Elementary Level: Place Value (Tens and Ones)
Mid Level: Addition and Subtraction of Large Numbers
High Level: Multiplying and Dividing Integers

Elementary Level (Kinder to Grade 2)

Subject: Place Value (Tens and Ones)

Alignment with Standards:

Mathematics:

• CCSS.MATH.CONTENT.1.NBT.B.2: Understand that the two digits of a two-digit number represent amounts of tens and ones.
  • Addressed through building, drawing, and matching numbers as tens and ones.
• CCSS.MATH.CONTENT.1.NBT.B.2.A: 10 can be thought of as a bundle of ten ones — called a “ten.”
  • Addressed through the use of base-ten blocks.
• CCSS.MATH.CONTENT.1.NBT.B.2.B: The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
  • Addressed through activities focusing on numbers 10-20.
• CCSS.MATH.CONTENT.1.NBT.B.2.C: 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).
  • Extended understanding of place value beyond 20 can be introduced if the student is ready.

Duration:

1-1.5 hours (can be split into shorter sessions)

Objective:

By the end of this lesson, children will be able to understand the concept of place value for numbers up to 20, using tens and ones through hands-on activities and games.

Materials Needed:

• Base-ten blocks: For representing tens and ones.
• Place value mats: To organize tens and ones (can be drawn on paper).
• Number cards: Cards with numbers 10-20.
• Drawing materials: Paper, markers, or crayons for drawing numbers as tens and ones.
• Place value matching game: Cards with numbers and their tens/ones representations.
• Whiteboard or chart paper: For modeling and practice.

Lesson Outline:

1. Introduction (10-15 minutes)

• Begin by explaining that numbers are made up of digits, and each digit has a place value.
• Introduce the concept of tens and ones:
  • Tens: Groups of ten.
  • Ones: Single units.
• Use base-ten blocks to show examples:
  • For example, the number 13 has 1 ten and 3 ones.
• Write numbers 10-20 on the board and model how to break them into tens and ones.

2. Activity 1: Building Numbers with Base-Ten Blocks (20-30 minutes)

• Provide the child with base-ten blocks and a place value mat.
• Call out a number (e.g., 14) and have the child build it using tens and ones blocks.
• Ask: “How many tens are in this number? How many ones?”
• Repeat with several numbers up to 20.

3. Activity 2: Drawing Numbers as Tens and Ones (20-30 minutes)

• Give the child paper and markers/crayons.
• Ask them to draw numbers as tens and ones. For example:
  • For 17, they could draw 1 ten (a rectangle or stick) and 7 ones (circles or dots).
• Encourage them to label their drawings (e.g., “1 ten + 7 ones = 17”).

4. Activity 3: Place Value Matching Game (20-30 minutes)

• Create or use pre-made cards for a matching game:
  • One set of cards has numbers (e.g., 12, 15, 19).
  • The other set has the corresponding tens and ones representations (e.g., 1 ten + 2 ones).
• Have the child match the number cards to their tens and ones representations.
• For added challenge, time the child or have them race against a sibling or parent.

5. Assessment (Optional)

• Provide a worksheet or activity where the child:
  • Writes the number of tens and ones for given numbers (e.g., 16 = ___ tens + ___ ones).
  • Draws tens and ones for a given number.
  • Matches numbers to their tens and ones representations.

Extension Ideas:

• Number Hunt: Have the child find objects around the house (e.g., 14 pencils) and group them into tens and ones.
• Place Value Bingo: Create a bingo game where the child matches numbers to their tens and ones representations.
• Interactive Games: Use online place value games or apps to reinforce the concept.

Mid Level (Grade 3 to 5)

Subject: Addition and Subtraction of Large Numbers

Alignment with Standards:

Mathematics:

• CCSS.MATH.CONTENT.4.NBT.B.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm.
  • Addressed through solving addition and subtraction problems with regrouping.
• CCSS.MATH.CONTENT.4.OA.A.3: Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations.
  • Addressed through solving multi-step word problems.
• CCSS.MATH.CONTENT.4.NBT.A.1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
  • Addressed through the use of place value and regrouping.

Duration:

1.5-2 hours (can be split into shorter sessions)

Objective:

Children will solve addition and subtraction problems with regrouping, including multi-step problems, through interactive exercises and practice.

Materials Needed:

• Whiteboard or chart paper: For modeling problems.
• Base-ten blocks or place value disks: For hands-on regrouping practice.
• Worksheets: Addition and subtraction problems with regrouping.
• Number cards: For creating multi-digit numbers.
• Interactive tools: Online math games or apps for practice (optional).
• Pencils, erasers, and paper: For solving problems.

Lesson Outline:

1. Introduction (10-15 minutes)

• Begin by reviewing the concept of place value (ones, tens, hundreds, thousands).
• Explain that when adding or subtracting large numbers, we sometimes need to regroup (borrow or carry over).
• Use base-ten blocks or place value disks to demonstrate regrouping:
  • For example, show how 10 ones can be regrouped into 1 ten, or 10 tens into 1 hundred.
• Write a simple addition and subtraction problem on the board (e.g., 456 + 278 or 723 – 486) and solve it step-by-step, emphasizing regrouping.

