PS166 4th and 5th Grade Math
Parent Workshop
October 30th, 2014
Math Consultant: Nicola Godwin
K-5 Math Teaching Resources LLC
In 4th Grade , instructional time focuses on three critical areas:
(1) developing understanding and fluency with multi-digit
multiplication, and developing understanding of dividing to find
quotients involving multi-digit dividends;
(2) Developing an understanding of fraction equivalence, addition and
subtraction of fractions with like denominators, and multiplication of
fractions by whole numbers,
(3) Understanding that geometric figures can be analyzed and
classified based on their properties, such as having parallel sides,
perpendicular sides, particular angle measures, and symmetry.
In 5th Grade , instructional time focuses on three critical areas:
(1) developing fluency with addition and subtraction of fractions, and
developing understanding of the multiplication of fractions and of
division of fractions in limited cases (unit fractions divided by whole
numbers and whole numbers divided by unit fractions)
(2) extending division to 2-digit divisors, integrating decimal
fractions into the place value system and developing understanding
of operations with decimals to hundredths, and developing fluency
with whole number and decimal operations;
(3) developing understanding of volume
Module 1: Place
Value, Rounding and
Algorithms for Addition
and Subtraction (25
Module 2
Multi-Digit
Multiplication and
Division (43 days)
Module 3
Unit Conversions
(7 days)
Module 5
Fraction Equivalence,
Ordering and
Operations (45 days)
Module 6
Decimal Fractions
(20 days)
Module 7
Exploring
Measurement with
Multiplication (20 days)
Module 1
Place Value and
Decimal Fractions
(20 days)
Module 2
Multi-Digit Whole
Number and Decimal
Fractions Operations
(35 days)
Module 3
Addition and
Subtraction of
Fractions (22 days)
Module 5
Addition and
Multiplication with
Volume and Area
(25 days)
Module 6
Problem Solving with
the Coordinate Plane
(40 days)
Module 4
Angle Measures and
Plane Figures
(20 days)
days)
Module 4
Multiplication and
Division of Fractions
and Decimal Fractions
(38 days)
4th Grade New York State
Common Core Mathematics Test
April 22nd – April 24th 2015
4th Grade: 2014 Testing Times
5th Grade New York State
Common Core Mathematics Test
April 22nd – April 24th 2015
5th Grade: 2014 Testing Times
4.NBT5 Multiply a whole number of up to four digits by a one-digit whole
number, and multiply two 2-digit numbers, using strategies based on place
value and the properties of operations. Illustrate and explain the calculation by
using equations, rectangular arrays, and/or area models
425 x 3 (3 x 1 digit)
Left to right showing partial products:
425
x 3 thinking:
1200 (3 x 400)
60 (3 x 20)
15 (3 x 5)
1,275
Area model:
3
400
1200
20
60
5
15
1200 + 60 + 15 = 1,275
4 x 1 Digit
1421
x
4
4000
1600
80
4
5,684
thinking:
(4 x 1000)
(4 x 400)
(4 x 20)
(4 x 1)
2 x 2 Digit
24
10
X 12 thinking:
200 (20 X10) 2
40 (20 X 2)
40 (4 X 10)
8 (4 X 2)
288
4
1000
400
4000
1600
20
80
1
4
4000 + 1600 +80 + 4 = 5,684
20
4
200
40
40
8
240
+ 48
288
Rectangular Array:
5.NBT5 Fluently multiply multi-digit whole numbers using the standard
algorithm
Digits that represent newly composed tens and hundreds are
written below the line instead of above 94. The 1 from 30x4=120
is placed correctly in the hundreds place and the digit 2 from
30x90=2700 is placed correctly in the thousands place. If these
digits had been placed above 94, they would be in incorrect places.
The 0 in the ones place of the second line is there because the
whole line of digits is produced by multiplying by 30 (not 3).
4.NBT6 Find whole-number quotients and remainders with up to
four-digit dividends and one-digit divisors, using strategies
based on place value, the properties of operations, and/or the
relationship between multiplication and division
Partial Quotients:
826 ÷ 6 =
2,725 ÷ 6 =
4.OA3 Solve multistep word problems posed with whole numbers and having
whole-number answers using the four operations, including problems in
which remainders must be interpreted. Represent these problems using
equations with a letter standing for the unknown quantity. Assess the
reasonableness of answers using mental computation and estimation
strategies including rounding.
