Lesson Topic: Date(s): 2 days5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Objectives/Essential Questions/K-U-D:The student will use problem solving, mathematical communication, mathematical reasoning, connections, and

representations to

Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and calcu-lators according to the context and nature of the computation in order to compute with whole numbers.

Create single-step and multistep problems involving the operations of addition, subtraction, multiplication, and division with and without remainders of whole numbers, using practical situations.

Estimate the sum, difference, product, and quotient of whole number computations.

Solve single-step and multistep problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers, using paper and pencil, mental computation, and calculators in which

– sums, differences, and products will not exceed five digits;– multipliers will not exceed two digits;– divisors will not exceed two digits; or– dividends will not exceed four digits.

Use two or more operational steps to solve a multistep problem. Operations can be the same or different.

Rationale: (communicate importance and how it relates to unit/previous unit/big picture) (why teach this way?--account for student background, readiness, demographics, learning styles)

Materials/Technology:Tree map, smartboard, sample word problems, vocab cards/word listhttp://www.visualthesaurus.com/cm/lessons/using-key-words-to-unlock-math-word-problems/

Hook/warm-up/bell-ringer/connection to prior learning: Refer to vocab wall and use tree map to review key words used in various operations of addition/Subtraction, multiplication/divisionContent/Direct Instruction (Specific Methods/Steps):1. Pre-assess each student by providing 4 word problems (one from each operation)-collect and check later to use for small group instruction.

2. Use tree map template on board to sort key words/phrases under correct category: ADDITION, SUBTRACTION, MULTIPLICATION, DIVISION. This is done whole group-sum, difference, more, less, total, product, quotient, in all, all together, addends, divisor, dividend, factors, each, equal, how many more,

Thinking/Processing of Content (Specific Activities/Steps):1. Provide sample word problems and highlight/breakdown by identifying key words phrases and determining what

Differentiation/Modifications Needed for Specific Students or Groups:

INT: Provide list of key words/phrases if students are having trouble coming up with them on their own.

EXT: Have students come up with sample problems for other students to solve.

operation(s) are needed to solve. Have children try to identify first on their own, then review and proceed as a whole group. These can be found at Bedford.k12.va.usInstructionMathcurriculum guides 5th grade link at TOP of pagescroll down to 5.4 word problems link

* Make note of transition plansCheck for Understanding: (formative and/or summative assessment) TSW independently break down 5 word problems by identifying which operations(s) should be used to solve it. TSW choose ONE problem to solve and show work for all steps.

Closure/Connections to future lesson: ID key phrases/terms is essential first step in problem solving.

Lesson Topic: Date(s): Day 35.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Objectives/Essential Questions/K-U-D:The student will use problem solving, mathematical communication, mathematical reasoning, connections, and

representations to

Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and calcu-lators according to the context and nature of the computation in order to compute with whole numbers.

Create single-step and multistep problems involving the operations of addition, subtraction, multiplication, and division with and without remainders of whole numbers, using practical situations.

Estimate the sum, difference, product, and quotient of whole number computations.

Solve single-step and multistep problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers, using paper and pencil, mental computation, and calculators in which

– sums, differences, and products will not exceed five digits;– multipliers will not exceed two digits;– divisors will not exceed two digits; or– dividends will not exceed four digits.

Use two or more operational steps to solve a multistep problem. Operations can be the same or different.

Rationale: (communicate importance and how it relates to unit/previous unit/big picture) (why teach this way?--account for student background, readiness, demographics, learning styles)Students must first be able to breakdown a problem using key words in order to determine what operation will be used before they can proceed with the computations.Materials/Technology:

Hook/warm-up/bell-ringer/connection to prior learning: Share completed tree map sort from previous days and see if there is anything to add to it. Questions about sort??Content/Direct Instruction (Specific Methods/Steps):

1. Review concepts of regrouping and carrying over when subtracting and adding. Provide 5 sample problems for children to do to show understand of this.

2. See I/E activities on right

Thinking/Processing of Content (Specific Activities/Steps):See above and attached template.* Make note of transition plans

Differentiation/Modifications Needed for Specific Students or Groups:

INT: If 3 or more wrong, then work in small group to walk-through and model the procedure with practice problems.

