Math News!
Grade 4, Module 2, Topic A
4th Grade Math
Module 2: Unit Conversions and Problem Solving with Metric
Measurement
Math Parent Letter
This document is created to give parents and students a better
understanding of the math concepts found in Eureka Math (© 2013
Common Core, Inc.) that is also posted as the Engage New York
Focus Area  Topic A: Metric Unit Conversions
Converting Units
Students review place value concepts while building fluency to
decompose or convert from larger to smaller units. They
learn 1 meter (m) is equal to 100 centimeters (cm) just as 1
hundred is equal to 100 ones. The table below continues this
thinking.
material which is taught in the classroom. Module 2 of Eureka Math
(Engage New York) covers Unit Conversions and Problem Solving
with Metric Measurement.
Focus Area  Topic A: Metric Unit Conversions
Words to Know:
Measurement – quantity as determined by comparison with a
standard unit
Convert - to express a measurement in a different unit
Distance -the length of the line segment joining two points
Students use this knowledge of unit conversion to solve
addition and subtraction problems involving mixed units.
Example Problem and Answer
Mixed Unit – refers to numbers that are paired but represent
individual entities or units. Take the number 35. Written this
way, it represents 35 ones. That is 35 of the same unit.
However, if we write 3 tens 5 ones, then we have mixed units
because the 3 and the 5 are conveying different meanings.
OBJECTIVES OF TOPIC A
 Express metric length measurements in terms of a
smaller unit; model and solve addition and subtraction
word problems involving metric length.
 Express metric mass measurements in terms of a
smaller unit; model and solve addition and subtraction
word problems involving metric mass.
 Express metric capacity measurements in terms of a
smaller unit; model and solve addition and subtraction
word problems involving metric capacity.
In this example, the units are added separately. The meters
are added together and the centimeters are added together.
Then the centimeters are converted to meters.
Can you think of another way to solve it?
Focus Area  Topic A: Metric Unit Conversions
Converting Units
Conversions between the units are recorded in a two-column
table. Recording the unit conversions in a table allows
students to see the ease of converting from a smaller unit to a
larger unit.
Module 2: Unit Conversions and Problem Solving with Metric
Measurement
Strategies for Adding and Subtracting Mixed Units
Addition and subtraction single-step problems of metric units
provide an opportunity to practice using simplifying strategies as
well as solve using the addition and subtraction algorithm. In
this next example, the student uses the simplifying strategy.
Example Problem and Answer
Jon had a cooler that had 32L 420mL of water in it. He
emptied a container with 13L 585mL of water into the
cooler. How much water is in the cooler now?
Strategies for Adding and Subtracting Mixed Units
Students will be taught several different strategies for adding
and subtracting mixed units. In the following example, the
student will use an algorithm strategy and decompose or
convert the kilograms to grams before solving.
Example Problem and Answer
Together, a squirrel and a beaver weigh 6 kg 230 g. If the
squirrel weighs 1 kg 255 g, how much does the beaver weigh?
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 4, Module 3, Topic B
4th Grade Math
Focus Area– Topic B
Module 3: Multi-Digit Multiplication and Division
Multiplication by 10, 100, and 1,000
Math Parent Letter
This document is created to give parents and students a
better understanding of the math concepts found in Eureka
Math (© 2013 Common Core, Inc.) that is also posted as the
Engage New York material which is taught in the
classroom. Module 3 of Eureka Math (Engage New York)
covers Multi-Digit Multiplication and Division. This
newsletter will discuss Module 3, Topic B.
Place Value Chart & Number Disks
B. Multiplication by 10, 100, and 1,000
Words to know
 Area Model
 Place Value Chart


Number Disk
Bundle
Helpful Hints!!!
ones x tens = tens
tens x tens = hundreds
hundreds x tens = thousands
40 x 10 = 4 tens x 1 tens
40 x 100 = 40 x 10 x 10 = 4 tens x 1 ten x 1 ten
Decompose – separate numbers into smaller numbers
40 x 20 =____
decompose 40 into 4 x 10, decompose 20 into 2 x 10
create an equation using the decomposed numbers
4 x 10 x 2 x 10 = ____
group ones and tens (4 x 2) x (10 x 10)
8 x 100 = 800
OBJECTIVE OF TOPIC B
1
Interpret and represent patterns when multiplying by 10,
100, and 1,000 in arrays and numerically.
