SIOP® Lesson Plan - DUSD



|Class/Subject Area(s): |Math |Grade Levels: |3rd – 5th |

|Unit/Theme: |Understanding Division |Lesson Duration: |60 - 75 min |

| |

|Common Core State Standards: (Preparation) |

|Represent and solve problems involving multiplication and division |

|3.OA.2 – Interpret whole-number quotients of whole numbers, e.g., interpret 56÷8 as the number of objects in each share when 56 objects are partitioned |

|equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. |

|Use place value understanding and properties of operations to perform multi-digit arithmetic |

|4.NBT.6 – Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the |

|properties of operations, and/or the relationship between multiplication and division. |

|Perform operations with multi-digit whole numbers and with decimals to hundredths |

|5.NBT.6 – Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the |

|properties of operations, and/or the relationship between multiplication and division. |

| |

|MP 1 – Make sense of problems and persevere in solving them |

|MP 2 – Reason abstractly and quantitatively |

|MP 3 – Construct viable arguments and critique the reasoning of others |

|MP 6 – Attend to precision |

|MP 7 – Look for and make use of structure |

|Content Objective(s): (Preparation) |

| |

|SWBAT represent and solve problems using strategies based on number sense. |

|Language Objective(s): (Preparation) |

| |

|SWBAT explain to a partner the strategy they used to solve a problem. |

|SWBAT listen to others' explanations and decide if they make sense. |

|HOTS: Higher Order Thinking Skills (Strategies, Interaction, Review/Assessment) |

| |

|How did you solve the problem? |

|Is there another strategy that you can use to solve the problem? |

|Key Vocabulary: (Building Background) |Supplementary Materials: (Lesson Preparation) |

|Content Vocabulary | |Word problem worksheet (double sided) |

|equal groups | |Counters (unifix cubes, base-10 blocks, etc.) |

|quotient | | |

|divisor | | |

|SIOP Features: |

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|Preparation |Scaffolding |Grouping Options |

| x |Adaptation of content | |Modeling |x |Whole class |

| x |Links to background | |Guided practice | |Small groups |

| x |Links to past learning | x |Independent practice |x |Partners |

| x |Strategies incorporated | x |Comprehensible input |x |Independent |

| |

|Integration of Processes |Application |Assessment |

| x |Reading |x |Hands-on |x |Individual |

| x |Writing |x |Meaningful |x |Group |

| x |Speaking | x |Linked to objectives |x |Written |

| x |Listening | x |Promotes engagement |x |Oral |

| |

|Lesson Sequence: |

|Connections to Prior Knowledge/ Building Background Information (Building Background) |

| |

|Do after routine – See ‘Unpacking the problem’ |

|Lesson and Activities (Comprehensible Input, Strategies, Interaction, |Key Questions & Expected Student Responses (Lesson Delivery) |

|Practice/Application, Lesson Delivery) | |

| | |

|Introduce Content and Language Objectives with the Class |The purpose of this number talk is to connect a ‘multiplying up’ strategy to division. Students may not |

| |be comfortable with this strategy, but this activity sets the stage in case students choose to use it in |

|Opening/Routine: Number Talk (15 minutes - whole class) |the future. By the end of the number talk the teacher will be able to have some knowledge of the class’ |

| |understanding of what division means. |

|Write one equation down at a time and record strategies that students used to solve it in their head. | |

| |What solutions did you get? |

|4 x 10 = g |Who can share a strategy to justify one of the given solutions? |

| |Who else used a similar strategy as ______? |

|4 x 5 = h |Does anybody have a different strategy? |

| | |

|4 x 4 = k |For b – d: Did anyone use something already written on the board to solve this equation? If so, please |

| |explain. If not, give the students time to try to figure out another strategy. |

|4 x 8 = m | |

| |For e, if students are struggling: |

|72 ÷ 4 = p |How is this equation different? |

| |What does division mean? |

| |What would be a word problem that could go with this equation? |

| |How did the work from the previous problems help you to solve this one? |

| | |

|Lesson/Activity: Measurement division word problem | |

| | |

|Unpacking the problem (Whole class – 5 minutes) |As students ask for more information, provide it if applicable. Encourage students to keep asking |

