Problem Solving – Lesson Plan Ideas (Gr.6-wk2)

These lessons are aligned with the Jamaica National Standards Curriculum (NSC) for Grade 6 Mathematics, specifically the Strand: Number, Number Operations, and Problem Solving.

Subject: Mathematics

Strand: Number

Grade 6 – Term 3 – Unit 1 – Week 2

Duration: 5 x 60 minutes

Focu Question: What real life problems can I solve using arithmetic and algebra?

Standard: Number Operation and Application:

Use the basic operations, number relationships, patterns, number facts, calculators and dynamic software to compute and estimate in order to solve real world problems involving fractions, percentages and decimals.

Attainment Target: Use models to explain their conceptual understanding of rational numbers (fractions).

Benchmarks: Apply and justify the use of a variety of problem solving strategies involving decimals and percentages.

Key Skills: Identify patterns, engage in meaningful discussions, write algebratic expressions, create patterns, problem solving, create designs, work collaboratively.

Key Vocabulary: patterns algebratic expression, decimals, percentages, designs models, problem-solve, area, perimeter, surface, pressure, weight.

Please the Content Outline for lesson plans below.

Day One:

Writing Story Problems with Decimals

Specific Objective: Students will be able to:

• Write story problems involving decimals and perform calculations using the four operations (addition, subtraction, multiplication, and division) to solve them.

Materials: Whiteboard or blackboard, Markers or chalk, Story problem handout (prepared in advance), Calculators (optional),

Engage – Introduction:

• Begin the lesson by engaging students in a brief discussion about real-life situations where decimals are used, such as money, measurements, or sports scores.
• Explain that today they will be learning how to create story problems involving decimals and use the four operations to find solutions.

Warm-up Activity:

• Distribute a worksheet with decimal calculations.
• Instruct students to solve the problems independently or in pairs.
• After completion, review the answers as a class, allowing students to share their strategies and explanations.

Explain – Guided Instruction:

• Display a story problem on the board, for example: “A group of friends went to a restaurant. Each person had a meal that cost $15.75. If there were 5 friends in total, how much did they spend in total?”
• Break down the problem by highlighting the important information (cost of each meal, number of friends).
• Discuss the operation(s) needed to solve the problem (multiplication and addition).
• Model the calculation step-by-step, emphasizing the use of decimals: $15.75 × 5 = $78.75.
• Encourage students to ask questions and provide additional examples if necessary.

Explore – Group Activity:

• Divide the class into small groups.
• Provide each group with a set of story problem cards. Each card should contain a different decimal story problem.
• Instruct the groups to solve the problems on the cards by writing the calculations needed to find the answer.
• Encourage creativity and ask students to create their own story problems if they finish early.
• Circulate the classroom to provide assistance and monitor progress.

Elaborate – Presentation and Discussion:

• Invite groups to share their story problems and the calculations they wrote to solve them.
• Discuss the variety of approaches used by different groups and provide feedback on their problem-solving strategies.
• Address any misconceptions or errors that arise during the discussion.
• Emphasize the importance of clear and concise language when writing story problems.

Evaluate – Conclusion and Reflection:

• Summarize the key points covered in the lesson, including the process of creating story problems with decimals and using the four operations to solve them.
• Ask students to reflect on the challenges they faced and what they learned about writing story problems with decimals.
• Provide opportunities for students to ask any remaining questions.

Extended Learning:

• Assign additional story problems as homework for students to practice independently.
• Create a “Problem of the Day” routine, where students solve a new decimal story problem at the beginning of each class.
• Introduce multi-step story problems involving decimals to challenge advanced students.

Note: Encourage students to show their work and explain their thinking when solving story problems. This will help develop their problem-solving skills and enhance their understanding of decimal operations.

Day Two & Three:

Identifying the ‘Hidden Question’ in a Two-Step Problem

Specific Objective: Students will be able to:

• Identify the ‘hidden question’ in a two-step problem and determine the operations needed to solve it.

Materials: Whiteboard or blackboard, Markers or chalk, Two-step problem handouts (prepared in advance), Index cards or slips of paper, Chart paper and markers

Engage – Introduction:

• Begin the lesson by discussing with students the concept of two-step problems.
• Explain that two-step problems require multiple operations to find the solution.
• Introduce the idea of a ‘hidden question’ within these problems, which is the specific question we need to answer to solve the problem.

Warm-up Activity:

• Display a two-step problem on the board or projector screen.
• Instruct students to independently or in pairs, identify the ‘hidden question’ within the problem.
• Allow a few minutes for students to think and discuss their answers.
• Invite a few students to share their responses and reasoning.