2
Multiply multiples of 10, 100, and 1,000 by single digits,
recognizing patterns.
3
Multiply two-digit multiples of 10 by two-digit multiples
of 1- with an area model.
Use number disks to represent 143
First, draw 1 circle in the
hundreds place to show 1
hundreds. Next draw 4 circles
in the tens place to show 4 tens.
Finally, draw 3 circles in the
ones place to show 3 ones.
Use a place value chart to multiply
Start by creating number disks
to represent 1 one. (the black
circle). Place a circle around
the group of 1 ones to show
that the group will moving as a
whole. To show that 1 one is being multiplied by ten,
draw an arrow to the tens place, and re-draw the group
of 1. Because it was multiplied by 10 it is no longer 1
one, it is now 1 ten. The circles are drawn differently
in order to show which number
disks have been moved already.
Another way to look at it is
having 1 group of 10 ones. 10
ones is equal to 1 ten. On this
chart bundle the 10 ones to make 1 ten. 10 x 1 = 10.
The same concept applies when multiplying 15 x 10.
Draw 15 on the place value chart. 1 ten and 5 ones
Multiply 5 ones by ten to get 5 tens.
(ones x tens = tens) Multiply 1
ten by tens to get 1 hundred.
(tens x tens = hundreds) 15 x
10 = 1 hundred 5 tens 0 ones
or 10 x 15 = 150
Area Model
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 4, Module 3, Topic C
Focus Area– Topic C
4th Grade Math
Module 3: Multi-Digit Multiplication and Division
Math Parent Letter
This document is created to give parents and students a
better understanding of the math concepts found in Eureka
Math (© 2013 Common Core, Inc.) that is also posted as the
Engage New York material which is taught in the
classroom. Module 3 of Eureka Math (Engage New York)
covers Multi-Digit Multiplication and Division. This
newsletter will discuss Module 3, Topic C.
Topic C. Multiplicative of up to Four Digits by SingleDigit Numbers
Words to know
 Partial Products
o
o
Represent 2 x 14 with disks
Begin by drawing disks to
represent 14. Look at the
number of times 14 is
multiplied by, 2. So repeat
the pattern twice. The chart
should have 14 represented
twice on the place value chart. Now add the ones
together. 4 ones + 4 ones = 8 ones. Next add the tens
together. 1 ten + 1 ten = 2 tens. 2 tens + 8 ones = 20
+ 8 = 28.
Represent 2 x 14 with partial products

Standard Algorithm
Things to Remember!!!
o
Multiplicative of up to Four Digits by Single-Digit
Numbers
To regroup or bundle a group of 10 ones means to
represent it as 1 ten.
To regroup or bundle a group of 10 tens means to
represent it as 1 hundred
Commutative Property is when numbers can be
swapped but the answer is the same.
OBJECTIVE OF TOPIC C
1
Use place value disks to represent two-digit by one-digit
multiplication.
2
Extend the use of place value disks to represent three- and
four-digit by one-digit multiplication.
3
Multiply three- and four-digit numbers by one-digit
numbers applying standard algorithm.
4
Connect area model and partial products method to
standard algorithm.
A partial product is written
vertically. 14 x 2 = ? First multiply
the ones column. 4 ones x 2 ones =
8 ones. Next multiply the tens
column. 1 ten x 2 tens = 2 tens.
8 ones + 2 tens = 28
Represent 5 x 24 with disks
Begin by drawing disks to represent 24. Look at the
number of times 24 is multiplied by, 5. So repeat the
pattern five times. The chart should have 24
represented five times on the place value chart. Look
in the ones place to see if
bundling could be used.
Yes, there are 2 groups of
10 ones that can be changed
to 2 tens. Circle the groups,
place an arrow showing
that those groups of 10 ones will be moved to the tens
place, then draw the circles to represent 2 tens in the
tens place. Look in the tens place to see if bundling
could be used. Yes, there is 1 group of 10 tens that can
be changed to 1 hundred. Circle the group, place an
arrow showing that the group of 10 tens will be moved
to the hundreds place, then draw the circles to
represent 1 hundred in the hundreds place. Now add
the ones together. There are 0 ones in the ones place.