EXT: If 4or more sample problems correct, then…partner them up and use dice roll to create their own +/- sets to solve. Provide template to fill in and have template

already include +/- across zeros. (see attached template to use)

Check for Understanding: (formative and/or summative assessment) Collect and review problems from dice roll to check for accuracy and understanding. INT group will be small group, so showing of work will be the assessment for understanding.

Closure/Connections to future lesson: Understanding of these processes are necessary in order to move on tomorrow to apply to word problems.

Lesson Topic: Date(s): Day 45.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Objectives/Essential Questions/K-U-D:The student will use problem solving, mathematical communication, mathematical reasoning, connections, and

representations to

Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and calcu-lators according to the context and nature of the computation in order to compute with whole numbers.

Create single-step and multistep problems involving the operations of addition, subtraction, multiplication, and division with and without remainders of whole numbers, using practical situations.

Estimate the sum, difference, product, and quotient of whole number computations.

Solve single-step and multistep problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers, using paper and pencil, mental computation, and calculators in which

– sums, differences, and products will not exceed five digits;– multipliers will not exceed two digits;– divisors will not exceed two digits; or– dividends will not exceed four digits.

Use two or more operational steps to solve a multistep problem. Operations can be the same or different.

Rationale: (communicate importance and how it relates to unit/previous unit/big picture) (why teach this way?--account for student background, readiness, demographics, learning styles)Students must first be able to breakdown a problem using key words in order to determine what operation will be used before they can proceed with the computations.Materials/Technology:

Hook/warm-up/bell-ringer/connection to prior learning: Sample +/- problem on board with volunteer to demonstrate the regrouping/carry-over process from previous day. Remind students of key words used to identify operations to be used (vocab wall)Content/Direct Instruction (Specific Methods/Steps):

1. On SmartBoard, post sample word problem (+/- operations only). As a class, ID the key words/phrases. ID info that will be used to solve problem and cross out info that is “extra” and not needed to solve problem. Have students solve on their own at their seats, then share answers and go over as a whole class.

2. In small groups (3 or 4) TSW use index cards to create and solve their own word problems using +/- operations. TSW choose one card from each category: topic, operation, numbers. They will then use these three cards to create their own problem.

3. Students can trade their word problem with other groups and breakdown, ID operations, and solve. Check answers with other group and discuss any discrepancies

Differentiation/Modifications Needed for Specific Students or Groups:

INT: Small group- assist with creating their own word problems and assist with steps needed to solve.

EXT: Students will create their own problems by coming up with own topics, numbers and operations.

so they can be resolved.Thinking/Processing of Content (Specific Activities/Steps):* Make note of transition plansCheck for Understanding: (formative and/or summative assessment) Provide students with a few sample +/- word problems to breakdown and solve independently and provide them with data to create and solve their own word problem. Collect, check for accuracy, and provide feedback. Allow students to make corrections.Closure/Connections to future lesson: Reminder to look for key phrases, unnecessary information that can be eliminated, identify operation before proceeding.

Lesson Topic: Date(s): Day 55.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Objectives/Essential Questions/K-U-D:The student will use problem solving, mathematical communication, mathematical reasoning, connections, and

representations to

Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and calcu-lators according to the context and nature of the computation in order to compute with whole numbers.

Create single-step and multistep problems involving the operations of addition, subtraction, multiplication, and division with and without remainders of whole numbers, using practical situations.

Estimate the sum, difference, product, and quotient of whole number computations.

Solve single-step and multistep problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers, using paper and pencil, mental computation, and calculators in which

– sums, differences, and products will not exceed five digits;– multipliers will not exceed two digits;– divisors will not exceed two digits; or– dividends will not exceed four digits.

Use two or more operational steps to solve a multistep problem. Operations can be the same or different.

Rationale: (communicate importance and how it relates to unit/previous unit/big picture) (why teach this way?--account for student background, readiness, demographics, learning styles)Students must first be able to breakdown a problem using key words in order to determine what operation will be used before they can proceed with the computations.Materials/Technology:Dice, template, calculators (to check work)Hook/warm-up/bell-ringer/connection to prior learning: Review rules for multiplying

Content/Direct Instruction (Specific Methods/Steps):1. Review multiplying with 2-digit multipliers . Provide 5

sample problems for children to do to show understand of this.

