6th Grade Mathematics - Orange Board of Education



1st Grade Mathematics

Unit 3 Curriculum Map:

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Table of Contents

|I. |Grade 1 Unit 3 Overview |p. 2 |

|II. |Common Core State Standards |p. 3-14 |

|III. |Misconceptions |p. 15-16 |

|IV. |IDEAL Math Block |p. 17 |

|V. |Math In Focus Lesson Structure |p. 18-19 |

|VI. |Transition Lesson Structure |p. 20 |

|VII. |Transition Guide Reference |p. 21 |

|VIII. |IDEAL Math Block Planning Template |p. 22-23 |

|IX. |Math In Focus Pacing Guide |p. 24-26 |

|X. |Pacing Calendar |p. 27-28 |

|XI. |Assessment Framework |p. 29 |

|XII. |PLD Rubric PLD Genesis Conversion Chart |p. 30 |

|XIII. |Connections to the Mathematical Practices |p. 31-32 |

|XIV. |Visual Vocabulary |p. 33-46 |

|XV. |Multiple Representations |p. 47-48 |

|XVI. |Chapter Quizzes |p. 49-53 |

XVII. Resources p. 54

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Grade1 Unit 3 Overview

|Unit 3: Chapters 9, 14-16 |

|In this Unit Students will |

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|Compare the length of objects directly and indirectly. (Chapter 9) |

|Order several objects according to length. (Chapter 9) |

|learn and apply strategies to do addition and subtraction mentally (Chapter 14) |

|How are calendars used to show days, weeks, and months of a year. (Chapter 15) |

|How are clocks used to read the time of the day? (Chapter 15) |

|How do we count, compare, and order numbers from 1 to 120? (Chapter 16) |

|How can numbers to 100 be added and subtracted with and without regrouping? (Chapter 16) |

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|Essential Questions |

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|How do we measure length directly and indirectly? |

|How can data collected be compiled into picture graphs or bar graphs? |

|How are calendars used to show days, weeks, and months of a year? |

|How are clocks used to read the time of the day? |

|How do we count, compare, and order numbers from 1 to 120? |

|How can numbers to 100 be added and subtracted with and without regrouping? |

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|Enduring Understandings |

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|Length and height can be compared using terms such as tall/taller/tallest, long/longer/longest, and short/shorter/shortest. |

|In measuring length we determine how many times a specific unit fits the object to be measured. |

|A mathematical concept associated with measuring time is the ability to arrange events in order using a calendar or a clock. |

|Pages in a calendar can be associated with corresponding ordinal numbers |

|There is an hour hand and a minute hand on a clock. |

|People can read time to the hour when the minute hand is at 12. |

|We can read time to the half hour when the minute hand is at the 6. |

|The ability to read a calendar and a clock relate to the notion of time, day, month and year in our everyday lives. |

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|Common Core State Standards: Chapter 9: Length |

|1.MD.1 |Order three objects by length; compare the lengths of two objects indirectly by using a third object. |

|First Grade students continue to use direct comparison to compare lengths. Direct comparison means that students compare the amount of an attribute in two objects without measurement. |

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|Example: Who is taller? |

|Student: Let’s stand back to back and compare our heights. Look! I’m taller! |

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|Example: Find at least 3 objects in the classroom that are the same length as, longer than, and shorter than your forearm. |

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|Sometimes, a third object can be used as an intermediary, allowing indirect comparison. |

|For example, if we know that Aleisha is taller than Barbara and that Barbara is taller than Callie, then we know (due to the transitivity of “taller than’) that Aleisha is taller than Callie, even if |

|Aleisha and Callie never stand back to back. This concept is referred to as the transitivity principle for indirect measurement. |

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|Example: The snake handler is trying to put the snakes in order- from shortest to longest. She knows that the red snake is longer than the green snake. She also knows that the green snake is longer than |

|the blue snake. What order should she put the snakes? |

|Student: Ok. I know that the red snake is longer than the green snake and the blue snake because, since it’s longer than the green, that means that it’s also longer than the blue snake. So the longest |

|snake is the red snake. I also know that the green snake and red snake are both longer than the blue snake. So, the blue snake is the shortest snake. That means that the green snake is the medium sized |

|snake. |

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|NOTE: The Transitivity Principle (“transitivity”)1 : If the length of object A is greater than the length of object B, and the length of object B is greater than the length of object C, then the length of |

|object A is greater than the length of object C. This principle applies to measurement of other quantities as well. |

|Example: Which is longer: the height of the bookshelf or the height of a desk? |