|“Today our friend Samantha wants to make apple pies. Has anyone made apple pies before? What is the |questions until all necessary information is given (how many apples she has; how many apples will go into|

|main thing that you need to make an apple pie (apples)? If Samantha has everything that it takes to make |each pie). |

|apple pies, as well as a bunch of apples, what information do you need to know in order to find out how | |

|many pies she can make?” |In order to help all students unpack the problem in greater detail, use the first set of number choices |

| |to talk about the problem. |

|Read the word problem with the class: | |

|Samantha has ______ apples. If she puts ______ apples in each pie, how |Once students pair share, have a whole class discussion around what you know from the problem. Make sure|

|many pies can she make? (78,6), (108, 6), (216, 6), (432, 12) |to ask clarifying questions until all students clearly understand the context. |

| | |

|- Turn and tell your partner one piece of information that you know from the problem. |Thumbs up if you think that she can make more than ____. Thumbs down if you think that she will make |

|- Do you think that Samantha will be able to make a large number of pies? Why or why not? |less. |

|- Will she be able to make more than 100 pies? 78? Turn and tell your partner why or why not. | |

|- Raise your hand if you have a strategy to solve this problem. |If all students have a strategy, send them off to solve the problem. If not, have the students ask you |

| |more questions to clarify their confusion. Continue to unpack the problem until you feel like the |

| |students are ready to solve it. |

|Solving the Problem (Independent work – 25 minutes) | |

| |This problem is a measurement division (number of groups unknown) problem. As students are solving the |

|Students are given time to solve the word problem. Encourage students to pick and use a number choice |problem, look for students that are solving it in a partitive (group size unknown) type way (i.e. they |

|that makes sense to them and is not too easy nor too hard. When they finish solving the problem and |have 6 pies drawn and are putting one apple at a time in each pie). These students are most likely not |

|completing the write up, they should turn the paper over and try to solve the problem using a different |understanding the context so they need to be asked clarifying questions to help them make sense of the |

|strategy. |context. |

| |What do the circles in your drawing represent – apples or pies? |

|As students solve the problem, the teacher walks around to monitor the students. As students share their|What information do we know from the story? |

|strategies with you, use knowledge of the problem solving trajectory to ask probing questions to help the|What is Samantha doing with the apples? |

|student to: |Does the story tell us how many pies Samantha makes? |

|make sense of the context |What are we trying to figure out? |

|make sense of their strategy | |

|try a more advanced strategy (refer to problem solving trajectory for division handout) |If you come to a student that uses a strategy on their paper that is clearly not the strategy that they |

| |used to solve the problem, ask probing questions to help them record the strategy that they actually |

|*Have counters (unifix cubes, base-10 blocks, etc.) available for students that would like to use them. |used. Students often put a direct modeling strategy (i.e. drawing a picture) on their paper when they |

| |actually used some type of relational thinking type strategy to solve the problem. |

| | |

| |While walking around, the teacher picks two to three students to share their work during the debrief. |

| |These students are picked based on where the teacher feels the class needs to go during the debrief. |

| |Some questions to consider when picking these students are: |

| |What student has not shared their thinking in entirety for a while? |

| |How did the class as a whole understand the problem? Was it too hard? Too easy? |

| |Based on the answers to these questions, pick strategies that would help lead a subgroup of the class in |

| |a particular direction. |

| |Is there a typical wrong solution? If so, pick a student to share that can work through it with the |

| |class. |

| |Is there a particular strategy that you would like shared? |

|Closure (Review/Assessment) |Key Questions & Expected Student Responses (Review/Assessment) |

| | |

|Debrief (Whole class – 15 minutes) |Why do you think they did _____? |

| |Predict what you think ______ is going to do next? Why? |

|Have selected students come up one at a time to share their strategy. As the student shares, the teacher|Are those pies or apples? |

|records what they are saying. The teacher continuously pauses the explanation to ask probing questions | |

