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 fifth grade.
Area Model
The area model is used to show multiplication. The rectangle below has a length of 2 units and a width of 4.9
units. Each part of the rectangle can be multiplied as follows:
4
2
.9
2 x .9
= 1.8
2x4=8
2 x 4.9 = (2 x 4) + (2 x .9)
2 x 4.9 = 8 + 1.8
2 x 4.9 = 9.8
Place Value Chart
The number 273.1 is represented below. When adding numbers, ten of one unit is traded for one of the next
unit to the left. (For example, 10 tenths are traded for 1 one.) When subtracting numbers, one of one unit is
traded for 10 of the next unit to the right. (For example, 1 ten is traded for 10 ones.)
Hundreds 200
+
Tens 70
Ones +
3
+
Tenths .1
=
273.1
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