Math  /  1st Grade  /  Unit 7: Adding with Place Value Within 100

Adding with Place Value Within 100

Students apply place value understanding to reason about tens and ones and to develop strategies for adding within 100. They explore how numbers change when tens and ones are added and use place value to make sense of sums. Students use place value understanding to subtract multiples of 10 from other multiples of 10.

Math

Unit 7

1st Grade

Unit Summary

In Unit 7, students apply and extend their place value understanding to develop strategies for adding within 100. Building on the work of Unit 6, where students learned that two-digit numbers are composed of tens and ones, this unit focuses on using that structure to reason about addition situations. Students develop strategies for adding tens, adding ones, and composing new tens as needed, using concrete models, drawings, and equations.

In Kindergarten, students composed and decomposed teen numbers and added within 10 using objects and drawings K.NBT.A.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. . Earlier 1st Grade units emphasized addition and subtraction within 20 and students developed strategies such as counting on, counting back, and making a ten. In Unit 6, students deepened their understanding of ten as a unit and learned to flexibly compose and decompose two-digit numbers. Unit 7 extends this work by applying place value reasoning to subtracting multiples of 10 from other multiples of 10, and to addition with tens and teen numbers as well as addition within 100.

In this unit, students reason about how adding and subtracting tens affects a number, noticing patterns in the base ten system and using the structure of tens and ones to make sense of addition and subtraction involving multiples of 10, teen numbers, and other two-digit numbers. MP.7 Look for and make use of structure.  Students use a variety of place value–based strategies, such as combining tens with tens and ones with ones, or counting on by tens and then ones, and compare these approaches as they solve problems. They represent their thinking with concrete models, drawings, and equations, compare strategies and repeatedly reason about the number of tens and ones in each sum. MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically. MP.8 Look for and express regularity in repeated reasoning.  These experiences emphasize that addition within 100 is grounded in understanding how tens and ones are composed, decomposed, and combined, rather than relying on memorized procedures or algorithms. 

The work that students engage with in this unit provides essential preparation for later work with extended place value and numbers and operations. By developing place value–based strategies for adding within 100, students are prepared to extend these methods to adding and subtracting with larger numbers. Looking ahead to 2nd Grade, this unit directly supports students’ ability to fluently add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction 2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. .

Unit Prep

Intellectual Prep

Intellectual Prep for All Units

  • Read and annotate the "Unit Summary" and "Essential Understandings" portions of the unit plan. 
  • Do all the Target Tasks and annotate them with the "Unit Summary" and "Essential Understandings" in mind. 
  • Take the Post-Unit Assessment.

Unit-Specific Intellectual Prep

Essential Understandings

  • Two-digit numbers are composed of tens and ones, and understanding this structure helps students add numbers within 100.
  • Many strategies for adding within 20, such as making a ten or counting on, can be extended to add tens and ones in two-digit numbers.
  • Understand the pattern when 10, or a multiple of 10, is subtracted from a multiple of 10: the tens decrease and the ones stay the same.
  • Reasoning about and understanding numbers is the foundation of addition within 100, and students benefit from comparing multiple strategies to solve problems efficiently.

Materials

To see all the materials needed for this course, view our 1st Grade Course Material Overview.

Vocabulary and Models

Unit Practice

Fluency Activities

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Lesson Map

Common Core Standards

Key

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

Number and Operations in Base Ten

  • 1.NBT.A.1 — Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
  • 1.NBT.B.2.A — 10 can be thought of as a bundle of ten ones — called a "ten."
  • 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. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
  • 1.NBT.C.5 — Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
  • 1.NBT.C.6 — Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), 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.

Operations and Algebraic Thinking

  • 1.OA.A.1 — Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
  • 1.OA.B.3 — Apply properties of operations as strategies to add and subtract. Students need not use formal terms for these properties. To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.)
  • 1.OA.B.4 — Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.
  • 1.OA.C.6 — 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).

Foundational Standards

Counting and Cardinality

  • K.CC.A.1

Number and Operations in Base Ten

  • 1.NBT.B.2
  • K.NBT.A.1

Operations and Algebraic Thinking

  • 1.OA.C.6
  • K.OA.A.2

Future Standards

Number and Operations in Base Ten

  • 2.NBT.B.5
  • 2.NBT.B.9
  • 3.NBT.A.2

Operations and Algebraic Thinking

  • 2.OA.A.1
  • 2.OA.B.2

Standards for Mathematical Practice

  • CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

  • CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

  • CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

  • CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

  • CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

  • CCSS.MATH.PRACTICE.MP6 — Attend to precision.

  • CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

  • CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.

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