|Student A: I used a pencil to measure the height of the bookshelf and it was 6 pencils long. I used the same pencil to measure the height of the desk and the desk was 4 pencils long. Therefore, the |

|bookshelf is taller than the desk. |

|Student B: I used a book to measure the bookshelf and it was 3 books long. I used the same book to measure the height of the desk and it was a little less than 2 books long. Therefore, the bookshelf is |

|taller than the desk. |

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|Another important set of skills and understandings is ordering a set of objects by length. Such sequencing requires multiple comparisons (no more than 6 objects). Students need to understand that each |

|object in a seriation is larger than those that come before it, and shorter than those that come after. |

|Example: The snake handler is trying to put the snakes in order- from shortest to longest. Here are the three snakes (3 strings of different length and color). What order should she put the snakes? |

|Student: Ok. I will lay the snakes next to each other. I need to make sure to be careful and line them up so they all start at the same place. So, the blue snake is the shortest. The green snake is the |

|longest. And the red snake is medium-sized. So, I’ll put them in order from shortest to longest: blue, red, green. |

|(Progressions for CCSSM: Geometric Measurement, The CCSS Writing Team, June 2012.) |

|1.MD.2 |Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the |

| |length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is |

| |spanned by a whole number of length units with no gaps or overlaps. |

|First Graders use objects to measure items to help students focus on the attribute being measured. Objects also lends itself to future discussions regarding the need for a standard unit. |

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|First Grade students use multiple copies of one object to measure the length larger object. They learn to lay physical units such as centimeter or inch manipulatives end-to-end and count them to measure a |

|length. Through numerous experiences and careful questioning by the teacher, students will recognize the importance of careful measuring so that there are not any gaps or overlaps in order to get an |

|accurate measurement. This concept is a foundational building block for the concept of area in 3rd Grade. |

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|Example: How long is the pencil, using paper clips to measure? Student: I carefully placed paper clips end to end. The pencil is 5 paper clips long. I thought it would take about 6 paperclips. |

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|When students use different sized units to measure the same object, they learn that the sizes of the units must be considered, rather than relying solely on the amount of objects counted. |

|Example: Which row is longer? |

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|Student Incorrect Response: The row with 6 sticks is longer. Row B is longer. |

|Student Correct Response: They are both the same length. See, they match up end to end. |

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|In addition, understanding that the results of measurement and direct comparison have the same results encourages children to use measurement strategies. |

|Example: Which string is longer? Justify your reasoning. |

|Student: I placed the two strings side by side. The red string is longer than the blue string. But, to make sure, I used color tiles to measure both strings. The red string measured 8 color tiles. The blue|

|string measure 6 color tiles. So, I was right. The red string is longer. |

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|NOTE: The instructional progression for teaching measurement begins by ensuring that students can perform direct comparisons. Then, children should engage in experiences that allow them to connect number |

|to length, using manipulative units that have a standard unit of length, such as centimeter cubes. These can be labeled “length-units” with the students. Students learn to lay such physical units |

|end-to-end and count them to measure a length. They compare the results of measuring to direct and indirect comparisons. |

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|(Progressions for CCSSM: Geometric Measurement, The CCSS Writing Team, June 2012.) |

|Common Core State Standards: Chapter 11: Graphs |

|1.MD.4 | |

| |Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how|

| |many more or less are in one category than in another. |

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|First Grade students collect and use categorical data (e.g., eye color, shoe size, age) to answer a question. The data collected are often organized in a chart or table. Once the data are collected, First |

|Graders interpret the data to determine the answer to the question posed. |

|They also describe the data noting particular aspects such as the total number of answers, which category had the most/least responses, and interesting differences/similarities between the categories. |

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|As the teacher provides numerous opportunities for students to create questions, determine up to 3 categories of possible responses, collect data, organize data, and interpret the results, First Graders |

|build a solid foundation for future data representations (picture and bar graphs) in Second Grade. |

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|Example: |

|Survey Station During Literacy Block, a group of students work at the Survey Station. |

|Each student writes a question, creates up to 3 possible answers, and walks around the room collecting data from classmates. |

|Each student then interprets the data and writes 2-4 sentences describing the results. |

|When all of the students in the Survey Station have completed their own data collection, they each share with one another what they discovered. |

|They ask clarifying questions of one another regarding the data, and make revisions as needed. |

|They later share their results with the whole class. |

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|Student: |

|The question, “What is your favorite flavor of ice cream?” is posed and recorded. |

|The categories chocolate, vanilla and strawberry are determined as anticipated responses and written down on the recording sheet. |

|When asking each classmate about their favorite flavor, the student’s name is written in the appropriate category. |

|Once the data are collected, the student counts up the amounts for each category and records the amount. |

|The student then analyzes the data by carefully looking at the data and writes 4 sentences about the data. |

