Math PRogressions 3-5

Order the learning progressions. Think about which grade level these might be linked to! Third Grade The major focus is multiplication, so students’ work with addition and subtraction is limited to the maintenance of fluency within 1000 for some students and building fluency to within 1000 for others. Students continue adding and subtracting within 1000, using strategies and algorithms based on place value, properties of operations, algorithms that are based on place value, properties of operations, and the relationship between addition and subtraction. Such fluency can serve as preparation for learning standard algorithms, if the computational methods used can be connected with those algorithms. Students use their place value understanding to round numbers to the nearest 10 or 100. They understand that moving to the right across the places in a number (e.g., 456), the digits represent smaller units. The special role of 10 in the base-ten system is important in understanding multiplication of one-digit numbers with multiples fo 10. Fourth Grade Students extend their work in the base-10 system, using standard algorithms to fluently add and subtract. They use methods based on place value and properties of operations supported by suitable representations to multiply and divide with multi-digit numbers. Students read numerals between 1,000 and 1,000,000, through understanding the role of the comma. Students work decimal notation through the hundredths place. Students become fluent with the standard algorithm for addition and subtraction. In fourth grade, students compute products of one-digit numbers and multi-digit numbers (up to four digits) and products of two two digit numbers. They divide multi-digit numbers (up to 4 digits) by one digit numbers. Students should use methods that they understand and can explain. Students work with finding products of one digit numbers and multiples of 10, 100, and 1000, as well as using the distributive property to allow numbers to be decomposed into base-ten units. Similarly, students find quotients of multiples of 10, 100, or 1000 and one-digit numbers. Fifth Grade Students extend their understanding of the base-ten system to decimals to the thousandths place, building on their Grade 4 work with tenths and hundredths. They become fluent with the standard multiplication algorithm with multi-digit whole numbers. They reason about dividing whole numbers with two-digit divisors, and reason about adding, subtracting, multiplying, and dividing decimals to hundredths. Students extend their understanding of the base-ten system to the relationship between adjacent places, how numbers compare, and how numbers round for decimals to thousandths. New learning is the use of whole number exponents to denote powers of 10. Students understand why multiplying by a power of 10 shifts the digits of a whole number or decimal that many places to the left. Students fluently compute products of whole numbers using the standard algorithm. Underlying the algorithm are the properties of operations and the base ten system. Students continue their work on division, extending it to computation of whole number quotients with dividends up to four digits and two digit divisors. Students use the same place value understanding for adding and subtracting decimals that they used for adding and subtracting whole numbers. General methods used for computing products of whole numbers extend to products of decimals, the expectations are limited to the thousandths, placing the decimal point appropriately in products of decimals. General methods used for computing quotients of whole numbers extend to decimals with the additional focus of placing the decimal point in the quotient.