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: |
| |
|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.
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- lesson plan themes by month
- water lesson plan for preschoolers
- watershed lesson plan activity
- lesson plan themes for toddlers by month
- preschool lesson plan templates blank pdf printable
- toddler lesson plan template printable
- school age lesson plan ideas
- free preschool lesson plan template printables
- daycare weekly lesson plan template
- school age lesson plan format
- lesson plan themes preschool
- school age lesson plan sample