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|Common Core State Standards: Chapter 14: Mental Math Strategies |

|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. |

|First Grade students use concrete materials, models, drawings and place value strategies to add within 100. They do so by being flexible with numbers as they use the base-ten system to solve problems. The |

|standard algorithm of carrying or borrowing is neither an expectation nor a focus in First Grade. Students use strategies for addition and subtraction in Grades K-3. |

|By the end of Third Grade students use a range of algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction to fluently add and subtract within |

|1000. Students are expected to fluently add and subtract multi-digit whole numbers using the standard algorithm by the end of Grade 4. |

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|Example: 24 red apples and 8 green apples are on the table. How many apples are on the table? |

|Student A: I used ten frames. I put 24 chips on 3 ten frames. Then, I counted out 8 more chips. 6 of them filled up the third ten frame. That meant I had 2 left over. 3 tens and 2 left over. That’s 32. So,|

|there are 32 apples on the table. 






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|Student B: I used an open number line. I started at 24. I knew that I needed 6 more jumps to get to 30. So, I broke apart 8 into 6 and 2. I took 6 jumps to land on 30 and then 2 more. I landed on 32. So, |

|there are 32 apples on the table. |

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|Student C: I turned 8 into 10 by adding 2 because it’s easier to add. So, 24 and ten more is 34. But, since I added 2 extra, I had to take them off again. 34 minus 2 is 32. There are 32 apples on the |

|table. |

|10 more than 73 is 83. So, there are 83 apples in the basket. |

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|Example: 63 apples are in the basket. Mary put 20 more apples in the basket. How many apples are in the basket? |

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|Student A: I used ten frames. I picked out 6 filled ten frames. That’s 60. I got the ten frame with 3 on it. That’s 63. Then, I picked one more filled ten frame for part of the 20 that Mary put in. That |

|made 73. Then, I got one more filled ten frame to make the rest of the 20 apples from Mary. That’s 83. So, there are 83 apples in the basket. |

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|[pic] |

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|Student B: I used a hundreds chart. I started at 63 and jumped down one row to 73. That means I moved 10 spaces. Then, I jumped down one more row (that’s another 10 spaces) and landed on 83. So, there are |

|83 apples in the basket. |

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|[pic] |

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|Student C: I knew that 10 more than 63 is 73. And 10 more than 73 is 83. So, there are 83 apples in the basket. |

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|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. |

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|First Graders build on their county by tens work in Kindergarten by mentally adding ten more and ten less than any number less than 100. First graders are not expected to compute differences of two-digit |

|numbers other than multiples of ten. Ample experiences with ten frames and the number line provide students with opportunities to think about groups of ten, moving them beyond simply rote counting by tens |

|on and off the decade. Such representations lead to solving such problems mentally. |

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|Example: There are 74 birds in the park. 10 birds fly away. How many birds are in the park now? |

|Student A: I thought about a number line. I started at 74. Then, because 10 birds flew away, I took a leap of 10. I landed on 64. So, there are 64 birds left in the park. |

|[pic] |

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|Student B I pictured 7 ten frames and 4 left over in my head. Since 10 birds flew away, I took one of the ten frames away. That left 6 ten frames and 4 left over. So, there are 64 birds left in the park. |

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|[pic] |

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|Student C I know that 10 less than 74 is 64. So there are 64 birds in the park. |

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|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 subtractions; relate the strategy to a written method and explain the |

| |reasoning used. |

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|First Grade students use concrete models, drawings and place value strategies to subtract multiples of 10 from decade numbers (e.g., 30, 40, 50). They often use similar strategies as discussed in 1.OA.4. |

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|Example: There are 60 students in the gym. 30 students leave. How many students are still in the gym? |

|Student A: I used a number line. I started at 60 and moved back 3 jumps of 10 and landed on 30. There are 30 students left. |

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|[pic] |

|Student B I used ten frames. I had 6 ten frames- that’s 60. I removed three ten frames because 30 students left the gym. There are 30 students left in the gym. |

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|[pic] |

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|Student C: I thought, “30 and what makes 60?”. I know 3 and 3 is 6. So, I thought that 30 and 30 makes 60. There are 30 students still in the gym. |