How would you interpret the remainder? (use a whole number, fraction,
decimal, or round up to the next whole number?)
a) CDs are on sale for $4.00. Peter has $30.00 in his wallet. How many CDs can he
buy?
b) Dad shared 30 large cookies equally onto 4 plates. How many cookies were on
each plate?
c) Mr. Smith gave his four children $30.00 to share equally. How much money did
each child get?
d) There are 30 children in a 4th grade class. Each table seats 4 children. How many
tables will be needed?
5.NBT6 Find whole-number quotients of whole numbers with up to
four-digit dividends and two-digit divisors, using strategies based
on place value, the properties of operations, and/or the relationship
between multiplication and division. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or area
models.
3,683 ÷ 16 = ?
Area model:
16
200
20
+10
230
3200
320
160
3, 680
3,683 ÷ 16 = 230 R3
5.NBT7 Add, subtract, multiply, and divide decimals to hundredths, using concrete
models or drawings and strategies based on place value, properties of operations,
and/or the relationship between addition and subtraction, relate the strategy to a written
method and explain the reasoning used.
5 x 2.5 = 12.5
30 hundredths are
shaded purple so
0.2 x 1.5 = 0.30
5.NBT7 Add, subtract, multiply, and divide decimals to hundredths,
using concrete models or drawings and strategies based on place
value, properties of operations, and/or the relationship between
addition and subtraction, relate the strategy to a written method and
explain the reasoning used.
5 x 2.5 = ?
Estimate: 5 x 3 = 15
2.5
X 5 Think:
2. 5 (5 x 5 tenths=25 tenths)
10.0 (5 x 2 ones)
12.5
or
5
2
0.5
10
2.5
= 12.5
25 (write the decimal as a whole number and multiply)
x5
100
25
125 Use my estimate to place the decimal point in the product
2.5 x 5 = 12.5
5.NBT7 Add, subtract, multiply, and divide decimals to hundredths,
using concrete models or drawings and strategies based on place
value, properties of operations, and/or the relationship between
addition and subtraction, relate the strategy to a written method and
explain the reasoning used.
9.8 x 46 = ?
9
40
6
360
54
Estimate: 10 x 46 = 460
0.8
32
4.8
392
+ 58.8
450.8
9.8
X 46 Think:
360.0 (40 x 9)
32.0 (40 x 0.8)
54.0 (6 x 9)
4.8 (6 x 0.8)
450.8
or
write the decimal as a whole number
and multiply. Use my estimate
to place the decimal point in the product.
98 x 46= 4508. My estimate was 460
so the product is 450.8.
Standards for Mathematical Practice
4th Grade 2014 Released Question (1 point)
A school has 17 tables in the cafeteria. Each table seats 12 students.
What is the greatest number of students that can be seated at these
tables?
A
114
B
184
C
194
D
204
Key: D
Measured CCLS 4.NBT. 5
Commentary: This question measures 4.NBT.5 by asking the student to multiply
two 2-digit numbers using strategies based on place value and the properties of
operations. In this case, two-digit multiplication is used to solve a real-world
problem.
4th Grade 2014 Released Question (2 points)
Andres is a baker. He baked 3,240 cookies in one week. He placed the
cookies in boxes containing 9 cookies each. What was the total number of
boxes Andres used?
Show your work.
Commentary: This question measures 4.NBT.6 because it assesses a student’s
ability to find a whole number quotient with up to a four-digit dividend and a one-digit
divisor.
4th Grade 2014 Released Question (3 points)
This question measures 4.OA.3
because it assesses the student’s
ability to solve a multi-step word
problem posed with whole numbers
and having a whole-number answer
using the four operations, including
problems in which remainders must
be interpreted.
5th Grade 2014 Released Question (1 point)
Commentary: This question measures 5.NBT.6 because it assesses a student’s
ability to find a whole number quotient of a whole number with a four-digit dividend
and a two digit divisor.

Short, ongoing routine that provides students with
meaningful ongoing practice with mental computation
to develop computational fluency.
Addition Number Talk – Adding up in chunks
The largest addend is kept whole and the other addend is chunked or broken
apart to add mentally
Example:
259 + 26=?
259 + 20 = 279
279 + 6 = 285
Subtraction Number Talk – Constant difference
Adjust each number in the problem by the same amount to make numbers
that are easier to work with mentally
Example: 257 – 67 =?
+3 +3
260 – 70 = 190
More Sample Questions:
https://www.engageny.org/resource/new-york-state-common-core-sample-questions
Video Lessons:
https://learnzillion.com/resources/39146#
https://www.khanacademy.org/
More Resources for each Standard:
http://www.k-5mathteachingresources.com/4th-grade-number-activities.html
http://www.k-5mathteachingresources.com/5th-grade-number-activities.html
DO YOU HAVE ANY QUESTIONS?