This year the Binghamton City School District is using math “modules” recommended by the New York State
Education Department. These modules are built around the Common Core Standards. Some of the models your
child will be using may not be familiar to you. Below are examples of the main models for fourth grade.
Array and Area Models
An array is an arrangement of a set of objects organized into equal groups in rows and columns. The
rectangular array is used to teach multiplication and leads to understanding area. The following what “3 x 4”
looks like as students move from 3rd to 4th grade:
3rd Grade
4th Grade
This array shows 400 x 3.
Multiplying hundreds: 4 hundreds × 3 = 12 hundreds
400 × 3 = 1200
Place Value Chart
The number 273 is represented below. When adding numbers, ten of one unit is traded for one of the next unit
to the left. (For example, ten ones are traded for one ten.) When subtracting numbers, one of one unit is traded
for 10 of the next unit to the right. (For example, one ten is traded for ten ones.)
Hundreds 200
Tens +
70
Ones +
3
=
273
Tape Diagram
The tape diagram (also called the Bar Model) is a way to represent word problems so that children can see how
the parts are related. Here is an example:
Sarah baked 125 cookies. She sold some of them. 18 were left. How many did she sell? 125 cookies
125 – 18 =
Sarah sold
Sold?
18 left
cookies.
Vertical Number Line
The vertical number line is used for rounding numbers. If students were asked to round 2,375 to the nearest
hundred, they could use the vertical number line as follows:
2,375 is between 23 hundreds (2,300) and 24 hundreds (2,400). The midway point between 2,300 and 2,400 is
2,350.
2,400
2,375
2,375 is above the midpoint.
2,375 rounds to 2,400.
2,350
2,400
2,300
We are excited that your child is experiencing this kind of math and will continue to learn about numbers in a
way that will lead to success for the rest of his or her school career.
If you have any questions about the math modules or math Common Core Standards, please contact either:
Tonia Thompson
Assistant Superintendent for
Curriculum, Instruction, and Accountability
(607) 762-8100, ext. 321
Brenda Lidestri
Director of Math, Science, and Technology
(607) 762-8100, ext. 308