Add the tens together. There are 4 tens in the tens
place. Add the hundreds together, there is 1 hundred
in the hundreds place. 1 hundred + 4 tens + 0 ones =
140.
Solve and represent 3 x 951 using a partial products drawing on the place value chart.
Record the partial product when multiplying each unit.
 1 one x 3 ones = 3 ones, draw 3 disks in the ones place.
 5 tens x 3 tens = 15 tens = 1 hundred + 5 tens, draw one disk in the hundreds
place and 5 disks in the tens place.
 9 hundreds x 3 hundreds is 27 hundreds = 2 thousands + 7 hundreds, draw 2
disks in the thousands place and 7 disks in the hundreds place.
 Add up the disks in each column of the place value chart then write the total
number of each column under the chart in the appropriate column.
Solve and represent 3 x 256 in a place value chart and relate the process to solving using the standard algorithm.
First draw the number disks to represent 256. It is multiplied by 3 so draw two
more sets of 256 to show that the number is multiplied by 3. Go though the sets to
bundle 10’s as needed. Write the number at the bottom of the place value chart in
the appropriate place.
Let’s look at the place value chart and compare it to the standard algorithm. In the
ones column there were 18 ones. We regrouped (bundled) 10 ones for 1 ten that left
8 ones. That is similar to what was done in the standard algorithm. 6 x 3 = 18, put
an 8 in the ones place and put the 1 ten on top of the 5 in the tens place. This same
concept occurred in the tens place. 5 x 3 + 1 = 16. Write 6 tens in the tens
column and 1 hundred was carried to the hundreds column. This process continues until there are no more numbers to multiply.
NOTE: Both ways to solve the standard algorithm is correct.
Solve 5 x 358 using a partial product algorithm and the standard algorithm and relate the two methods.
In partial product algorithm, when multiplying the ones, the ones are written on
the first line, when multiplying the tens, the tens are written on the second line,
and so on. When using the standard algorithm, in the ones column only the ones
are written, the tens are written on top or beneath the tens column. For
example, in the standard algorithm, when multiplying 8 x 5, there are 4 tens and
0 ones. Write the 0 under the ones column and write the 4 tens on top of the
tens column. Now multiply 5 x 5. 5 x 5 = 25, but there are still 4 tens to add to
the 25 tens. So 2 hundreds + 5 tens + 4 tens = 29 tens = 2 hundreds and 9 tens.
Write the 9 in the tens column and write the 2 in the hundreds column. And
continue the process until there are no more numbers to multiply and add. Writing the numbers on top or on the bottom of the
problem is correct as long as it is in the correct column.
Word problems using a tape diagram and standard algorithms
Jonas and Cindy are making candied apples. Jonas purchased 534 grams of apples. Cindy purchased 3 times as many grams of apples.
How many grams of apples did they purchase together?
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 4, Module 3, Topic D
4th Grade Math
Module 3: Multi-Digit Multiplication and Division
Math Parent Letter
This document is created to give parents and students a
better understanding of the math concepts found in Eureka
Math (© 2013 Common Core, Inc.) that is also posted as the
Engage New York material which is taught in the
classroom. Module 3 of Eureka Math (Engage New York)
covers Multi-Digit Multiplication and Division. This
newsletter will discuss Module 3, Topic D.
Topic D. Multiplication Word Problems
Things to Remember!!!
o
Read the word problem carefully to figure out
what steps are needed to solve each problem.
Focus Area– Topic D
Multiplication Word Problems
Multi-Step Problems
The table shows the cost of party favors found in 1
party bag. Each guest receives 2 balloons, 3 lollipops,
and 1 bracelet. What is the total cost for 8 guests?
Item
1 balloon
1 lollipop
1 bracelet
Cost
24¢
12¢
34¢
One bag = $1.18
2 balloons
3 lollipops
1 bracelet
24¢ x 2 = 48¢
12¢ x 3 = 36¢
34¢ x 1 = 34¢
They paid for the party favors with a $20 bill. How much
change should they expect back?