2. Activity 1: Hands-On Regrouping Practice (20-30 minutes)

• Provide the student with base-ten blocks or place value disks.
• Give them a problem to solve (e.g., 548 + 376 or 832 – 459).
• Have them use the blocks/disks to model the problem and regroup as needed.
• Ask: “Why did you need to regroup? How did regrouping help you solve the problem?”

3. Activity 2: Solving Multi-Step Problems (30-40 minutes)

• Write multi-step word problems on the board or provide a worksheet. For example:
  • “Sarah has 548 stickers. She buys 276 more. Then she gives 189 stickers to her friend. How many stickers does Sarah have now?”
• Guide the student through solving the problem step-by-step:
  1. Add 548 + 276.
  2. Subtract 189 from the result.
• Encourage the student to check their work by solving the problem in reverse or using estimation.

4. Activity 3: Interactive Exercises (20-30 minutes)

• Use online math games or apps that focus on addition and subtraction with regrouping.
• Alternatively, create a “math scavenger hunt” by hiding number cards around the room. The student must find the cards, create multi-digit numbers, and solve addition or subtraction problems with regrouping.

5. Assessment (Optional)

• Provide a worksheet or quiz with a mix of addition and subtraction problems, including multi-step word problems.
• Alternatively, have the student create their own multi-step word problem and solve it.

Extension Ideas:

• Real-World Application: Have the student solve problems related to real-life scenarios, such as budgeting or measuring distances.
• Timed Challenges: Set a timer and see how many problems the student can solve correctly in a set amount of time.
• Peer Teaching: Have the student teach the concept of regrouping to a sibling or parent.

High Level (Grade 6 to 8)

Subject: Multiplying and Dividing Integers

Alignment with Standards:

Mathematics:

• CCSS.MATH.CONTENT.7.NS.A.2: Apply and extend previous understandings of multiplication and division to multiply and divide rational numbers.
  • Addressed through multiplying and dividing integers.
• CCSS.MATH.CONTENT.7.NS.A.2.A: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers.
  • Addressed through the rules for multiplying and dividing integers.
• CCSS.MATH.CONTENT.7.NS.A.3: Solve real-world and mathematical problems involving the four operations with rational numbers.
  • Addressed through real-world examples and scenarios.

Duration:

1.5-2 hours (can be split into shorter sessions)

Objective:

Children will apply the rules for multiplying and dividing integers through integer grid puzzles and real-world examples.

Materials Needed:

• Whiteboard or chart paper: For modeling problems and rules.
• Integer grid puzzles: Pre-made or create your own (e.g., a grid where rows and columns multiply/divide to a given integer).
• Number cards: Positive and negative integers for hands-on practice.
• Worksheets: Multiplying and dividing integer problems.
• Real-world examples: Scenarios involving temperature, debt, or elevation changes.
• Interactive tools: Online integer games or apps (optional).
• Pencils, erasers, and paper: For solving problems.

Lesson Outline:

1. Introduction (10-15 minutes)

• Begin by reviewing the concept of integers (positive and negative whole numbers, including zero).
• Introduce the rules for multiplying and dividing integers:
  1. Positive × Positive = Positive
  2. Positive × Negative = Negative
  3. Negative × Positive = Negative
  4. Negative × Negative = Positive
  • The same rules apply to division.
• Write examples on the board and solve them step-by-step (e.g., 3 × (-4) = -12; (-6) ÷ (-2) = 3).

2. Activity 1: Integer Grid Puzzles (30-40 minutes)

• Provide the child with an integer grid puzzle. For example:
  • A 3×3 grid where the product of each row and column is given.
  • The child must fill in the missing integers using the rules of multiplying and dividing integers.
• Alternatively, create a puzzle where the child solves multiplication and division problems to uncover a hidden picture or message.
• Encourage the child to explain their reasoning as they solve the puzzle.

3. Activity 2: Real-World Examples (30-40 minutes)

• Present real-world scenarios that involve multiplying and dividing integers. For example:
  • Temperature Change: If the temperature drops by 3°C each hour for 4 hours, what is the total change in temperature?
  • Debt: If you owe $5 to each of 3 friends, what is your total debt?
  • Elevation: A submarine descends 10 meters every minute. How far has it descended after 6 minutes?
• Have the child write and solve the problems using integers.
• Discuss how the rules for multiplying and dividing integers apply to each scenario.

4. Activity 3: Interactive Exercises (20-30 minutes)

• Use online integer games or apps that focus on multiplying and dividing integers.
• Alternatively, create a “math relay” where the student solves a series of integer problems to advance through a course or complete a challenge.

5. Assessment (Optional)

• Provide a worksheet or quiz with a mix of multiplying and dividing integer problems, including real-world scenarios.
• Alternatively, have the child create their own real-world problem involving integers and solve it.

Extension Ideas:

• Integer War: Play a card game where the child draws two cards (positive or negative integers) and multiplies or divides them. The player with the highest absolute value wins the round.
• Integer Art: Have the child create a piece of art using a coordinate grid, where the coordinates are determined by solving integer multiplication and division problems.
• Research Project: Have the child research how integers are used in real-world fields such as finance, science, or engineering.