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Grade 1 UbD Math Unit Planning 2014 to 2015 PS 105 Unit/Book(s)/Topic Unit 7/Book 8/Addition and Subtraction, part IV Approximate Days or Dates 35 to 40 days Stage 1 - Identify Desired Results Learning Outcomes What relevant goals will this unit address? (must come from curriculum; include specific Common Core standards) Extend the counting sequence. 1.NBT.1: Count 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. 1.NBT.2: Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 1.NBT.2.A: 10 can be thought of as a bundle of ten ones — called a "ten." 1.NBT.2.B: The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. 1.NBT.2.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). 1.NBT.3: Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. Use place value understanding and properties of operations to add and subtract 1.NBT.4: Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 1.NBT.5: Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. 1.NBT.6: Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Enduring Understandings What understandings about the big ideas are desired? (what you want students to understand & be able to use several years from now) What misunderstandings are predictable? Essential Questions What are the Essential Questions? Are there any potential cross-curricular connections during this chapter? Students will understand that... Essential Question: Making Ten is a strategy we can use to help us add without counting. When you add two-digit numbers you can add tens to tens and ones to ones or you can keep one number whole, add the tens, and then add the ones of the second number. Why is 10 the Most Useful Number? Cross-curricular connections… Related misconceptions… Knowledge: What knowledge will student acquire as a result of this unit? This content knowledge may come from the chapter’s goals, or might also address prerequisite knowledge that students will need for this unit. Skills: What skills will students acquire as a result of this unit? List the skills and/or behaviors that students will be able to exhibit as a result of their work in this unit. Students will know… Students will be able to… Addition facts to 10 fluently. Subtraction facts within 10 fluently. Addition facts to 20 strategically. Subtraction facts to 20 strategically. Count to 120 starting at any number in the sequence. Count to 100 by2s, 5s, and tens. Count large sets of objects by organizing them into groups of ten. Compose and decompose numbers from 11 to 19 into tens ones and some further ones. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. Mentally find 10 more or 10 less than a two-digit number. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract multiples of ten from other multiples of ten. Stage 2 – Assessment Evidence Evidence Through what evidence (work samples, observations, quizzes, tests, journals or other means) will students demonstrate achievement of the desired results? Formative and summative assessments used throughout the unit to arrive at the outcomes. Brief Written Description of the Performance Task The final performance assessment is administered during a class period. The task can be read to the students. The students are allowed to use any tools or materials they normally use in their classroom. Task Description: This task allows students to demonstrate their understanding of place value. Throughout the task they are required to show understanding of whole numbers, understand that two digits of a twodigit number represent amounts of tens and ones, compare two two-digit numbers based on meanings of the tens and ones digits, and compose and decompose numbers in flexible ways. Rubric for Assessment: The rubric section contains a scoring guide and performance level descriptions for the task. Scoring Guide: The points highlight each specific piece of student thinking and explanation required of the task and help teachers see common misconceptions (which errors or incorrect explanations) keep happening across several papers. The scoring guide can then be used to refer back to the performance level descriptions. Performance level descriptions provide score ranges for each level, which are assessed using the scoring guide. Performance Level Description and Cut Scores Performance is reported at four levels: 1 through 4, with 4 as the highest. Level 1: Demonstrates Minimal Success (0 – 2 points) Level 2: Performance Below Standard (3 – 4 points) Level 3: Performance at Standard (5 - 6 points) Level 4: Achieves Standards at a High Level (7 -9 points) Student Self-Assessment How will students reflect upon or self-assess their learning? Stage 3 – Learning Plan # Content Goal Notes Investigation 1: Counting Beyond 100 1.1 Ten Turns 1.2 Revisiting the 100 Chart 1.3A Counting to 120 and Beyond 1.4 Counting Strips Notes Investigation 2: Twos, Fives, and Tens 2.1 How Many Hands? 2.2 2.3 More Problems About Twos Twos and Fours 2.4 How Many Fingers? 2.5 How Many Squares? 