It takes 25 more to get to 150 and 600 more to get to 750.
OBJECTIVE OF TOPIC D
1
Solve two-step word problems, including multiplicative
comparison.
2
Use multiplication, addition, and subtraction to solve
multi-step word problems.
They would receive $10.56 change.
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 4, Module 3, Topic E
4th Grade Math
Focus Area– Topic E
Module 3: Multi-Digit Multiplication and Division
Division of Tens and Ones with Successive Remainders
Math Parent Letter
This document is created to give parents and students a
better understanding of the math concepts found in Eureka
Math (© 2013 Common Core, Inc.) that is also posted as the
Engage New York material which is taught in the
classroom. Module 3 of Eureka Math (Engage New York)
covers Multi-Digit Multiplication and Division. This
newsletter will discuss Module 3, Topic E.
Modeling a Division Problem
Topic E. Division of Tens and Ones with Successive
Remainders
Words to know





dividend
divisor
quotient
remainder
array





number bond
area model
standard division
tape diagram
place value chart
There are 15 students in Science class separated into 5
groups. How many students are in each group?
Model with an Array
How many students all together? 15
How many groups of students? 5
How many per group? 3
Start by creating the 5 groups, draw
5 larger circles. Next ask yourself
“Do I have enough to give every
group one student?” Yes, you can place one student in
each group. Continue until there are no more students
to group. 15 has no remainder when divided into 5
groups. To check your work skip count by 5’s to 15.
5, 10, 15. Or 5 x 3 = 15
Things to remember!!!
Always label your work when creating an area model.
The remainder represents the amount left over after
dividing. For example 16 cannot be divided exactly by 5.
The closest you can get without going over is 5 x 3 =15
which is 1 less than 16. 16 5 = 3 r1
Place Value Disks are circles with a number written inside
of them in order to represent place value.
represents
ones place,
represents tens place and
represents
hundreds place.
OBJECTIVE OF TOPIC E
1
Solve division word problems with remainders.
2
Understand and solve division problems with a
remainder using the array and area model.
3
Understand and solve two-digit dividend division
problems with a remainder in the ones place by
using number disks.
4
Represent and solve division problems requiring
decomposing a remainder in the tens.
5
Find whole number quotients and remainders.
6
Explain remainders by using place value and
understanding and models.
7
Solve division problems without remainders using
the area model.
8
Solve division problems with remainders using
the area model.
Modeling a Division Problem with Remainders
In Lesson 14 students will represent a division problem
using an array, a number bond, and a tape diagram.
Modeling a Division Problem with Remainders
In Lesson 15 students will represent a division problem
using an area model.
There are 16 students in a Science class separated into 5 groups.
How many students are in each group?
Represent using an area model
Three important questions
How many students all together? How many groups of
students? How many per group?
Represent using an array
Start by creating the 5
groups, draw 5 larger circles.
Next ask yourself “Do I have
enough to give every group
one student?” Yes, you can
place one student in each
group. There were 16, 1
student was placed in each
group, so 16 – 5 = 11. There
are 11 students that still need
to be placed into groups.
Continue this process until
each student is placed. The 1
left is the remainder.
Represent using a number bond
The top circle is always the
total number, in this case 16.
The number on the left is
always groups that can be
made. This number will
always be the highest multiple
of the group. 15 is the largest
multiple of 5, which does not
go over the total number of students. The number on the
right is always the remainder. The amount left over after
the number is divided evenly.
Represent using a tape diagram
The tape diagram is similar to
the array, instead of circles
there are numerals. In this
tape diagram the bar is
separated into 5 sets of 3’s.
Skip count by three 5 times.
3, 6, 9, 12, 15. 15 plus the
remainder of 1. 15 + 1 = 16. That is the number of
students the Science class. This is a way that the answer can
be checked. Another way is to multiply. 5 x 3 = 15 Next
add the remainder. 15 + 1 = 16. These are great ways to
check your work.
An area model is faster to
draw and it represents the
same division problem.
The total number is 16.
That is the area of the
model. The number of
groups is 5. That is the
length or the width of the
area model. Mark off
squares 5 at a time, count 5, 10, 15. Now we have to
represent the remainder. Draw one more box to
represent the remainder of 1. The total number of
squares is 16. The quotient is 3 the remainder is 1.
