Math / 2nd Grade / Unit 4: Place Value with Numbers to 1,000 & Money
Students extend their place value knowledge to 1,000 and use this knowledge to represent and compare three-digit numbers. Students are also introduced to money, identifying coins and their value, and determining the value of coin collections.
Math
Unit 4
2nd Grade
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In Unit 4, 2nd grade students build on their understanding of place value with the introduction of a new unit, a hundred. By extending their understanding that 10 ones form a ten, they learn that 10 tens form a hundred. With their knowledge of a hundred, students further their understanding of three-digit numbers by expanding their count sequence to 1,000. Their work with place value is reinforced by their work with money as they identify coins and determine the value of coin collections, as well as put this to work in context with one-step and two-step word problems.
In Topic A, students learn about a hundred and three-digit numbers (2.NBT.A.1). They use concrete base ten blocks to build three-digit numbers and understand that these numbers are made of hundreds, tens, and ones. As they build their concept of numbers with multiple hundreds they also are introduced to the idea that 10 hundreds make a thousand. That is the extent of students' understanding about a thousand as that is where their count sequence ends. Throughout the topic, students work on identifying and building three-digit numbers. They understand that three-digit numbers can be re-written with more than 10 units of ones or tens. This work lays the foundation for adding and subtracting with rebundling. Students also learn to read and write numbers in all forms including, unit form, number form, and expanded form (2.NBT.A.3).
In Topic B, students extend their formal count sequence to include multiple hundreds and end their sequence at 1,000 (2.NBT.A.2). This is pivotal to students' number sense formation as students cannot reliably add and subtract to numbers they have not counted. In this topic, students also locate numbers on a number line and use a number line as a tool to compare and order three-digit numbers. Students were introduced to number lines in Unit 3 with their work with measurement and adding and subtracting within 100. This is the first time they will see the number line extended beyond 100, to 1,000. Beyond the number line, students also use their place value knowledge to compare and order three-digit numbers by reasoning about the number of hundreds, tens, and ones in each number (2.NBT.A.4).
Finally, in Topic C students see place value in action with their work with money and coins. They focus on identifying coins and their value in order to find the value of coin collections. Using their knowledge that 10 tens make a hundred, students see that their work with dimes is similar as 10 dimes makes 100 cents, or a new unit, a dollar. Students' work with money primarily stays within a dollar; they reason how to make a dollar or get change from a dollar. This reinforces student work of adding and subtracting within a 100 from Unit 2. In working with coins, students also continue to work on skip-counting as they count coin groupings flexibly by 10s, 5s, and 1s (2.NBT.A.2). Students continue their application of their work with money as they solve one-step and two-step word problems involving money situations (2.MD.C.8). The end of the unit continues their grade-level work with two-step word problems as they explore combining add to and take from change unknown problem types, considered to be middle difficulty subtypes with easier results unknown subtypes (2.OA.A.1). By the end of Grade 2, students should be proficient in these types of two-step word problem combinations with addition and subtraction.
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The following assessments accompany Unit 4.
Have students complete the Mid-Unit Assessment.
Use the resources below to assess student understanding of the unit content and action plan for future units.
Post-Unit Assessment
Post-Unit Assessment Answer Key
Use student data to drive instruction with an expanded suite of assessments. Unlock Pre-Unit and Mid-Unit Assessments, and detailed Assessment Analysis Guides to help assess foundational skills, progress with unit content, and help inform your planning.
Suggestions for how to prepare to teach this unit
Pictorial or concrete base ten blocks
Example: Represent 248 with base 10 blocks
Place value chart
Number line
Coin models
Tape diagram
Example: A grocery store sells 172 red apples and 86 green apples/ How many apples did the grocery store sell?
The central mathematical concepts that students will come to understand in this unit
Terms and notation that students learn or use in the unit
base 10 blocks
compare
equal
expanded form
less than
nickel
number line
penny
place value chart
quarter
standard form
tape diagram
unit form
word form
To see all the vocabulary for Unit 4, view our 2nd Grade Vocabulary Glossary.
The materials, representations, and tools teachers and students will need for this unit
Hundreds Place Value Chart (one per student)--can be placed in a sheet protector or laminated and used with a dry erase marker
Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.
Topic A: Understanding and Representing Three Digit Numbers
Compose and represent a hundred.
2.NBT.A.1 2.NBT.A.1.A
Model and compose three-digit numbers with hundreds, tens, and ones using base ten blocks.
2.NBT.A.1 2.NBT.A.1.A 2.NBT.A.1.B
Represent and compose three digit numbers using hundreds, tens, and ones.
2.NBT.A.1
Model and compose three-digit numbers in situations where there are more than 9 tens and ones.
Use unit form to represent three-digit numbers using understanding of place value and base ten.
2.NBT.A.3
Read, write, and represent three-digit numbers in standard form, word form, and unit forms.
Read, write, and represent three-digit numbers using understanding of place value and expanded form.
Read, write, and represent three-digit numbers in all forms.
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Topic B: Reasoning with Numbers to 1000
Use place value understanding to count to 1,000 and reason about three-digit numbers.
2.NBT.A.2
Locate three-digit numbers on a number line.
Skip-count by 5s, 10s, and 100s to find numbers on a number line.
Compare 2 three-digit numbers using a number line.
2.NBT.A.4
Compare 2 three-digit numbers using place value.
Order three-digit numbers using place value knowledge and number lines to explain thinking.
2.NBT.A.2 2.NBT.A.4
Topic C: Place Value in Action - Money and Word Problems
Understand the value of dimes, nickels, and pennies.
2.MD.C.8
Use counting to find the value of groups of dimes, nickels, and pennies.
2.MD.C.8 2.NBT.A.2
Understand the value of quarters and find the value of coin collections.
Understand the value of 100 cents and 1 dollar.
Make change from a dollar and make a dollar with coins.
2.MD.C.8 2.OA.A.1
Solve word problems with money situations.
Solve two-step word problems with money situations.
Solve two-step word problems with add to change unknown and take from change unknown.
2.OA.A.1
Key
Major Cluster
Supporting Cluster
Additional Cluster
The content standards covered in this unit
2.MD.C.8 — Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?
2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
2.NBT.A.1.A — 100 can be thought of as a bundle of ten tens — called a "hundred."
2.NBT.A.1.B — The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
2.NBT.A.2 — Count within 1000; skip-count by 5s, 10s, and 100s.
2.NBT.A.3 — Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
2.NBT.A.4 — Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
2.OA.A.1 — Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Standards covered in previous units or grades that are important background for the current unit
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 — Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
1.NBT.B.3 — Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
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.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.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.D.8 — Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ – 3, 6 + 6 = _.
Standards in future grades or units that connect to the content in this unit
2.NBT.B.6 — Add up to four two-digit numbers using strategies based on place value and properties of operations.
2.NBT.B.7 — Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
2.NBT.B.8 — Mentally add 10 or 100 to a given number 100—900, and mentally subtract 10 or 100 from a given number 100—900.
3.NBT.A.1 — Use place value understanding to round whole numbers to the nearest 10 or 100.
3.NBT.A.3 — Multiply one-digit whole numbers by multiples of 10 in the range 10—90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
4.NBT.A.3 — Use place value understanding to round multi-digit whole numbers to any place.
4.NF.A.1 — Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
3.OA.D.8 — Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
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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