1.NBT.C.4

Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Although this standard involves only adding a two-digit number with a muliple of ten, students will understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

 

Summary:

Although this standard focuses on addition, showing students that addition and subtraction are closely related will help them "see" the reasoning in what they are doing. Once students have demonstrated a firm understanding of the place value of two-digit numbers, they are ready to add a two-digit number and a one-digit number, and two two-digit numbers (one of which is a multiple of ten (which avoids the process or regrouping) . Further, students understand that in addition digits in the ones place are added; digits in the tens place are added; and sometimes composing a ten is necessary. Further, students understand that in addition and subtraction, digits in the ones place are added and subtracted; and, digits in the tens place are added and subtracted. This fluency with addition and subtraction should be done through a variety of operation strategies. Additionally, students can explain their reasoning through verbal communication as well as a variety of representations including pictures, drawings and models.


Understanding the Standard:


    • Provide students with problems to perform the following operations: 1. add a two-digit number and a one-digit number; 2. add a two-digit number and a multiple of ten; 3. add two two-digit numbers. (Students can initially be given addition problems that do not require regrouping, and then addition problems that do require composing a ten.)
    • Provide students with a variety of manipulatives and technologies which can aid in their practice of addition and subtraction through 100.
    • Base-10 manipulatives can be used to show students how to concretely model addition and to reinforce the idea of place value, of adding tens and tens, ones and ones, and when necessary, composing a ten.

      Specific Questions to Focus Instruction:


        • Can students add and subtract two-digit numbers?
        • Are students able to demonstrate mastery of place value by adding only those digits in the ones positions and then adding only those digits in the tens position (if regrouping is not necessary)? When necessary, can students compose a ten?
        • Can students add a two-digit number and a one-digit number?
        • Can students add a two-digit number and a multiple of ten?
        • Can students use different concrete models to add, and can they relate these strategies to a written method of addition?
        • Can students explain the reasoning behind the strategy used?


          Skills

          Prior to: Students are able to show mastery in adding and subtracting one-digit numbers.

          At Grade Level: Students can add and subtract two-digit numbers through 100, showing an understanding of the value each digit possesses.

          Moving Beyond: Students will build upon prior knowledge to explore the concept of regrouping in addition and subtraction with two-digit numbers. Further, they will begin to add and subtract three-digit numbers, first with no regrouping and then moving on to regrouping in a variety of positions. Go to 2.NBT.B.7 to see the progression of related skills.