The Progressions Documents: A Resource for Teachers
Looking for some professional reading that will aid your understanding of the Common Core State Standards? The Progressions Documents for the Common Core State Standards in Mathematics may be exactly what you have been searching for. The writers of the Eureka Math modules took great care in studying the Progressions both before and while the assessments, objectives, overviews, and lessons within the modules were being written. This is one reason why there is such wonderful coherence throughout the modules and why the progression of the modules makes mathematical sense. Teachers are now, more than ever, recognizing the strength of their students’ prior learning
The Progressions Documents, housed on the University of Arizona website, were written prior to the Common Core State Standards. They are a series of documents that the progression of the mathematics specific to each of the domains of the Common Core State Standards (CCSS). The awesome thing about these documents is how they show the coherence and connectedness of the math within and across grade levels (i.e., how the math taught within one grade level sets students up for success with the next). The Progressions Documents are a great resource for teachers to supplement their understanding of math. Let’s look, for example, at the Number and Operations in Base Ten, K-5 Progression in Eureka
The Number and Operations in Base Ten, K-5 Progression begins with an introduction of the base-ten system and explains how work with the base-ten system intertwines with students’ work with counting and cardinality and with the four basic operations. Units of base-ten and their relationships are introduced and then are followed by an explanation of computations as they relate to the composing and decomposing of base-ten units. The solution strategies (evident in the Grade 2 modules) are explained and introduced as are different computational methods. Make-a-ten strategies and composing and decomposing a ten are explained. Also stressed is students’ initial work with concrete models and drawings and the absolute importance of student discussion and explanation of the math. The document calls out the Standards for Mathematical Practice (MPs) and explains the importance of the MPs in the movement to the initial understanding and then use of the standard algorithms. Finally, the document explains in detail, grade level by grade level, the progression of the math within the Number and Operations in Base Ten (NBT) domain.
What follows are some of the central ideas that are explained within the NBT Progression. You will likely recognize these ideas as the Common Core State Standards. If you are confused about what the NBT Standards mean at your grade level, the NBT Progression does a great job of explaining the math and giving strategies and explanations for understanding the Standards.
Things to note when reviewing the NBT Progression:
the commonalities from one grade level to the next.
how initial work with a concept focuses on place value strategies and properties of operations.
how students are gradually introduced to larger numbers and how the same strategies taught in earlier grades apply to work with larger units.
how student success with the required fluencies is supported through early introduction and repeated exposure within the grades levels prior to that in which students are expected to be fluent.
(Note that the concepts listed are inclusive of those within the NBT domain and do not reflect standards within the other domains.)
Central Concepts of the NBT Progression (K-5)
Paying special attention to 10
Viewing the whole numbers from 11–19 as ten ones and some more ones; interpreting the teen numbers
Viewing ten ones as a unit of a ten
Viewing the decade numbers in spoken and written form
Understanding the two digits within a two-digit number as representing the amount of tens and ones
Comparing two two-digit numbers and using the symbols of <, >, and =
Computing sums within 100
Mental calculations of 10 more and 10 less
Finding differences of multiples of 10
Viewing ten tens as a unit of a hundred
Understanding that the unit within each place is 10 of the unit associated with the place to its right
Making connections between spoken form, written form, and expanded form
Learning the counting sequence from 100 to 1,000
Skip-counting by 5s, 10s, and 100s
Comparing three-digits numbers
Fluently adding and subtracting within 100
Adding and Subtracting within 1,000
Explaining how computation methods work
Adding up to four two-digit numbers using place value strategies and properties of operations
Fluently adding and subtracting within 1,000 using place value strategies, properties of operations, or the relationship between addition and subtraction; focusing on methods that generalize to work with larger numbers
Rounding to the nearest 10 or 100
Multiplying one-digit numbers by a multiple of 10 using place value strategies and properties of operations
Fluently adding and subtracting multi-digit numbers through 1,000,000 using standard algorithms
Reading and writing numerals between 1,000 and 1,000,000 in standard form, written form, and expanded form
Comparing multi-digit numbers
Rounding multi-digit numbers to any place value
Understanding that the value of each place is 10 times the value of the place to its immediate right; digits shift one place to the left when multiplied by 10
Multiplying and dividing with multi-digit numbers using place value strategies and properties of operations
Multiplying two two-digit numbers
Computing quotients of multi-digit numbers and one-digit numbers with remainders using place value strategies, properties of operations, and/or the relationship between multiplication and division
Working with denominators of 10 and 100 in preparation to extend the base-ten system to non-whole numbers
Writing mixed numbers (where denominators are 10 or 100) in expanded form
Expressing the value of numbers in different forms (e.g., 0.24 as twenty-four hundredths or 2 tenths, 4 hundredths)
Extending the understanding of the base-ten system to thousandths
Using whole number exponents to denote powers of 10
Fluently computing the products of whole numbers using the standard algorithm
Dividing by two-digit divisors
Adding, subtracting, multiplying, and dividing decimals to hundredths
The Progressions are a great resource for personal professional growth and mathematical understanding. Be sure to read the Progressions in their entirety to discover or rediscover the reasoning behind the math, the complexities students will face, and how to help students overcome difficulties.