In Lesson 16 students will represent a division problem
using standard division and a place value chart.
Represent using standard division
Standard division is
just dividing using
numerals. What
number can be
multiplied by 5 and is
the closest to 16? 3. 5
x 3 = 15, write that
number below the 16.
Subtract 16 – 15 = 1. 5 cannot be divided into 1 so this
is your remainder.
Represent using place value chart
Divide the bottom of the place
value chart into the number of
groups needed. For this
problem it is divided into 5
groups. Start with the largest
place value group, you have 1
ten. Can I separate 1 ten into 5
groups? No, so we decompose
the 1 ten into 10 ones. Now fair
share the 16 ones into the 5
groups. Remember to mark off
each one as you place it in a
group. There are 3 ones in each
group and 1 remaining which
has not been placed in a group.
The answer is 3 r1 or 3
remainder 1.
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 4, Module 3, Topic F
Focus Area– Topic F
4th Grade Math
Reasoning with Divisibility
Module 3: Multi-Digit Multiplication and Division
Math Parent Letter
This document is created to give parents and students a
better understanding of the math concepts found in Eureka
Math (© 2013 Common Core, Inc.) that is also posted as the
Engage New York material which is taught in the
classroom. Module 3 of Eureka Math (Engage New York)
covers Multi-Digit Multiplication and Division. This
newsletter will discuss Module 3, Topic F.
Identify Factors and Product
What are the two multiplication sentences that
represent the arrays above?
1x6= 6
and
2x3=6
Topic F. Reasoning with Divisibility
The same product is represented in both sentences.
Words to know
 Factor
 Products
 Multiple
What are the factors of 6? 1, 2, 3, 6



Composite Number
Prime Number
Associative Property
Things to remember!!!
The Commutative Property says you can swap numbers (or
change order) and still get the same answer.
1 x 6 = 6 and 6 x 1 = 6
Look at the list of factors, draw an arrow to connect the
factor pairs.
Notice that 2 and 3 are the middle factor pair. We have
checked all numbers up to 2. There are no numbers
between 2 and 3, so we have found all factors of 6.
1x5=5
Find another factor pair for 5.
OBJECTIVE OF TOPIC F
1
Find factor pairs for numbers to 100 and use
understanding of factors to define prime and composite.
2
Use division and the associative property to test for
factors and observe patterns.
3
Determine whether a whole number is a multiple of
another number.
4
Explore properties of prime and composite numbers to
100 using multiples.
5x1=5
2, 3, and 4 are not factors of 5, so 5 has only one set of
factors. Numbers that have exactly two factors, 1 and
itself are called prime numbers. Numbers that have at
least one other factor beside 1 and itself are called
composite numbers.
Factors can also be written in a table.
27
1
35
27
1
35
5
7
Use division to find factors of larger numbers.
What is a multiple?
How can one find out if 3 is a factor of 48? Divide 48 by 3.
Count by 3’s to 30.
0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
What if there is a remainder?
If there is a remainder then 3 is not
a factor of 48.
What pattern is being used when counting?
Add 3 to the number said
3 is a factor of 48 because there
are no remainders when divided.
When we skip count by a whole-number, the numbers
said are called multiples.
Use the associative property to find additional factors
How are multiples different from factors.
When listing factors, we listed them and were done,
multiples can go on forever.
Find the factors of 48.
Is 5 a factor of 48?
No, any number multiplied by 5 ends with a 0 or a 5.
Is 2 a factor of 48?
Yes, 2 is a factor of all even numbers.
Is 84 a multiple of 12?
Yes, 12 x 7 = 84 or count 12, 24, 36, 48, 60, 72, 84
Is 1 a factor of 48?
Yes, 1 is a factor of all numbers.
Using the associative
property, since 3 x 4 = 12
we also know that 84 is
also a multiple of 3 and 4.
Is 3 a factor of 48?
Yes, we divided 48 by 3 and had no remainders.
We also know that 3, 4, 8,
and 12 are also factors of 84.
Is 6 a factor of 48?