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|[pic] |

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| |Apply properties of operations as strategies to add and subtract. |

|1.OA.3 | |

|Elementary students often believe that there are hundreds of isolated addition and subtraction facts to be mastered. However, when students understand the commutative and associative properties, they are |

|able to use relationships between and among numbers to solve problems. First Grade students apply properties of operations as strategies to add and subtract. Students do not use the formal terms |

|“commutative” and “associative”. Rather, they use the understandings of the commutative and associative property to solve problems. |

|Students use mathematical tools and representations (e.g., cubes, counters, number balance, number line, 100 chart) to model these ideas. |

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|Commutative Property of Addition |

|Associative Property of Addition |

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|The order of the addends does not change the sum. |

|For example, if |

|8 + 2 = 10 is known, then |

|2 + 8 = 10 is also known. |

|The grouping of the 3 or more addends does not affect the sum. |

|For example, when adding 2 + 6 + 4, the sum from adding the first two numbers first (2 + 6) and then the third number (4) is the same as if the second and third numbers are added first (6 + 4) and then the|

|first number (2). The student may note that 6+4 equals 10 and add those two numbers first before adding 2. Regardless of the order, the sum remains 12. |

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|Commutative Property Examples: Cubes |

|A student uses 2 colors of cubes to make as many different combinations of 8 as possible. |

|When recording the combinations, the student records that 3 green cubes and 5 blue cubes equals 8 cubes in all. In addition, the student notices that 5 green cubes and 3 blue cubes also equal 8 cubes. |

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|Associative Property Examples: Number Line: _____ = 5 + 4 + 5 |

|Student A: First I jumped to 5. Then, I jumped 4 more, so I landed on 9. Then I jumped 5 more and landed on 14. |

|[pic] |

|Student B: I got 14, too, but I did it a different way. First I jumped to 5. Then, I jumped 5 again. That’s 10. Then, I jumped 4 more. See, 14! |

|[pic] |

|Mental Math: There are 9 red jelly beans, 7 green jelly beans, and 3 black jelly beans. How many jelly beans are there in all? |

|Student: “I know that 7 + 3 is 10. And 10 and 9 is 19. There are 19 jelly beans.” |

| |Understand subtraction as an unknown-addend problem |

|1.OA.4 | |

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|Use representations to model related addition and subtraction facts using objects, pictures, numbers, and words. |

|Identify parts of addition and subtraction equations using the terms addend, missing addend, and total. |

|Explain their reasoning to the teacher and to classmates |

|Use the relationship between addition and subtraction to practice basic facts. |

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|Given change unknown problem situations, students begin to understand the relationship between addition and subtraction. |

|Students often find learning subtraction facts to be more challenging than learning addition facts. Thinking about subtraction as finding a missing addend helps students connect what they don’t know to |

|what they do know and to begin to work with subtraction facts as part of a fact family. This strategy is known as the think addition strategy for learning subtraction facts. Although there are other |

|strategies for learning subtraction facts, the think addition strategy reinforces both addition and subtraction facts. |

| |Relate counting to addition and subtraction |

|1.OA.5 | |

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|Use a variety of materials to continue to work on counting strategies to find sums and differences of basic facts through sums of 10. |

|Explain their thinking using a counting strategy for finding the answer to an addition or subtraction fact with sums to 10. |

|Look for patterns as they use counting strategies, including for which facts counting is efficient. |

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|Counting All (addition): The student counts out fifteen counters. The student adds two more counters. The student then counts all of the counters starting at 1 (1, 2, 3, 4,…14, 15, 16, 17) to find the |

|total amount. |

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|Counting On (addition): Holding 15 in her head, the student holds up one finger and says 16, then holds up another finger and says 17. The student knows that 15 + 2 is 17, since she counted on 2 using her|

|fingers. |

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|Counting All (subtraction): The student counts out twelve counters. The student then removes 3 of them. To determine the final amount, the student counts each one (1, 2, 3, 4, 5, 6, 7, 8, 9) to find out |

|the final amount. |

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|Counting Back (subtraction): Keeping 12 in his head, the student counts backwards, “11” as he holds up one finger; says “10” as he holds up a second finger; says “9” as he holds up a third finger. Seeing |

|that he has counted back 3 since he is holding up 3 fingers, the student states that 12 – 3 = 9. |

