In this lesson plan, your learner will focus on adding two-digit numbers by partitioning them into tens and ones. The lesson will be divided into two stages: adding without crossing the tens boundary and adding with crossing the tens boundary.
Key Concepts for Adding Two-Digit Numbers by Partitioning
Partitioning: Partitioning a number means breaking it down into smaller parts. For two-digit numbers, this involves splitting the number into tens and ones, which makes calculations simpler for learners. For example, the number 34 can be partitioned into 30 (tens) and 4 (ones).
Adding Without Crossing the Tens Boundary: In the first part of the lesson, we focus on examples where the sum of the ones digits stays within 10. This helps learners build confidence and understand the process without the complexity of carrying over.
Adding with Crossing the Tens Boundary: In the second part of the lesson, we progress to examples where the sum of the ones digits is 10 or more, requiring learners to carry over to the next ten.
Visual and Practical Tools: Using part-part-whole models and base-ten blocks helps learners visualize the partitioning of two-digit numbers and then adding the tens and ones to find the sum. These tools make the abstract concepts more concrete and understandable.
Teaching Plan
The following activities will help your learner develop confidence in adding two-digit numbers by partitioning. Be sure to work at a pace that is comfortable for your learner.
Examples and visuals to support the lesson:
1. Review of Adding Tens and Ones
Begin by reviewing known concepts and strategies that will be useful for the lesson:
Partitioning a given two-digit number into tens and ones.
Strategies for bridging ten.
Adding a single-digit number to a two-digit number.
Adding two multiples of ten.
Adding multiples of ten to a two-digit number.
Use a real-world shopping context with items priced as single-digit numbers, multiples of ten, teen numbers, and other two-digit numbers. For example, mug = £3, toy car = £5, book = £20, computer game = £40, three flowers = £12. Pose questions to practice different addition scenarios:
"How much does a mug and a toy car cost?" (two single-digit numbers)
"How much does a book and a computer game cost?" (two multiples of ten)
"How much does a book and a toy car cost?" (multiple of ten and a single-digit number)
"How much does a book, a mug, and a car cost?" (multiple of ten and two single-digit numbers)
"How much do three flowers and a toy car cost?" (two-digit number and a single-digit number)
"How much does a book, a computer game, and a mug cost?" (two multiples of ten and a single-digit number)
Highlight that known facts and strategies should be used rather than counting-on methods. Visual representations should support understanding, not calculation. Encourage your learner to calculate answers mentally and explain the strategies used. For example:
"I use number facts within ten; three pounds plus five pounds is equal to eight pounds."
"I know that two plus four is equal to six, so two tens plus four tens is equal to six tens; the total is sixty."
Skill Check
I can split numbers into tens and ones and add with multiples of ten.
2. Review of Addition with Partitioning
Once your learner has mastered the concepts practiced in the first step, prepare for the addition of two two-digit numbers by first working with the addition of two multiples of ten and two single-digit numbers.
Use the shop scenario to explore these types of questions, for example: "How much does a computer game, a book, a toy car, and a mug cost?" (40 + 20 + 5 + 3)
Use base-ten blocks and equations to demonstrate the strategy. First, add the tens (40 + 20 = 60). Then add the ones (5 + 3 = 8). Lastly, add the total of the tens and ones (60 + 8 = 68).
Present the items/numbers in different orders to explore whether the order of the addends affects the total cost. Include situations such as: 40 + 5 + 20 + 3.
This practice will facilitate progression to adding two-digit numbers by partitioning them and adding the tens and ones.
Skill Check
I can add two-digit numbers together by adding their ones together and adding their tens together.
3. Addition Without Crossing the Tens Boundary
Present a two-digit addition problem where a tens boundary is not bridged, such as calculating the total cost of a bike (£45) and a construction set (£23).
Ask your learner how they could calculate the total cost and see if they can link it to previous examples.
Use base-ten blocks and part-part-whole models to represent the calculation.
Highlight that although adding two two-digit numbers is new, the steps involved are familiar once the numbers are partitioned into tens and ones.
After working with concrete and pictorial support, transition to using equations.