2. See I/E activities on right

Thinking/Processing of Content (Specific Activities/Steps):* Make note of transition plans

Differentiation/Modifications Needed for Specific Students or Groups:

INT: Small group to review, model and assist with 2 digit multiplication.

EXT: Dice roll with template-roll dice to fill in template and then solve. Check work using calculator.

Check for Understanding: (formative and/or summative assessment) Use calculator to independently check work in EXT group. INT group-check and offer corrective feedback when necessary.

Closure/Connections to future lesson:

Lesson Topic: Date(s): Day 65.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Objectives/Essential Questions/K-U-D:The student will use problem solving, mathematical communication, mathematical reasoning, connections, and

representations to

Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and calcu-lators according to the context and nature of the computation in order to compute with whole numbers.

Create single-step and multistep problems involving the operations of addition, subtraction, multiplication, and division with and without remainders of whole numbers, using practical situations.

Estimate the sum, difference, product, and quotient of whole number computations.

Solve single-step and multistep problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers, using paper and pencil, mental computation, and calculators in which

– sums, differences, and products will not exceed five digits;– multipliers will not exceed two digits;– divisors will not exceed two digits; or– dividends will not exceed four digits.

Use two or more operational steps to solve a multistep problem. Operations can be the same or different.

Rationale: (communicate importance and how it relates to unit/previous unit/big picture) (why teach this way?--account for student background, readiness, demographics, learning styles)Students must first be able to breakdown a problem using key words in order to determine what operation will be used before they can proceed with the computations.Materials/Technology:topic cardsHook/warm-up/bell-ringer/connection to prior learning: Sample multiplication problem on board with volunteer to demonstrate the process from previous day. Remind students of key words used to identify operations to be used (vocab wall)Content/Direct Instruction (Specific Methods/Steps):

1. On SmartBoard, post sample word problem (x operations only). As a class, ID the key words/phrases. ID info that will be used to solve problem and cross out info that is “extra” and not needed to solve problem. Have students solve on their own at their seats, then share answers and go over as a whole class.

2. In small groups (3 or 4) TSW use index cards to create and solve their own word problems using the multiplication operation. TSW choose one card from each category: topic and numbers. They will then use these two cards to create their own problem.

3. Students can trade their word problem with other groups and breakdown, ID operations, and solve. Check answers with other group and discuss any discrepancies

Differentiation/Modifications Needed for Specific Students or Groups:

INT: Small group- assist with creating their own word problems and assist with steps needed to solve.

EXT: Students will create their own problems by coming up with own topics and numbers

so they can be resolved.

Thinking/Processing of Content (Specific Activities/Steps):* Make note of transition plansCheck for Understanding: (formative and/or summative assessment) Provide students with a few sample multiplication word problems to breakdown and solve independently and provide them with data to create and solve their own word problem. Collect, check for accuracy, and provide feedback. Allow students to make corrections.Closure/Connections to future lesson: Reminder to look for key phrases, unnecessary information that can be eliminated, identify operation before proceeding.

Lesson Topic: Date(s): 75.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Objectives/Essential Questions/K-U-D:The student will use problem solving, mathematical communication, mathematical reasoning, connections, and

representations to

Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and calcu-lators according to the context and nature of the computation in order to compute with whole numbers.

Create single-step and multistep problems involving the operations of addition, subtraction, multiplication, and division with and without remainders of whole numbers, using practical situations.

Estimate the sum, difference, product, and quotient of whole number computations.

Solve single-step and multistep problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers, using paper and pencil, mental computation, and calculators in which

– sums, differences, and products will not exceed five digits;– multipliers will not exceed two digits;– divisors will not exceed two digits; or– dividends will not exceed four digits.

Use two or more operational steps to solve a multistep problem. Operations can be the same or different.

Rationale: (communicate importance and how it relates to unit/previous unit/big picture) (why teach this way?--account for student background, readiness, demographics, learning styles)Students must first be able to breakdown a problem using key words in order to determine what operation will be used before they can proceed with the computations.Materials/Technology:Dice, template, calculators (to check work)Hook/warm-up/bell-ringer/connection to prior learning: Review rules for dividing (DSMB)

Content/Direct Instruction (Specific Methods/Steps):1. Review dividing with 2-digit divisors and 4-digit

dividends . Provide 5 sample problems for children to do to show understand of long division

2. See I/E activities on right

Thinking/Processing of Content (Specific Activities/Steps):* Make note of transition plans

Differentiation/Modifications Needed for Specific Students or Groups:

INT: Small group to review, model and assist with 2/4-digit division (DMSB)

EXT: Dice roll with template-roll dice to fill in template and then solve. Check work using calculator.