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|1.OA.6 |Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading|

| |to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums |

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|Use a variety of materials to develop understanding of strategies in adding and subtracting numbers with sums to 10. |

|Explain their strategy for finding the answer to an addition or subtraction fact with sums to 10, using objects, pictures, words, and numbers. Students should use strategies that are efficient and make |

|sense to them. Not all students will use the same strategy. |

|Demonstrate fluency for addition and subtraction facts with sums to 10. |

|Extend use of strategies to facts with sums to 20, using concrete, pictorial, and symbolic representations. |

|Explain their thinking for extended facts, using objects, pictures, words, and numbers. |

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|As students become comfortable with counting on strategies they should begin to have opportunities to us other strategies so they do not become dependent on counting, which beyond adding or subtracting 1 |

|or 2 is inefficient. |

|Students need experiences with physical counters and ten frames to develop conceptual understanding of strategies prior to skill drill, and practice. Although fluency requires accuracy with reasonable |

|speed (about 3 seconds per fact), it is best reached with a foundation of conceptual understanding and efficient strategies. Premature drill and practice does not produce fluency. |

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|1.OA.8 |Determine the unknown whole number in an addition or subtraction equation relating three whole numbers |

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|After solving various problems using concrete materials, write equations to represent their work symbolically. |

|Solve for the unknown in various positions in addition and subtraction equations. |

|Explain how they found the unknown value in an equation. |

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|First Graders use their understanding of and strategies related to addition and subtraction as described in 1.OA.4 and 1.OA.6 to solve equations with an unknown. Rather than symbols, the unknown symbols |

|are boxes or pictures. |

|Common Core State Standards: Chapter 15: Calendar and Time |

| |Tell and write time in hours and half-hours using analog and digital clocks. |

|1.MD.3 | |

|Students need lots of practice with telling time and in transferring their skills from an analog clock to a digital representation. The use of individual clocks with moving parts allows for students to |

|have practice with the concrete experience of telling time. A lesson in moving the minute hand forward in time, and not backwards, is necessary for correct depiction of time on an analog clock. |

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|Relate the telling of time to everyday activities within the classroom. Integrate this skill by surveying the class on times they go to bed, times they get up, times they arrive at school in order for this|

|skill to be more meaningful to their everyday lives. Additionally, look for opportunities throughout the day to incorporate time and the length of activities. |

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|The teacher can talk about and discuss with students, more specifically, 60 seconds in 1 minute, and 60 minutes in one hour, and 12 hours in the morning, 12 hours in the afternoon/evening, is easier for |

|students to understand (they can see this actually happen on a clock). It is best to go smallest unit to largest unit, as the larger the unit, the more abstract for young children. |

|Common Core State Standards: Chapter 16: Numbers to 120 |

|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. |

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|Count on from a number ending at any number up to 120. |

|Recognize and explain patterns with numerals on a hundreds chart. |

|Understand that the place of a digit determines its value. For example, students recognize that 24 is different from and less than 42.) |

|Explain their thinking with a variety of examples. |

|Read and write numerals to 120. |

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|Students extend the range of counting numbers, focusing on the patterns evident in written numerals. This is the foundation for thinking about place value and the meaning of the digits in a numeral. |

|Students are also expected to read and write numerals to 120. |

|1.NBT.2 | |

| |Understand that the two digits of a two-digit number represent amounts of tens and ones. |

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|This standard outlines a helpful progression for developing an initial understanding of place value, the concept that the location or place of a digit within a two-digit or three-digit numeral determines |

|the value of that digit. |

|1.NBT.2a |10 Can be thought of as a bundle of ten ones – called a “ten.” |

|Given objects such as counters, linking cubes, or ten frames, students bundle or group 10 ones to make a ten. |

|Develop vocabulary to refer to a group of 10 as 1 ten. |

|Differentiate between 1 ten (a bundle) and 10 ones. |

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|Students begin to unitize or consider 10 ones as a group or unit called a ten. Rather than seeing 10 individual cubes, they can link those cubes and make a group of 1 ten. |

|1.NBT.2c |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). |

|Once students have a firm grasp of the concepts of teen numbers being made up of 1 ten and some ones, they continue to explore with multiples of ten (10, 20, 30, 40, 50, 60, 70, 80, 90) as groups of ten |

|with no ones leftover. This prepares students for understanding place value with numbers greater than 20. |

|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 with their real meaning. Rather than use aids such as alligators or Pac-Man, it may help students who confuse the symbols to think that the open end of the symbol is always closest to the greater number and the closed end is always pointed to the lesser number. It is also important to give students opportunities to change the order of the numbers to see how it impacts the symbols and their meaning.