Encourage your learner to describe the steps in full sentences:
"First, I partition the forty-five into forty and five, and the twenty-three into twenty and three." (45 = 40 + 5 and 23 = 20 + 3)
"Forty plus twenty is equal to sixty." (40 + 20 = 60)
"Five plus three is equal to eight." (5 + 3 = 8)
"Sixty plus eight is equal to sixty-eight." (60 + 8 = 68)
Provide practice with missing number problems and real-life contexts. Use questions where the first and second addends vary in size, the position of the equals sign changes, and different measures are used. For example:
"There is seventy-five milliliters of water in a glass. Yasmin pours another fifteen milliliters of water into the glass. What is the total volume of water in the glass?" (augmentation/joining)
"Mr. Garcia has thirty-six footballs. Mr. Millet has forty-three tennis balls. How many balls are there altogether?" (aggregation/part-part-whole)
Use the following stem sentences to guide your learner:
"First, I partition the ___ into ___ and ___, and the ___ into ___ and ___."
"___ plus ___ is equal to ___."
"___ plus ___ is equal to ___."
"And ___ plus ___ is equal to ___."
"So, ___ plus ___ is equal to ___."
Skill Check
I can add two-digit numbers together by splitting them into tens and ones and then finding the sum.
4. Preparation for Crossing the Tens Boundary
Review addition of two, three, or four numbers, using real-life examples to demonstrate crossing the tens boundary. Use items in a shop to create relatable problems.
For example: "How much does a train set, a drum, and a bear cost?" (£50 + £10 + £3). "How much does a train set and a boat cost?" (£50 + £13).
Use base-ten blocks and part-part-whole models to represent the calculation.
Highlight the steps involved in partitioning the addends and recombining them after addition.
Transition to using equations, encouraging your learner to describe the steps:
"First, I partition the fifty into fifty and zero, and the thirteen into ten and three." (50 = 50 + 0 and 12 = 10 + 3)
"Fifty plus ten is equal to sixty." (50 + 10 = 60)
"Zero plus three is equal to three." (0 + 3 = 3)
"Sixty plus three is equal to sixty-three." (60 + 3 = 63)
Provide practice with missing number problems and real-life contexts:
"How much does a train set, a ball, and a doll cost?" (£50 + £6 + £7)
"How much does a book, a ball, an aeroplane, and a doll cost?" (£20 + £6 + £30 + £7)
Skill Check
I can add numbers where the ones digits add up to 10 or more.
5. Addition Crossing the Tens Boundary
Present a problem where the tens boundary is crossed, such as calculating the total cost of a scooter (£26) and a doll’s house (£37).
Ask your learner how they could calculate the total cost and see if they can link it to previous examples.
Use base-ten blocks and part-part-whole models to represent the calculation.
Highlight the steps involved in partitioning the addends and recombining them after addition.
Transition to using equations, encouraging your learner to describe the steps:
"First, I partition the twenty-six into twenty and six, and the thirty-seven into thirty and seven." (26 = 20 + 6 and 37 = 30 + 7)
"Twenty plus thirty is equal to fifty." (20 + 30 = 50)
"Six plus seven is equal to thirteen." (6 + 7 = 13)
"Fifty plus thirteen is equal to sixty-three." (50 + 13 = 63)
Explore an additional strategy by adding the partitioned parts of one of the two-digit numbers to the whole of the other two-digit number.
For example, when adding 26 + 37, have your learner partition 37 only. (26 + 30 + 7)
Have them add 26 to the multiple of ten. (26 + 30 = 56)
Then add 7. If necessary, provide a number line or number chart to demonstrate crossing over sixty. (56 + 7 = 63)
Compare the two strategies (partitioning one addend vs. partitioning both), by asking:
"What’s the same? What’s different?"
Both strategies give the correct answer and use skills from prior learning. The "partitioning one addend" strategy has fewer steps.
Provide practice with missing number problems and real-life contexts. For example:
"A sunflower is seventy-five centimeters tall. It then grows another seventeen centimeters. How tall is the sunflower now?" (augmentation/joining)
"Mr. Garcia has thirty-eight footballs. Mr. Millet has forty-three tennis balls. How many balls are there altogether?" (aggregation/part-part-whole)
Skill Check
I can solve different types of problems that involve adding two-digit numbers by splitting them into tens and ones and then finding the total.
Summary
By the end of this lesson, your learner should be confident in adding two-digit numbers by partitioning them into tens and ones. Using real-world scenarios, part-part-whole models, and base-ten blocks will help them progress to solving equations and missing number problems. This foundation supports flexible and efficient calculation strategies while preparing your learner for working with larger numbers.
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Skill Check