Check for Understanding: (formative and/or summative assessment) Use calculator to independently check work in EXT group. INT group-check and offer corrective feedback when necessary.

Closure/Connections to future lesson:

Lesson Topic: Date(s): Day 85.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Objectives/Essential Questions/K-U-D:The student will use problem solving, mathematical communication, mathematical reasoning, connections, and

representations to

Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and calcu-lators according to the context and nature of the computation in order to compute with whole numbers.

Create single-step and multistep problems involving the operations of addition, subtraction, multiplication, and division with and without remainders of whole numbers, using practical situations.

Estimate the sum, difference, product, and quotient of whole number computations.

Solve single-step and multistep problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers, using paper and pencil, mental computation, and calculators in which

– sums, differences, and products will not exceed five digits;– multipliers will not exceed two digits;– divisors will not exceed two digits; or– dividends will not exceed four digits.

Use two or more operational steps to solve a multistep problem. Operations can be the same or different.

Rationale: (communicate importance and how it relates to unit/previous unit/big picture) (why teach this way?--account for student background, readiness, demographics, learning styles)Students must first be able to breakdown a problem using key words in order to determine what operation will be used before they can proceed with the computations.Materials/Technology:topic cardsHook/warm-up/bell-ringer/connection to prior learning: Sample division problem on board with volunteer to demonstrate the process from previous day. Remind students of key words used to identify operations to be used (vocab wall)Content/Direct Instruction (Specific Methods/Steps):

4. On SmartBoard, post sample word problem (division operations only). As a class, ID the key words/phrases. ID info that will be used to solve problem and cross out info that is “extra” and not needed to solve problem. Have students solve on their own at their seats, then share answers and go over as a whole class.

5. In small groups (3 or 4) TSW use index cards to create and solve their own word problems using the division operation. TSW choose one card from each category: topic and numbers. They will then use these two cards to create their own problem.

6. Students can trade their word problem with other groups and breakdown, ID operations, and solve. Check answers with other group and discuss any discrepancies

Differentiation/Modifications Needed for Specific Students or Groups:

INT: Small group- assist with creating their own word problems and assist with steps needed to solve.

EXT: Students will create their own problems by coming up with own topics and numbers

so they can be resolved.

Thinking/Processing of Content (Specific Activities/Steps):* Make note of transition plansCheck for Understanding: (formative and/or summative assessment) Provide students with a few sample division word problems to breakdown and solve independently and provide them with data to create and solve their own word problem. Collect, check for accuracy, and provide feedback. Allow students to make corrections.Closure/Connections to future lesson: Reminder to look for key phrases, unnecessary information that can be eliminated, identify operation before proceeding.

Lesson Topic: Date(s): Day 95.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Objectives/Essential Questions/K-U-D:The student will use problem solving, mathematical communication, mathematical reasoning, connections, and

representations to

Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and calcu-lators according to the context and nature of the computation in order to compute with whole numbers.

Create single-step and multistep problems involving the operations of addition, subtraction, multiplication, and division with and without remainders of whole numbers, using practical situations.

Estimate the sum, difference, product, and quotient of whole number computations.

Solve single-step and multistep problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers, using paper and pencil, mental computation, and calculators in which

– sums, differences, and products will not exceed five digits;– multipliers will not exceed two digits;– divisors will not exceed two digits; or– dividends will not exceed four digits.

Use two or more operational steps to solve a multistep problem. Operations can be the same or different.

Rationale: (communicate importance and how it relates to unit/previous unit/big picture) (why teach this way?--account for student background, readiness, demographics, learning styles)

Materials/Technology:Vocab wall, tree map from day 1 that breaks down key words/phrases for each operation

Hook/warm-up/bell-ringer/connection to prior learning: Review tree map from day 1, key words/phrases to look for in problemsContent/Direct Instruction (Specific Methods/Steps):

1. Share multi-step word problem on SmartBoard that involves at least 2 different operations. Break down by highlighting key terms/phrases, ID operations to be used, and discuss approaches for which operation to perform first.