- 1.NBT.4

Students who do not know basic facts may be inaccurate computing with two-digit numbers. As those students continue to work on facts, physical models will help in adding accurately. Be sure that all students have ample experience with adding physical models on place value charts, counting on by benchmark numbers (tens and ones), using a hundreds chart, and using ten frames as appropriate. Make explicit connections among written physical models, strategies, and written formats.

- 1.NBT.5

Since understanding the concept of 10 more or 10 less leads to understanding additional place value concepts, students who depend on counting or using their fingers have not met this standard. Students who cannot determine 10 more or 10 less than a number from 1 to 100 need more experience with concrete materials, such as linking cubes or bundles of straws. Finding patterns on the hundreds chart is also helpful, but the language can be confusing for some students.

- 1.NBT.6

Some students may subtract the digits in the tens place but ignore the digits in the ones place. Ask them to describe what they are subtracting in terms of place value. For example, in subtracting 70-40, students should say they are taking 4 tens from 7 tens (or 7 tens minus 4 tens). Have them put concrete models on the place value chart and then subtract or physically remove the 4 tens from the 7 tens. They describe the difference as 3 tens. Ask them how to write 3 tens (30) and how many ones are in that number. They should explain why there are 0 ones and why it is necessary to put the digit 0 in the ones place.

- 1.MD.4

Some students may pose a question that has too many choices such as “What is your favorite color?” To help with this error, ensure students limit the categories to only three choices. Some students may not realize that they have not collected data from every student in the class. To help with this error, make sure students know the total number of classmates who will be answering the question. Some students may not be able to summarize with statements like, “The majority of the students like or have --,” or similar statements. To help with this, review and discuss summary statements.

Math In Focus Lesson Structure

|LESSON STRUCTURE |RESOURCES |COMMENTS |

|Chapter Opener |Teacher Materials |Recall Prior Knowledge (RPK) can take place just before the pre-tests|

|Assessing Prior Knowledge |Quick Check |are given and can take 1-2 days to front load prerequisite |

| |Pre-Test (Assessment Book) |understanding |

| |Recall Prior Knowledge | |

|The Pre Test serves as a diagnostic | |Quick Check can be done in concert with the RPK and used to repair |

|test of readiness of the upcoming |Student Materials |student misunderstandings and vocabulary prior to the pre-test ; |

|chapter |Student Book (Quick Check); Copy of the |Students write Quick Check answers on a separate sheet of paper |

| |Pre Test; Recall prior Knowledge | |

| | |Quick Check and the Pre Test can be done in the same block (See |

| | |Anecdotal Checklist; Transition Guide) |

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| | |Recall Prior Knowledge – Quick Check – Pre Test |

|Direct Involvement/Engagement |Teacher Edition |The Warm Up activates prior knowledge for each new lesson |

|Teach/Learn |5-minute warm up |Student Books are CLOSED; Big Book is used in Gr. K |

| |Teach; Anchor Task |Teacher led; Whole group |

|Students are directly involved in | |Students use concrete manipulatives to explore concepts |

|making sense, themselves, of the |Technology |A few select parts of the task are explicitly shown, but the majority|

|concepts – by interacting the tools, |Digi |is addressed through the hands-on, constructivist approach and |

|manipulatives, each other, and the | |questioning |

|questions |Other |Teacher facilitates; Students find the solution |

| |Fluency Practice | |

|Guided Learning and Practice |Teacher Edition |Students-already in pairs /small, homogenous ability groups; Teacher |

|Guided Learning |Learn |circulates between groups; Teacher, anecdotally, captures student |

| | |thinking |

| |Technology | |

| |Digi | |

| | |Small Group w/Teacher circulating among groups |

| |Student Book |Revisit Concrete and Model Drawing; Reteach |

| |Guided Learning Pages |Teacher spends majority of time with struggling learners; some time |

| |Hands-on Activity |with on level, and less time with advanced groups |

| | |Games and Activities can be done at this time |

| | | |

|Independent Practice |Teacher Edition |Let’s Practice determines readiness for Workbook and small group work|

| |Let’s Practice |and is used as formative assessment; Students not ready for the |

|A formal formative | |Workbook will use Reteach. The Workbook is continued as Independent |

|assessment |Student Book |Practice. |

| |Let’s Practice |Manipulatives CAN be used as a communications tool as needed. |

| | |Completely Independent |

| |Differentiation Options |On level/advance learners should finish all workbook pages. |

| |All: Workbook | |

| |Extra Support: Reteach | |

| |On Level: Extra Practice | |

| |Advanced: Enrichment | |

| Extending the Lesson |Math Journal | |

| |Problem of the Lesson | |

| |Interactivities | |

| |Games | |

| Lesson Wrap Up |Problem of the Lesson |Workbook or Extra Practice Homework is only assigned when students |

