition between theconcrete representation and the written numeral.b. 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).Once students understand the concept that 10 tens can be bundled to make 1 hundred, they explore multiples of 100 usingpictures, numbers, and words. Although not explicitly stated, representing, describing, and reading all numbers from 1 to 999 areincluded in this standard.What the TEACHER does:What the STUDENTS do: Give the students bundles of 10 straws to group into onehundred. Use concrete materials to bundle groups of 10 to representnumbers including 100, 200, 300, . . . 900 as bundles of 1hundreds with no tens and no ones. Place concrete representations on a place value chart toreinforce that the number is made up of hundreds and notens and no ones. Describe the multiples of 100 using words that include thenumber of groups of a hundred to reinforce understandinga hundred as a unit that is different from tens and ones. Forexample,10 tens200 is 2 bundles of 10 tens. 300 is 3 bundles of 10 tens.1 hundredNumber and Operations in Base Ten 99

What the TEACHER does (continued):What the STUDENTS do (continued): Build on experiences of bundling 10 tens into 1 hundred bygiving students tasks in which they bundle more tens into2 hundreds, 3 hundreds. Placing bundles of hundred on aplace value chart reinforces the concept that these numbersrepresent bundles of 1 hundred with no tens and no ones.For example, 300 is represented by 3 hundreds, 0 tens, and0 ones (Reproducible 11). Use concrete materials to represent any number from 1 to999 by making as many groups of hundreds as possible andplacing those in the hundreds place on a place value chart.Place any leftover tens in the tens place and ones in theones place. Describe the representation using numbers and words. Forexample,hundredstensones Pose questions that reinforce the concept that each groupof 10 tens makes 1 hundred. Ask students to describe thenumber of straws in terms of the number of hundreds. Forexample, 5 bundles of 100 would be 500. Connect physical and pictorial representation with writtennumerals for multiples of 100. Discuss why the digit 0 mustbe in the tens place and ones place. Use formative assessment protocols, including tasks, studentexplanations, and worksheets to determine if studentsunderstand unitizing and can describe multiples of 100 upto 900 as a number of hundreds with no tens and no ones. Begin to provide experiences with other numbers up to999. Extend experiences of bundling hundreds with someleftover tens. Put the straws on the place value chart andhave students describe the number and write the numeral. Extend experiences to numbers that would include tens andones so students need to bundle to make as many hundredsas possible and as many tens as possible with some onesleftover. Explicitly connect work with concrete materials and placevalue charts to pictures, verbal descriptions, and writingnumbers. Guide students to make explicit connections betweenconcrete materials and pictorial representations for placevalue. As students orally describe a number in terms ofplace value, they also connect that understanding to thewritten numeral. Give a number from 100 to 999 for students to constructusing straws and describe the value of each place.4 hundreds5 tensone400501 451 Write the numerals and identify how the written numbershows the number of hundreds, tens, and ones. Connect words to the written numeral. For example, 3hundreds, 2 tens, and 4 ones is written as 324 and read asthree hundred twenty-four.100 The Common Core Mathematics Companion: The Standards Decoded, Grades K–2

Addressing Student Misconceptions and Common ErrorsWatch for students who reverse digits. These students need additional opportunities to decompose numbers into groups ofhundreds, tens, and ones and put them in the correct place on a place value chart. Describing the number in terms of hundreds,tens, and ones should be followed by writing the numeral below the concrete representation.Observe students who may be counting hundreds, tens, and ones separately.For example,they count as100,200,300 . . .10, 20 . . .1, 2, 3rather than counting as 300, 20, 3 . . . 323.These students need additional practice relating the representation or picture to the accurate word name for the number.GRADE 2NotesNumber and Operations in Base Ten 101

100 The Common Core Mathematics Companion: The Standards Decoded, Grades K–2 Pose questions that reinforce the concept that each group of 10 tens makes 1 hundred. Ask students to describe the number of straws in terms of the number of hundreds. For example, 5 bundles of 100 would be 500.

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