Students learn to compare numbers, round to any place value, work towards fluency with the standard algorithms for adding and subtracting, and solve multi-step word problems involving addition and subtraction.
In the first unit for Grade 4, students extend their work with whole numbers and use this generalized understanding of the place value system in the context of comparing numbers, rounding them, and adding and subtracting them.
Students understanding of the base ten system begins as early as Kindergarten, when students learn to decompose teen numbers as ten ones and some ones (K.NBT.1). This understanding continues to develop in Grade 1, when students learn that ten is a unit and therefore decompose teen numbers into one ten (as opposed to ten ones) and some ones and learn that the decade numbers can be referred to as some tens (1.NBT.1). Students also start to compare two-digit numbers (1.NBT.2) and add and subtract within 100 based on place value (1.NBT.3—5). In second grade, students generalize the place value system even further, understanding one hundred as a unit (2.NBT.1) and comparing, adding, and subtracting numbers within 1,000 (2.NBT.2—9). In Grade 3, place value (NBT) standards are additional cluster content, but they still spend time fluently adding and subtracting within 1,000 and rounding three-digit numbers to the nearest 10 and 100 (3.NBT.1—2).
Thus, because students did not focus heavily on place value in Grade 3, Unit 1 begins with where things left off in Grade 2 of understanding numbers within 1,000. Students get a sense of the magnitude of each place value by visually representing the place values they are already familiar with and building from there. Once students have a visual and conceptual sense of the “ten times greater” property, they are able to articulate why a digit in any place represents 10 times as much as it represents in the place to its right (4.NBT.1). Next, students write multi-digit numbers in various forms and compare them (4.NBT.2). Comparison leads directly into rounding, where Grade 4 students learn to round to any place value (4.NBT.3). Next, students use the standard algorithms for addition and subtraction with multi-digit numbers (4.NBT.4) and apply their algorithmic knowledge to solve word problems. The unit culminates with multi-step word problems involving addition and subtraction, using a letter to represent the unknown quantity, then using rounding to assess the reasonableness of their answer (4.OA.3), allowing for students to connect content across different clusters and domains (4.NBT.A, 4.NBT.B, and 4.OA.B).
Throughout the unit, students will repeatedly look for and make use of structure, specifically the structure of the place value system (MP.7). Students develop an understanding that a digit in any place represents 10 times as much as it represents in the place to its right, then apply that understanding of structure to compare, round, and add and subtract multi-digit whole numbers.
In subsequent grade levels, students generalize their base ten understanding to decimals. While students do some work with tenths and hundredths later on in Grade 4 (4.NF.5—7), students in Grade 5 are able to extend the decimal system to many more place values, seeing that a digit represents $$\frac{1}{10}$$ of what it represents in the place to its left (5.NBT.1—3). Students subsequently round, compare, and operate on decimals as they did with numbers greater than one in Grade 4. Thus, this unit sets a precedent for a deep understanding of the number system that supports much of their mathematical knowledge later this year and in years to come.
Pacing: 22 instructional days (19 lessons, 2 flex days, 1 assessment day)
This assessment accompanies Unit 1 and should be given on the suggested assessment day or after completing the unit.
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4.NBT.A.1
4.NBT.A.2
4.NBT.A.3
4.NBT.B.4
Review place value understanding for numbers within 1,000.
4.NBT.A.1
4.NBT.A.2
Build numbers to 10,000 and write numbers to that place value in standard, unit, and expanded form.
4.NBT.A.1
4.NBT.A.2
4.NBT.A.3
Model and write numbers to 10,000 with more than 9 of any unit in standard and unit form.
4.NBT.A.1
4.NBT.A.2
Build numbers to 1,000,000 and write numbers to that place value in standard and unit form.
4.NBT.A.1
Multiply and divide single units by 10. Recognize that a digit represents 10 times the value of what it represents in the place to its right.
4.NBT.A.1
Multiply and divide multiple units by 10. Apply the property of “ten times greater” in the context of problems.
4.NBT.A.2
Read and write multi-digit numbers using base-ten numerals, number names, and expanded form.
4.NBT.A.2
Compare numbers based on the meanings of the digits using >, <, or = to record the comparison.
4.NBT.A.2
4.NBT.A.3
Locate multi-digit numbers on a number line and explain their placement.
4.NBT.A.3
Round multi-digit numbers to their largest place value.
4.NBT.A.3
Round multi-digit numbers to any place value.
4.NBT.A.3
Round multi-digit numbers to any place value in more complex cases, including those involving real-world contexts and/or assessing the reasonableness of that estimate.
4.NBT.B.4
Fluently add multi-digit whole numbers using the standard algorithm involving up to two compositions. Solve one-step word problems involving addition.
4.NBT.B.4
Fluently add multi-digit whole numbers using the standard algorithm involving multiple compositions. Solve one-step word problems involving addition.
4.OA.A.3
4.NBT.B.4
Solve multi-step word problems involving addition and assess the reasonableness of answers.
4.NBT.B.4
Fluently subtract multi-digit whole numbers using the standard algorithm involving up to two decompositions. Solve one-step word problems involving subtraction.
4.NBT.B.4
Fluently subtract multi-digit whole numbers using the standard algorithm involving multiple decompositions. Solve one-step word problems involving subtraction.
4.OA.A.3
4.NBT.B.4
Solve multi-step word problems involving subtraction and assess the reasonableness of answers.
Key: Major Cluster Supporting Cluster Additional Cluster
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