| |Homework (Workbook , Reteach, or |fully understand the concepts (as additional practice) |

| |Extra Practice) |Reteach Homework (issued to struggling learners) should be checked |

| | |the next day |

| | | |

| End of Chapter Wrap Up |Teacher Edition |Use Chapter Review/Test as “review” for the End of Chapter Test Prep.|

|and Post Test |Chapter Review/Test |Put on your Thinking Cap prepares students for novel questions on the|

| |Put on Your Thinking Cap |Test Prep; Test Prep is graded/scored. |

| | |The Chapter Review/Test can be completed |

| |Student Workbook |Individually (e.g. for homework) then reviewed in class |

| |Put on Your Thinking Cap |As a ‘mock test’ done in class and doesn’t count |

| | |As a formal, in class review where teacher walks students through the|

| |Assessment Book |questions |

| |Test Prep | |

| | |Test Prep is completely independent; scored/graded |

| | |Put on Your Thinking Cap (green border) serve as a capstone problem |

| | |and are done just before the Test Prep and should be treated as |

| | |Direct Engagement. By February, students should be doing the Put on |

| | |Your Thinking Cap problems on their own |

TRANSITION LESSON STRUCTURE (No more than 2 days)

• Driven by Pre-test results, Transition Guide

• Looks different from the typical daily lesson

|Transition Lesson – Day 1 |

| |

|Objective: |

|CPA Strategy/Materials |Ability Groupings/Pairs (by Name) |

| | |

| | |

| | |

| | |

| | |

|Task(s)/Text Resources |Activity/Description |

| | |

| | |

| | |

| | |

| | |

Grade 1 Unit 3 Transition Guide References:

|Chapter 14 |Objective |Additional Reteach Support |Additional |Kindergarten Progression |

| | | |Extra Practice Support | |

|Lesson 1 |Mental Addition |1B, pp.93-100 |1B, pp.69-70 |Find parts and wholes in |

| | | | |addition and subtraction |

| | | | |stories. Ch. 17 and 18) |

|Chapter 15 |Objective |Additional Reteach Support |Additional |Kindergarten Progression |

| | | |Extra Practice Support | |

|Lesson 1 |Using a calendar |1B, pp. 105-110 |1B, pp. 75-76 |Know the days of the week |

| | | | |and months of a year (Ch. |

| | | | |11) |

|Lesson 2 |Telling time to the hour |1B, pp. 111-116 |1B, pp. 77-80 | |

|Lesson 3 |Telling time to the half hour. |1B, pp. 117-122 |1B, pp. 81-86 | |

|Chapter 16 |Objective |Additional Reteach Support |Additional |Kindergarten Progression |

| | | |Extra Practice Support | |

|Lesson 1 |Counting to 120 |1B, pp. 123-130 |1B, pp. 97-102 |Count and write numbers |

| | | | |0-20. (Ch. 1, 2, 4, and 6)|

|Lesson 2 |Place value |1B, pp. 131-134 |1B, pp. 103-106 | |

|Lesson 3 |Comparing, ordering, and patterns |1B, pp. 135-144 |1B, pp. 107-110 | |

|Chapter 9 |Objective |Additional Reteach Support |Additional |Kindergarten Progression |

| | | |Extra Practice Support | |

|Lesson 1 |Compare two things |1A, pp.153-160 |1A, pp. 141-142 |Compare and order lengths and |

| | | | |heights using non-standard |

| | | | |units (Ch.15). |

|Lesson 2 |Comparing more than two things |1A, pp.161-166 |1A, pp. 143-146 | |

|Lesson 3 |Using a start line |1A, pp.167-168 |1A, pp. 147-148 | |

|Lesson 4 |Measuring things |1A, pp. 169-172 |1A, pp.149-150 | |

|Lesson 5 |Finding length |1A, pp. 173-176 |1A, pp. 151-156 | |

|Chapter 11 |Objective |Additional Reteach Support |Additional |Kindergarten Progression |

