Primary Standards:
MAFS.1.NBT.3.4 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. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
Connecting Standards
MAFS.1.NBT.3.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
Content Knowledge:
In the prior Unit, students focused on adding or subtracting tens with tens. In this Unit, students will now work with addition problems involving adding ones with ones, adding both tens to tens and ones to ones. Students will also experience that in both situations, sometimes they will have more than ten ones, and that ten of these ones can be combined to form an additional ten, which then can be combined with the other tens. This concept at first glance seems like a very simple idea but should not be taken for granted as it is the essential building block to understanding all operations in the base-ten number system.
At this level, the goal is for students to use what they know about place value to find the sum, not to memorize a traditional algorithm. They should use objects (base-ten blocks and snap cubes), drawings, hundred charts, ten frames, and number lines to explore this addition process.
As students work with objects and drawings, it is important they connect these understandings to recordings, including seeing patterns on a hundred chart, jumps on a number line, and with equations. As students add numbers, such as 28 + 5 or 36 + 27, using objects, drawings, and the number themselves, they discover through repeated investigations that when they combine the ones from each addend, they can compose a new group of 10. These insights strengthen our students’ understanding of place value and how our base-ten number system works and is an important reason why place value instruction should occur along with addition and subtraction.
GCG 1 – Learning Goal: As a Mathematician, I will be able to Add a 1-Digit Number to a 2-Digit Number
- Step 1: Use concrete models, drawings, and place value language to add ones to a two-digit number (without making a ten)
- Step 2: Use concrete models, drawings, and place value language to add ones to a two-digit number that leads to making a ten
- Step 3: Use number lines to represent the addition of a 1-digit number to a 2-digit number
GCG 2 – Learning Goal: As a Mathematician, I will be able to Add Tens and Ones Without Making a Ten
- Step 1: Use concrete models, drawings, and place value language to add a 2-digit number by a 2-digit number (without making a ten)
- Step 2: Use number lines to add a 2-digit number to a 2-digit number (without making a ten)
- Step 3: Use partial sums to add a 2-digit number to a 2-digit number with an equation (without making a ten)
GCG 3 – Learning Goal: As a Mathematician, I will be able to Add Tens and Ones by Making a Ten
- Step 1: Use concrete models, drawings, and place value language to add a 2-digit number to a 2-digit number (by making a ten)
- Step 2: Use number lines to add a 2-digit number by a 2-digit number (by making a ten)
- Step 3: Use partial sums to add a 2-digit number to a 2-digit number with an equation (by making a ten)