Yes, 6 x 8 = 48
4 x 6 = 4 x (2 x 3)
is the original problem
Is this number sentence true?
48 = 6 x 8 = (2 x 3) x 8
The associative property says
that when we are multiplying
all numbers together we can
multiply the numbers in any
order and still get the same
answer.
In the problem above, we can move our parentheses and
multiply 4 x 2 first then multiply the answer by 3.
4 x 2 = 8 and 8 x 3 = 24.
Use the associative property to see that 2 and 3 are both
factors of 48. The associative property means that it does
not matter how you group numbers when you multiply.
2 x 3 = 6 Move the parentheses so that 3 is associated with
the 8 instead of the 2.
3 x 8 = 24 and 24 x 2 = 48
3 x 2 = 6 Move the parentheses so that 2 is associated with
the 8 instead of the 3.
2 x 8 = 16 and 16 x 3 = 48
The commutative property states that you can swap
numbers over or change the order of the numbers and the
answer will remain the same, so 2 x 3 = 6 and 3 x 2 = 6.
We know that we can use the associative property next to
solve the problem.
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 4, Module 3, Topic G
4th Grade Math
Focus Area– Topic G
Module 3: Multi-Digit Multiplication and Division
Division of Thousands, Hundreds, Tens & Ones
Math Parent Letter
This document is created to give parents and students a
better understanding of the math concepts found in Eureka
Math (© 2013 Common Core, Inc.) that is also posted as the
Engage New York material which is taught in the
classroom. Module 3 of Eureka Math (Engage New York)
covers Multi-Digit Multiplication and Division. This
newsletter will discuss Module 3, Topic G.
Place Value Charts
and
Topic G. Division of Thousands, Hundreds, Tens, & Ones
Words to know



place value chart
standard division
tape diagram



number bond
area model
decompose
Draw 6 ones, divide it
into 3 groups. There are
2 ones in each group.
Draw 6 tens, divide it
into 3 groups. There are
2 tens in each group.
Regrouping with a place value chart
OBJECTIVE OF TOPIC G
1
2
3
4
5
6
7
8
Divide multiples of 10, 100, and 1,000 by singledigit numbers.
Represent and solve division problems with up to
a three-digit dividend numerically and with
number disks requiring decomposing a remainder
in the hundreds place.
Represent and solve three-digit dividend division
with divisors of 2, 3, 4, and 5.
Represent numerically four-digit dividend
division with divisors of 2, 3, 4, and 5,
decomposing a remainder up to three times.
Solve division problems with a zero in the
dividend or with a zero in the quotient.
Interpret division word problems as wither
number of groups unknown or group size
unknown.
Interpret and find whole number quotients and
remainders to solve one-step division word
problems with larger divisors of 6, 7, 8, and 9.
Explain the connection of the area model of
division to the long division algorithm for threeand four-digit dividends.
Notice on the place value chart in the top row on the
top line the value is 54. When dividing being with the
tens place on the place value
chart. 50 is divided into 4
groups (each row represents
one group). Place 1 ten in
each group. This leaves 1
ten that cannot be divided
evenly into 4 groups. Circle
the ten and decompose it to
10 ones, making sure to circle the ten and draw the
arrow to show that it has been moved to the ones place.
Next divide the 14 ones into 4 groups. Notice the line
drawn through the circles on the top row, this is to
help students remember if the number (circle) has been
counted already when dividing. Each group has 3 ones
and there are 2 ones remaining. 4 can be divided into
54 how many times? 1 ten and 3 ones remainder 2 ones
or 13 r2 times
The Jonesville Hotel has a total of 600 rooms. That is 3 times as
many rooms as the Donaldsville Hotel. How many rooms are
there in the Donaldsville Hotel?
Draw a tape diagram to model this problem.
The Thomasville High School is replacing the seats in the
football stadium. They purchased 750seats and 34 seats were
donated. There are 3 sections for seats and they want to place
the same number of seats in each section. How many seats
would be in each section? How many seats do they have left?
First find the total number of seats. 750 + 34 = 784
Next divide to solve the problem. Each section will have
261 seats and there will be one seat left that will not be used
in the stadium.