Explain – Guided Instruction:

• Introduce a new two-step problem to the class, for example: “Sam has $25. He wants to buy a book for $15 and save the rest. How much money will Sam save?”
• Read the problem aloud and ask students to follow along, identifying the ‘hidden question.’
• Discuss the problem as a class, focusing on the operations needed to solve it.
• Model the step-by-step process of solving the problem, explaining each operation and its purpose: $25 – $15 = $10.
• Emphasize the importance of understanding the ‘hidden question’ before attempting to solve the problem.

Explore – Group Activity:

• Divide the class into small groups.
• Distribute two-step problem cards to each group, ensuring each card contains a different problem.
• Instruct the groups to identify the ‘hidden question’ in their assigned problem and determine the operations needed to solve it.
• Encourage students to discuss and collaborate within their groups.
• Provide support and guidance as needed while circulating the classroom.

Elaborate – Presentation and Discussion:

• Ask each group to share their problem and the ‘hidden question’ they identified.
• Have each group explain the operations they would use to solve the problem.
• Write the ‘hidden questions’ on the board or chart paper, creating a class reference for future use.
• Facilitate a discussion on different strategies and approaches used by the groups.
• Address any misconceptions or questions that arise during the discussion.

Evaluate – Conclusion and Reflection:

• Summarize the key points covered in the lesson, emphasizing the importance of identifying the ‘hidden question’ in a two-step problem.
• Ask students to reflect on the process of identifying the ‘hidden question’ and how it helps in finding the solution.
• Provide opportunities for students to ask any remaining questions.

Extended Learning:

• Assign additional two-step problems as homework for students to practice independently.
• Encourage students to create their own two-step problems, swap with a partner, and identify the ‘hidden question’ within each other’s problems.
• Challenge advanced students with more complex two-step problems or multi-step problems.

Note: Encourage students to explain their reasoning and strategies when identifying the ‘hidden question.’ This will help develop their problem-solving skills and improve their ability to analyze and solve multi-step problems.

Day Four & Five:

Please the Content Outline for lesson plans below.

Writing and Solving Mathematical Sentences for a Two-Step Problem

Specific Objective: Students will be able to:

• write and solve mathematical sentences for a two-step problem.

Engage – Introduction:

• Begin the lesson by discussing the importance of mathematical sentences in representing and solving problems.
• Explain that today, students will learn how to write and solve mathematical sentences for two-step problems.

Warm-up Activity:

• Display a two-step problem on the board or projector screen.
• Instruct students to individually or in pairs, write a mathematical sentence that represents the problem.
• Give students a few minutes to think and discuss their answers.
• Invite a few students to share their mathematical sentences and explain their reasoning.

Explain – Guided Instruction:

• Introduce a new two-step problem to the class, for example: “A store sells notebooks for $2 each. If Sarah bought 5 notebooks and also bought a pen for $1.50, how much did she spend in total?”
• Read the problem aloud and ask students to follow along.
• Discuss the problem as a class, highlighting the key information and operations needed to solve it.
• Model the process of writing a mathematical sentence to represent the problem step by step: $2 × 5 + $1.50 = $10 + $1.50 = $11.50.
• Emphasize the importance of using appropriate mathematical symbols and the order of operations.

Explore – Group Activity:

• Divide the class into small groups of 3-4 students.
• Distribute two-step problem cards to each group, ensuring each card contains a different problem.
• Instruct the groups to write mathematical sentences that represent their assigned problems.
• Encourage students to discuss and collaborate within their groups.
• Provide support and guidance as needed while circulating the classroom.

Elaborate – Presentation and Discussion:

• Ask each group to share their problem and the mathematical sentence they wrote to represent it.
• Have each group explain their reasoning and the operations involved in solving the problem.
• Write the mathematical sentences on the board or chart paper, creating a class reference for future use.
• Facilitate a discussion on the different approaches used by the groups.
• Address any misconceptions or questions that arise during the discussion.

Evaluate – Conclusion and Reflection:

• Summarize the key points covered in the lesson, emphasizing the process of writing and solving mathematical sentences for two-step problems.
• Ask students to reflect on the importance of using mathematical language to accurately represent and solve problems.
• Provide opportunities for students to ask any remaining questions.

Extended Learning:

• Assign additional two-step problems as homework for students to practice independently.
• Encourage students to create their own two-step problems and exchange them with a partner to solve.
• Challenge advanced students with more complex two-step problems or multi-step problems.

Note: Encourage students to explain their reasoning and strategies when writing and solving mathematical sentences. This will help deepen their understanding of problem-solving skills and mathematical concepts.