Mass.gov
Massachusetts Department of Elementary and Secondary Education
Go to Selected Program Area
Massachusetts State Seal
News School/District Profiles School/District Administration Educator Services Assessment/Accountability Family & Community  
 Become an Educator  Licensure  >  Career Advancement  Teaching/Learning  Preparing Educators  
>
>
>
>
>
>
>

Archived Information

Mathematics Curriculum Framework - November 2000

Learning Standards by Strand

Number Sense and Operations
for Grades 3-4

cross symbol
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
solid circle symbol
Understand meanings of operations and how they relate to one another
solid triangle symbol
Compute fluently and make reasonable estimates

Learning Standards

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:

4.N.1
Exhibit an understanding of the base ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; demonstrating an understanding of the values of the digits; and comparing and ordering the numbers. cross symbol
4.N.2
Represent, order, and compare large numbers (to at least 100,000) using various forms, including expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3. cross symbol
4.N.3
Demonstrate an understanding of fractions as parts of unit wholes, as parts of a collection, and as locations on the number line. cross symbol
4.N.4
Select, use, and explain models to relate common fractions and mixed numbers (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12, and 1-1/2), find equivalent fractions, mixed numbers, and decimals, and order fractions. cross symbol
4.N.5
Identify and generate equivalent forms of common decimals and fractions less than one whole (halves, quarters, fifths, and tenths). cross symbol
4.N.6
Exhibit an understanding of the base ten number system by reading, naming, and writing decimals between 0 and 1 up to the hundredths. cross symbol
4.N.7
Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the numbers in those classes. Use these in the solution of problems. cross symbol
4.N.8
Select, use, and explain various meanings and models of multiplication and division of whole numbers. Understand and use the inverse relationship between the two operations. solid circle symbol
4.N.9
Select, use, and explain the commutative, associative, and identity properties of operations on whole numbers in problem situations, e.g., 37 x 46 = 46 x 37, (5 x 7) x 2 = 5 x (7 x 2). solid circle symbol
4.N.10
Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money. solid circle symbol
4.N.11
Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related problems, e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500. solid triangle symbol
4.N.12
*Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently. solid triangle symbol
4.N.13
Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and efficiently. Interpret any remainders. solid triangle symbol
4.N.14
Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up to five-digit numbers), and multiplication (up to three digits by two digits). solid triangle symbol
4.N.15
Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for division of up to a three-digit whole number with a single-digit divisor (with or without remainders). solid triangle symbol
4.N.16
Round whole numbers through 100,000 to the nearest 10, 100, 1000, 10,000, and 100,000. solid triangle symbol
4.N.17
Select and use a variety of strategies (e.g., front-end, rounding, and regrouping) to estimate quantities, measures, and the results of whole-number computations up to three-digit whole numbers and amounts of money to $1000, and to judge the reasonableness of the answer. solid triangle symbol
4.N.18
Use concrete objects and visual models to add and subtract common fractions. solid triangle symbol

* Although this standard is appropriate as stated for this grade span, the state assessment program as the 3-4 grade span will test multiplication of only up to two digits by two digits at the present time.

 

Exploratory Concepts and Skills

  • Extend multiplication and division to larger-digit numbers.
  • Use models to explore multiplication and division with fractions (to twelfths) and decimals.
  • Investigate number theory concepts, e.g., prime and composite numbers.
  • Investigate the concept of ratio, e.g., the number of students to the number of teachers.
  • Use concrete objects and visual models to add and subtract common decimals.
  • Explore numbers less than zero by extending the number line and by using familiar applications such as temperature.
  • Use concrete objects and visual models to add and subtract common decimals.
  • Investigate the distributive property of multiplication over addition for single-digit multipliers, e.g., 7 x 15 is equivalent to 7 x (10 + 5) is equivalent to 7 x 10 + 7 x 5.

 

< Previous Page
Number Sense and Operations
Learning Standards for Grades 1-2
Next Page >
Number Sense and Operations
Learning Standards for Grades 5-6



Last Updated: November 1, 2000
E-mail this page| Print View| Print Pdf  
Massachusetts Department of Elementary and Secondary Education Search · Site Index · Policies · Site Info · Contact ESE