Look at the image above, a tape diagram is drawn. A tape
diagram uses a rectangle(s) with numbers to represent the
number in a word problem. Now that numbers are getting
bigger a rectangle is used to represent the number instead of
drawing dots or pictures. A tape diagram allows the
student to visualize the problem. The image also has a
sample of a standard division problem and a place value
chart. Students can use various tools to solve word
problems.
Students will compare standard division to a tape diagram
and find the relations between the two tools used for
solving division problems.
In one day, the donut shop made 719 chocolate donuts.
They sold all of them by the dozen. A few donuts were left
over and the baker took them home. How many donuts
did the baker take home?
There are 719 donuts sold in sets of 12. The donut
shop sold 59 boxes of donuts and the baker took 11
donuts home.
Students will also learn how to divide using number
bonds and area models.
Drawing an area model to solve
:
Draw a rectangle with a width
of 6 (This is the known side).
Six times how many hundreds
gets us as close as possible to an
area of 1200? 2 hundreds.
(200 x 6 = 1200) How many
hundreds remain? Zero. (1242
– 1200 = 42) We have 42 units
left with a width of 6. Six times
how many units gets us close
to 4 tens? 5 ones. (5 x 6 = 30)
Add 5 ones to the length. How many tens remain? 1
ten 2 ones. (42 – 30 = 12) We have 12 units remaining.
Six times how many units gets us close to 1 ten 2 ones?
2 ones. (2 x 6 = 12) How many remain? Zero. Then
length of the unknown side is 200 + 5 + 2 = 207
Create a number bond to solve
:
A number bond is similar to an area
model. Follow the same steps as the
area model. How many hundreds,
tens, etc? Recording the numbers as
the problem is being solved. Look
at the number bond that is separated
into 5 bonds. Sometimes it is easier
to divide with smaller numbers.
Not all students will decompose the
numbers in the same way, but as
long as the number bonds add up to the number they
are decomposing the answer will remain the same.
1200 + 30 + 12 = 1242 and 600 + 300 + 300 + 30 +
12 = 1242. When dividing both answers will be 207.
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 4, Module 3, Topic H
4th Grade Math
Focus Area– Topic H
Module 3: Multi-Digit Multiplication and Division
Multiplication of Two-Digit by Two-Digit Numbers
Math Parent Letter
This document is created to give parents and students a
better understanding of the math concepts found in Eureka
Math (© 2013 Common Core, Inc.) that is also posted as the
Engage New York material which is taught in the
classroom. Module 3 of Eureka Math (Engage New York)
covers Multi-Digit Multiplication and Division. This
newsletter will discuss Module 3, Topic H.
Multiply using an area model and partial product
Topic H. Multiplication of Two-Digit by Two-Digit
Numbers
Multiply using an area model standard algorithm
Students are introduced to the multiplication algorithm for
two-digit by two-digit numbers. The lessons in Topic H
provide a firm foundation for understanding the process of
the algorithm. Students will make a connection from the
area model to the partial product to the standard algorithm.
54 x 42
Multiply using a place value chart
Draw disks to show 22.
Draw arrows to show 10 times
that amount.
Draw 4 groups of 22 to
represent 4 times that amount.
Solve: 8 hundreds 8 tens
4 x (10 x 22) = 880
Draw a rectangle. Write the numbers in expanded form,
or in each place value. This will determine how to
subdivide the rectangle.
40 + 2 vertically and 54 + 4 horizontally
OBJECTIVE OF TOPIC H
1
Multiply two-digit multiples of 10 by two-digit
numbers using a place value chart.
2
Multiply two-digit multiples of 10 by two-digit
numbers using the area model.
3
Multiply two-digit by two-digit numbers using
four partial products.
Transition from four partial products to the
standard algorithm for two-digit by two-digit
multiplication.
4
Label the area model. Write the expressions that
represent the area in each of the smaller rectangles and
solve each of those equations.
Add the product of the first row together.
(2 x 4) + (2 x 50) = 100 + 8 = 108
Add the products of the second row together.
(40 x 4) + (40 x 50) = 160 + 2000 = 2,160
Next add the sum of both rows together.
108 + 2,160 = 2,268
54 x 42 = 2,268
This information was generously shared by LPSS, Lafayette, LA