2.6 How Many Feet? Lesson Notes/Planned Differentiation This first investigation focuses on ensuring that the students understand the numbers from 1 to at least 120 (NBT.1). The Ten Turns game also works on the skill of counting on from higher numbers. If you would like additional center activities to assist with differentiation, see the link to the right. You can teach this lesson as written, with the whole class playing Ten Turns, or you can use it as one of several centers. If you do it as a center, be sure all the students get sufficient time to play it. Do this lesson as written, but add the DAFC so that there are three centers. This lesson REPLACES 1.3. Do this lesson as written. If you prefer only three centers, eliminate Missing Numbers. Note that you can have students check their Counting Strips with a calculator (type +1=== and the calculator will count). This lesson is a continuation of 1.3A. This investigation focuses on counting by twos, fives, and tens, which is an essential component of place value. If you would like additional center activities to assist with differentiation, see the link to the right. This lesson seems too simple to do as written. Try using the How Many Hands activity as one of several centers. And see the differentiation advice on TG p. 56. You can do this as written, but have something planned for early finishers. You can do this as written. Be sure to focus the discussion at the end on student strategies for BOTH recording and combining. You can do this as written. Note that SAB page 26 is an optional challenge for those students who finish page 25. Do this as written, but add the DAFC if you would like a third center activity. Note that this lesson continues the next two days. This is a continuation of session 2.5. Additional Resources or Math Centers http://www.k5mathteachingresources.com/CountingActivities.html Optional centers today Missing Numbers Ten Turns DAFC Counting Strips What’s Missing? Missing Numbers Ten Turns Counting Strips What’s Missing? Missing Numbers Ten Turns http://www.k5mathteachingresources.com/CountingActivities.html How Many Hands? Ten Turns? DAFC How Many Squares? Problems About Twos, Fours, and Fives DAFC (optional) How Many Squares? Problems About Twos, Fours, and Fives DAFC (optional) 2.7 How We Counted This is a continuation of session 2.5. 2.8 Notes N/A Investigation 3: Tens 3.1 Addition Combinations 3.2 Roll Tens 3.3 and 3.4 and 3.5 Notes Ten Plus/Equivalent Expressions 4A.1 How Many Cubes? 4A.2 Adding and Subtracting 10 4A.3 Adding with Cubes SKIP This Session This investigation focuses on the essential strategy of Making a Ten. For example, to add 8 + 6, we want students to think 8 + 2 = 10 and 4 more makes 14. It is essential to use your DAFC during this investigation and to ensure that your data is up to date about the strategies your students have mastered. If you would like additional center activities to assist with differentiation, see the link to the right. This lesson is ONLY necessary for students who do not yet know their combinations of ten fluently. You could SKIP to the next lesson, and have those students play make ten memory or another make ten game during the DAFC. Roll Tens is a great game that can be differentiated by the size of the board (30, 50, or 100). The game is greatly enhanced if you provide each pair with an index card with the questions, “How many cubes do we need to finish the row? How many cubes do we need to fill our mat?” One partner rolls the dice, adds cubes to the mat, and their partner asks them the two questions. Note that each partner is sharing one game board. Half the class should play this game while the other half does the DAFC and then switch. This is another great game that focuses explicitly on the Making Ten strategy. You can have the whole class play it or make fewer game boards and use it as one of two or three centers. Repeat these three centers for another few days. Leave 10 minutes at the end of each day for the discussions in the TG page 113 and page 118 and page 122. This is a REALLY important investigation because it helps students make progress in multi-digit addition and subtraction strategies that they need for second grade. If time allows, consider taking two or three days for each of these lessons so that students have plenty of time to learn the strategies. Do this activity as the teacher-led center while choosing two of the other three centers that you have been doing. The goal here is to help all students improve their understanding of using tens and ones. Save time for the discussion in the TG page CC94. Do this lesson as written, but with the option of including a third center if you prefer. Since there are two new centers here, consider repeating this for another day or two if you are finding it valuable for your students. Do this lesson as written, but with the option of including a third center if you prefer. Since there are once again two new centers here, consider repeating this for another day or two if you are finding it valuable for your students. 4A.4 and 4A.5 How Many Now? Investigation 4: Adding and Subtracting with 2-Digit Numbers Unit Assessment Do this lesson as written, but with the option of including a third center if you prefer. Since there are once again two new centers here, consider repeating this for another day or two if you are finding it valuable for your students. How Many Squares? Problems About Twos, Fours, and Fives DAFC (optional) http://www.k5mathteachingresources.com/numer ation-activities.html Roll Tens DAFC Ten Plus Roll Tens DAFC How Many Cubes? Ten Plus Roll Tens DAFC Plus or Minus Ten Adding or Subtracting Ten Teacher’s Choice Adding One to Ten Cubes Adding Ten Teacher’s Choice Build and Remove How Many Now? Teacher’s Choice Post-Unit Reflection Considerations Comments Required Areas of Study: Was there alignment between outcomes, performance assessment and learning experiences? Adaptive Dimension: For struggling students: Did I make purposeful adjustments to the curriculum content (not outcomes), instructional practices, and/or the learning environment to meet the learning needs and diversities of all my students? For students who need a challenge: Suggested Changes: How would I do the unit differently next time?