|of the student that is sharing as well as the entire class. |As multiple strategies are shared, ask probing questions to help students make sense of the various |

| |strategies (Math Practice 3). Depending on what direction your class needs to go, some possible |

|Once a student finishes sharing their strategy: |questions are: |

|Teacher: “Turn to your partner and take turns explaining ______’s strategy. The first student will say,|How are (student a)’s and (student b)’s strategies similar? How are they different? |

|‘First, ____ did _______.’ The next student will say, ‘Then she/he did _____.’ Continue back and forth |Where are the apples is _______’s strategy? Where are the pies? |

|until you have explained the entire strategy together.” |How are (student a)’s and (student b)’s equations similar? How are they different? How can you connect |

|After everyone has pair-shared, bring the class back together and have one student explain the strategy |the equation to the strategy used? |

|used. |If we were to use ______’s strategy for this different number choice, how do you think that they would |

| |solve it? |

|After the selected students have shared: | |

|Teacher: “If you were to solve a similar problem like this again, whose |Key Ideas of Division to Emphasize: |

|strategy would you want to try to use and why? What strategy do you think |The strategy used reflected the measurement division context that was given – Where are the pies? Where |

|is the most efficient for you? Turn and tell your partner.” |are the apples? |

| |Students understand the problem in terms of the context; can solve the problem and know where to find the|

| |answer; and can put the answer back in terms of the context (Math Practices #1&2) |

|Collect the students’ work in order to plan the next day’s lesson. |Students begin to develop strategies to help them understand division as pulling out equal groups. (Math |

| |Practice 7) |

|Review Content and Language Objectives with the class |Division is not just repeated subtraction. It is also the inverse of multiplication. |

|- Did we meet our objectives (thumbs up/down)? |There are many sense-making strategies that can be used to solve a division problem. Make particular |

| |notice of strategies that are based on place value, the properties of operations, and/or the relationship|

| |between multiplication and division. (Math Practice 7) |

| |

|Following the Lesson – Using formative assessment to plan the next lesson |

| |

|Sort the students’ work from least sophisticated to most sophisticated. |

|Where are most of the students on the division problem-solving trajectory? (See ‘Strategies for Solving Division Problems’) |

|Where does the class need to go next? |

|What category of student work (based on the sorting) would we like to focus on tomorrow? |

|Which students demonstrated this strategy? |

|What next steps do these students need? |

|What would be a good follow-up problem for this group of students? |

|Should we continue with measurement division or should we try a different problem type (i.e. partitive division) |

|What number choices will help encourage these next steps? |

|What strategies will we look for to share during the debrief? |

Name: ___________________________ Date: ________________

Circle the number choice you would like to use:

|(72, 6) |(108, 6) |(216, 6) |(432, 12) |

Samantha has ______ apples. If she puts ______ apples in each pie, how many pies can she make?

Strategy 1:

Solution: __________________________________________

Number Sentence: ___________________________________

Explanation: _________________________________________________

____________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Strategy 2:

Solution: __________________________________________

Number Sentence: ___________________________________

Explanation: _________________________________________________

____________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Strategies for Solving Division Problems

Direct Modeling – Having to see every single number

• By Ones

• By Tens and Ones

Counting Strategies

• Skip-counting

• Repeated addition/subtraction

• Doubling

• Combination of skip-counting and counting on by one

Relational / Invented Strategies – The student clusters the groups in some way and will not physically list every group from the problem.

• Complex doubling

• Partitioning (Decomposes and represents as division or multiplication)

o Non-decade multiples

o Decade multiples

• Decomposing the dividend into Decade Numbers

• Compensating

• Doubling/halving – Ratio Strategies

• Special Case Strategies

Based on information from the book, Children's Mathematics: Cognitively Guided Instruction, by Carpenter, et al.

Sorting Student Work

for Division Problems

|Direct Modeling |Counting |Relational/ |Standard Algorithm |Invalid Strategy |

| | |Invented Algorithm | | |

| | | | | |

Based on information from the book, Children's Mathematics: Cognitively Guided Instruction, by Carpenter, et al.

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