Combinations of 10 Lesson 1

  • Making Tens with Mac and Cheese

    Lesson 1 of 4
    Kindergarten and 1st grade

    45-60 minutes


    Using macaroni, students model combinations through 10 and record a written expression.


    For each student:


    Accommodation: Ell students will need frontloading of vocabulary. decompose, expression, combinations, addend, commutative

    Teacher needs to distribute a bag of 10 macaroni and Mac and Cheese Work Mat to each student. Instruct the students to count out 6 pieces of macaroni.

    Teacher asks the question “How can we place our 6 macaroni into the 2 bowls? Students discuss options with a partner and teacher asks for 1 group to model. Teacher will record the expression on the board.

    2 macaroni bowl illustrations with 4 and 2 macaronis respectively

    Teachers asks "Is there another way we can place our macaroni in the bowls?"

    Students are sent back to their seats to explore ways to identify the missing combinations of 6 using the Macaroni and Cheese Work Mat (download from Materials section above).

      Accommodation: Students that need more modeling can stay with the teacher for additional support.

    After 5 minutes teacher brings students back to discuss, share, and identify the missing combinations of 6.

    • How many different ways can we put 6 noodles in two bowls? [6+0, 1+5, 4+2, 3+3, 2+4, 5+1, 0+6]
    • Have we found them all?
    • How do you know that we found all the combinations? Possible student responses: {“We have used all the numbers to 6 and the commutative property.”}

    Teacher models the combinations of 6 on the Macaroni and Cheese Recording Sheet. Answers will vary based on number choices.

    To stimulate curiosity and increase student motivation, lead the class in a brief Visible Thinking routine called "I see, I think, I wonder". This type of experience sets the stage for inquiry-based learning. Encouraging students to be creative and thoughtful with their observations and interpretations, which helps promote discourse in the classroom. (MP 1, 7, 8) More research and graphic organizers for this routine can be found online.

    Under the picture (above) post or state the following: "Complete each of the three sentences related to this picture."


    • Students are given a Macaroni and Cheese Recording Sheet and asked to identify as many combinations to 10 as possible.

     Accommodation: Students can work in pairs or alone
    Teachers can color code the bowls for students that need visual assistance transferring concrete macaroni to the work mat.
    As students are working and exploring combinations of ten, teacher is walking around and asking:

    • What do you notice? [Sample answer: “ I took away one macaroni each time to get a new combination.”}

    {“I have eight and two to get another combination, one goes up and one goes down.”}

    • Have you found any shortcuts? [Sample answer: “I used the commutative property.”]
    • Does anyone see a relationship between the number of macaroni and the number of expressions? [Sample answer: “The number of expressions is always one more than the macaroni.”]

    Continue to allow groups and individuals to explore with combinations to 10. After 10 minutes have students return to the carpet with their recording sheet and share all the combinations to 10 they have identified.

    As the students share combinations the teacher records the identified pairs on a recording sheet. Questions to consider while recording combinations:

    • How many do we have? Can we find another pair?
    • How will I know when I have all possible combinations? Possible student responses: “You will have all thecommutative pairs.”
    • How can we organize to be sure we have them all?

     Possible student responses: “We can make a chart starting with zero.”



    Students will pick a number between 1-9 and complete the Macaroni and Cheese Recording Sheet based on their new number. The teacher will lead the students in a discussion of how many expressions they discovered for each number. This can be done by writing the numbers one through 10 on the board (# of Macaroni). Teacher calls on students to identify and share the number of combinations/expressions they found for the number they choose (# of combinations).

    # of Macaroni (teacher) # of Combinations (students)
    1 2
    2 3
    3 4
    4 5
    5 6
    6 7
    6 8
    6 9
    6 10

    Ask the following questions:

    • What did you notice about the relationship between the number of macaroni and the number of expressions? (MP 7) [The number of combinations is always one more than the number of macaroni].
    • Can you predict how many sets of addends you will have for any given number? (MP 8) [The number of combinations will always be 1 more than the number of macaroni]


    Students will record three ways to make 10. Accommodation: Some students may need to use the bowls and macaroni.


    Students can make macaroni bracelets with 10 pieces of macaroni and a pipe cleaner. These can be an additional tool throughout the lessons as the student builds a conceptual understanding of combinations of 10.

    Teacher Reflection

    • Which students had to use the macaroni to complete the activity?
    • Which students could generate expressions without the manipulatives?
    • What patterns did students notice in order to generate the equations?
    • How many noticed the commutative property of addition?

    Leave your thoughts in the comments below.

    Related Material

    Navigating through Algebra PreK‐2 NCTM ‐ “Two Shapes” pg.41

    This book demonstrates how some of the fundamental ideas of algebra can be introduced, developed, and extended. By Carole Greenes, Mary Cavanagh, Linda Dacey, Carol Findell, and Marian Small

    Other Lessons in This Activity

    Lesson 2 of 4

    Use cubes to model combinations of ten; explore the different addend pairs, and play a card game to apply their understanding.

    Lesson 3 of 4

    Students use ten-frames to model combinations of ten. They explore the different addend pairs, and play a game to apply their understanding.

    Lesson 4 of 4

    Students explore multiple ways to make ten with tens frames and drawings, with a final project of a class book.

  • Comments


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      The first grade standard is labeled wrong. The standard reads for 1.OA.6... however, it is labeled 1.OA.2

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  • Essential Question(s)

    • What do you notice about number combinations within 10?
    • Can you predict how many sets of addends you will have for any given number?


    CCSS, Content Standards to specific grade/standard

    • 1.OA.C.2 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
    • K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
    • K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

    CCSS, Standards for Mathematical Practices

    • SMP 7 Look for and make use of structure.
    • SMP 8 Look for and express regularity in repeated reasoning.

    PtA, highlighted Effective Teaching Practice and/or Guiding Principle CCSS

    • Implement tasks that promote reasoning and problem solving.
    • Facilitate meaningful mathematical discourse.