2. Walk through and model how to solve the problem.

Thinking/Processing of Content (Specific Activities/Steps):Entertain various suggestions for how to solve the problem and discuss what would and would not work and why…

* Make note of transition plans

Differentiation/Modifications Needed for Specific Students or Groups:

INT: none for intro lesson

Check for Understanding: (formative and/or summative assessment) Observations based on level of participation and discussions held

Closure/Connections to future lesson: ID key phrases/terms is essential first step in problem solving.

Lesson Topic: Date(s): Day 105.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Objectives/Essential Questions/K-U-D:The student will use problem solving, mathematical communication, mathematical reasoning, connections, and

representations to

Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and calcu-lators according to the context and nature of the computation in order to compute with whole numbers.

Create single-step and multistep problems involving the operations of addition, subtraction, multiplication, and division with and without remainders of whole numbers, using practical situations.

Estimate the sum, difference, product, and quotient of whole number computations.

Solve single-step and multistep problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers, using paper and pencil, mental computation, and calculators in which

– sums, differences, and products will not exceed five digits;– multipliers will not exceed two digits;– divisors will not exceed two digits; or– dividends will not exceed four digits.

Use two or more operational steps to solve a multistep problem. Operations can be the same or different.

Rationale: (communicate importance and how it relates to unit/previous unit/big picture) (why teach this way?--account for student background, readiness, demographics, learning styles)

Materials/Technology:Poster-sized word problems (4) spread out around room, Dan Mulligan problem solving worksheetsHook/warm-up/bell-ringer/connection to prior learning: Review tree map from day 1, key words/phrases to look for in problemsContent/Direct Instruction (Specific Methods/Steps):1. Gallery walk-break up into 4 groups (each of mixed levels so that kids can help each other) and rotate through room to spend ~10 minutes at each problem. Work within small group to breakdown and solve each problem on their individual Dan Mulligan 5-Steps to problem solving worksheets.

Thinking/Processing of Content (Specific Activities/Steps):Share ideas among peers and come up with agreed-upon approach to solving.* Make note of transition plans

Differentiation/Modifications Needed for Specific Students or Groups:

INT: Ask questions about procedures being used, suggest steps or operations, etc.

Check for Understanding: (formative and/or summative assessment) Collect and review approaches to problem solving. Check for steps followed, evidence of breaking down problems and accuracy of answers. Provide feedback and have students “rework” the next day if needed.

Closure/Connections to future lesson:

Lesson Topic: Date(s): Day 115.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Objectives/Essential Questions/K-U-D:The student will use problem solving, mathematical communication, mathematical reasoning, connections, and

representations to

Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and calcu-lators according to the context and nature of the computation in order to compute with whole numbers.

Create single-step and multistep problems involving the operations of addition, subtraction, multiplication, and division with and without remainders of whole numbers, using practical situations.

Estimate the sum, difference, product, and quotient of whole number computations.

Solve single-step and multistep problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers, using paper and pencil, mental computation, and calculators in which

– sums, differences, and products will not exceed five digits;– multipliers will not exceed two digits;– divisors will not exceed two digits; or– dividends will not exceed four digits.

Use two or more operational steps to solve a multistep problem. Operations can be the same or different.

Rationale: (communicate importance and how it relates to unit/previous unit/big picture) (why teach this way?--account for student background, readiness, demographics, learning styles)

Materials/Technology:Poster-sized word problems (4) spread out around roomHook/warm-up/bell-ringer/connection to prior learning: Review key words/phrases

Content/Direct Instruction (Specific Methods/Steps):1. Return individual problem-solving sheets from Day 10 for students to read over feedback within small groups. As a whole class, go over each problem from Day 10 and discuss key terms/phrases, operations used, and procedure for following.

Thinking/Processing of Content (Specific Activities/Steps):Reviewing feedback with small groups* Make note of transition plans

Differentiation/Modifications Needed for Specific Students or Groups:

INT: Go over problems with kids individually or small group if they need further assistance.

EXT: Kids can create and solve their own multi-operational problems

Check for Understanding: (formative and/or summative assessment) Done within small group intervention for those who are still struggling

Closure/Connections to future lesson: Review steps for breaking down, ID key words/phrases, determining operation and following steps within operation.