| | | |Extra Practice Support | |

|Lesson 1 |Picture Graphs |1B, pp.15-20 |1B, pp.19-22 |Making, reading and |

| | | | |interpreting graphs. (Ch. 11) |

|Lesson 2 |More Picture Graphs |1B, pp.21-24 |1B, pp. 23-26 | |

|Lesson 3 |Tally Charts and Bar Graphs |1B, pp. 25-31 |1B, pp. 27-30 | |

IDEAL MATH BLOCK PLANNING TEMPLATE

Provides guidance during planning sessions

|CCSS | |

|& | |

|OBJ:(| |

|s) | |

| | |

| | |

| | |

| | |

| |Fluency: | |

| |Strategy/Tool | |

| |Getting Ready | |

|Math |Launch | |

|In | | |

|Focus| | |

| |Exploration | |

| | | |

| |Independent Practice | |

| |Summary | |

| | | |

| |D.O.L | |

| | | |

|Diffe|Small Group | |

|renti|Instruction | |

|ation|CCSS: | |

|:: | | |

|Math |OBJ: | |

|Works| | |

|tatio| | |

|ns | | |

| |Tech. Lab | |

| |CCSS: | |

| |Problem Solving Lab | |

| |CCSS: | |

| | | |

| |OBJ: | |

| |Fluency Lab | |

| |CCSS: | |

| |Strategy: | |

| | | |

| | | |

| |Tool: | |

| | | |

| |Math Journal | |

| |CCSS: | |

| |OBJ: | |

Math In Focus Pacing Guide

|Activity |Description |CCSS |Days |Lesson Notes |

|Pre-Test Ch. 14 |Addition and subtraction facts |1.OA.3 |1 |Differentiate: |

|Chapter Opener: |The part-whole concept in number bonds |1.OA.4 | |Assign instructional groups based on |

|Mental Math Strategies |Place values of numbers to 20 |1.OA.6 | |results. |

| | |1.OA.8 | | |

| | |1.NBT.5 | | |

|14.1 Mental Addition |Mentally add 1-digit numbers. | |2 |Day 1: |

| |Mentally add a 1-digit number to a 2-digit number. | | |ST: p. 138-140 |

| |Mentally add a 2-digit number to tens. | | | |

| | | | |Day 2: |

| | | | |ST: p. 141-142 |

| | | | |SW: p. 99-102 |

|14.2 Mental Subtraction |Mentally subtract 1-digit numbers. | |2 |Day 1: |

| |Mentally subtract a 1-digit number from a 2-digit number. | | |ST: p. 143-146 |

| |Mentally subtract tens from a 2-digit number. | | | |

| | | | |Day 2: |

| | | | |ST: p. 147-149 |

| | | | |SW: p. 103-104 |

|Ch. 14 Quiz |Mid chapter assessment | |½ | |

|Put On Your Thinking Cap |Thinking Skills | |½ | |

| |Identifying patterns and relationships | | | |

| |Problem Solving Strategies | | | |

| |Make a systematic list | | | |

| |Work backward | | | |

|Spiral Review Day: | | |2 |Math Workstations |

|Unit 1 and 2 | | | | |

|Ch. 14 Test Prep: | | |½ | |

|Time Allotted | | |8.5 | |

|Chapter 15: Calendar and Time |

|Pre-Test 15 |Determine whether students have the prior knowledge |1.MD.3 |1 |Differentiate based on student data from |

|Chapter Opener | | | |pre-test. |

|15.1 Using a Calendar |Know the days of the week and the months of the year, and | |1 |Use real calendars |

| |seasons of the year. | | |Use manipulatives and model often |

|15.2 Telling Time to the Hour |Use the term o’clock to tell the time to the hour. Read and| |1 | |

| |show time to the hour on a clock. Read and show time to the| | | |

| |hour on a digital clock. | | | |

|15.3 Telling Time to the Half |Read time to the half hour. | |1 | |

|Hour |Use the term half past. | | | |

| |Read and show time to the half hour on a digital clock. | | | |

|Chapter 15 Quiz |Mid chapter assessment | |½ | |

|Put on Your Thinking Cap | | |½ |DO NOT SKIP |

|Spiral Review Day | | |2 | |

|Chapter 15 Test Prep | | |½ | |

|Time Allotted | | |7.5 | |

|Chapter 16: Numbers to 120 | | | |

|Pre-Test 16 |Determine whether students have the prior knowledge: |1.NBT.1 |1 |Differentiate based on student data from |

|Chapter Opener: |Count and write numbers 1 to 40; Apply numbers to 40 in |1.NBT.2 | |pre-test. |

|Numbers to 120 |addition and subtraction |1.OA.5 | | |

|16.1 Counting to 120 |Read, write and count on from 41 to 120. | |1 | |

|16.2 Place Value |Show objects up to 100 as tens and ones. | |1 | |

|16.3 Comparing, Ordering, and |Compare numbers to 100 using the symbols >, ................
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