th
4
Grade Math Journals
Numbers and Operations in Base Ten
• Tom wrote the number 36,648. He said that the 6 on the
left was 10 times the value of the 6 on the right. Mark said
that the 6 on the right was a tenth of the value of the 6 on
the left. Who is correct? Explain your thinking.
• Jack wrote 2,0641,460 in expanded form as (2 x 1,000,000)
+ (6 x 100,000) + (1 x 10,000) + (4 x 100) + (6 x 10). Is Jack
correct? Explain your thinking.
• Write 3 different 6 digit numbers. Show how your write
each number in standard from, word form, and expanded
form.
• If Brianna rounded a number to 60, what could that
number be?
• Alex rounds two numbers to the nearest hundred and add
them together for a sum of 500. What might those two
numbers be? Show 5 possible equations.
Numbers and Operations in Base Ten
• How many tens are there in 600? Explain your thinking.
• Which place value would you use to compare the
numbers 106,734 and 106,726. Why would you use
that number?
• Jill thinks of a number. When she rounds the number
to the nearest hundred it is 400. When she rounds it to
the nearest ten it is 380. What might that number be?
• What is the largest 7 digit number that you can make?
Write the number in standard form, word form, and
expanded form.
• Write two 3-digit numbers less than 500. Write and
solve an addition and related subtraction number story
using these numbers and solve.
Numbers and Operations in Base Ten
• How many tens are there in 8,000. Explain your
thinking and describe how you solved.
• How would you compare 965,381 and 965,450? Write
and inequality using <, >, or =. Explain how you
compared them and use place value terms in your
explanation.
• Place the following numbers on a number line: 43,128 ;
22,012 ; 417 ; 298 ; 3 ; 117,323
• Seventy million eight hundred thirty three thousand
seven hundred and twenty nine. Write this number in
both standard and expanded form. Are standard and
expanded form different or alike? Which place value
has the largest digit?
• Round 747,363 to the nearest hundred. Which number
did you change and why?
Numbers and Operations in Base Ten
• Would you rather have $588 rounded to the nearest
ten, or nearest hundred? Explain your answer.
• If your teacher has 27 students and 32 books, how
many extra books do they have? Explain how you got
your answer.
• Write the directions to explain how to solve the
following 422,412 + 213,321.
• 843 < 845. How would this be different if these
numbers were rounded to the nearest ten? How did
you figure out the answer?
• Tom subtracts a 3-digit number from a 3-digit number
and gets a correct answer of 471. What might the two
numbers be?
Numbers and Operations in Base Ten
• Count the people in your class and multiply that
number by 10. Round it to the nearest ten. What is
your answer?
• If you have read 22 pages in a 100 page book, how
many pages do you have left to read? Explain how you
found your answer.
• Round 876,543 to the nearest ten thousand. Which
number changed? Did the number get larger or
smaller? Compare the two numbers with an inequality
and place them both on a number line.
• Write the directions to explain how find the difference
between 4,223 and 2,132 and solve the problem.
• You are building a wall and you need 400 bricks. You
have used 302 so far, and you have 78 left. Do you have
enough bricks to finish?
Numbers and Operations in Base Ten
• The following multiplication problems have the same
product 9 x 24 and 24 x 9. What property of
multiplication makes that true? Find two other
multiplication equations that have this product. Explain
your strategy.
• Each classroom in a school have 23 students in it. There
are 9 classrooms in the school. How many students are
in the school?
• What is the difference between 1,000,000 and
223,423? Write the directions to explain how to solve
the problem.
• Write a multiplication and related division story
problem and solve them.
• How many groups of 6 are there in 48? Show how to
use a picture or diagram to solve this problem.
Numbers and Operations in Base Ten
• Imagine a classroom with 11 rows of 8 chairs. Draw a
picture that shows this, and solve for the total number
of chairs.
• I have 4 dozen cookies to display at the bake sale. I
want to place them in rows of 5. How many rows of 4
can I make? Write the steps for solving the problem
and solve.
• Explain how you know that 3 x 3 is less than 8 x 8
without finding the product.
• How are multiplication and division alike? How are
they different.
• Write a story problem using the numbers 48, 6, and 8.
Numbers and Operations in Base Ten
• Write a number sentence using the commutative
property of addition.
• Write a word problem for 25 x 12. Show how you
could use the distributive property to solve this
problem.
• Emily has 20 dolls and 5 shelves. How many dolls
must fit on each shelf? Use a representation.
• Three kids win a $5,000 prize! How much money
does each kid get? How did you figure this out?
• Explain how knowing 5 times 5 is 25 helps you
figure out what 25 divided by 5 is.
Numbers and Operations in Base Ten
• How many times can 4 go into 4,826? How many are
left? Write out the steps that you took.
• Eight students decide to rake leaves to make money
after school. They all raked the same amount of yard,
and would up clearing 64 yards! How many yards did
each student rake? How did you solve this problem?
• Create a number story that involves multiplying the
factors 25 and 16 and solve your problem. What
equation could you write using the inverse operation?
• Tom adds 2 three-digit numbers and gets a correct
answer of 829. What might the two numbers be? Show
three possible solutions.
Operations and Algebraic Thinking
• Lucy has 5 times as many crayons as Janet. If Lucy has 30
crayons, how many does Janet have? Write an equation
using a letter for the unknown (a variable) and solve.
• Draw an array showing 5 x 7 and draw an array showing 7
x5. Do they equal the same thing? Explain the
mathematical property that this demonstrates.
• Describe the Associative Property of Multiplication, the
Commutative Property of Multiplication, and the
Distributive Property of Multiplication.
• There are 30 students in Mrs. Galloway’s class. Each
student was asked to bring 24 pencils to class. How any
total pencils are there in the class?
• 30 is ____ times as much as 6. Describe how you would
solve.
Operations and Algebraic Thinking
• Tyler live 36 miles away from Dollywood. Timothy lives 6 miles away
from Dollywood. How many times as far from Dollywood does Tyler
live compared to Timothy?
• A magazine costs $4.00. A book costs six times as much. How much
does the book cost? Write an equation using a letter for the
unknown (a variable) and solve.
• Jack has saved three times as much money as his sister. If Jack has
saved $60.00, how much has his sister saved?
• Heather and Mike have 15 stickers to put on 3 pieces of paper. Is
this a multiplication or division problem? Explain your answer.
• A blue jacket costs $36.00. A read jacket costs $6.00. How many
times as much does the blue jacket cost compared to the red
jacket?
Operations and Algebraic Thinking
• Dan went to the store and bought 5 bags of books. Each
bag has 7 books in it. Is this a multiplication or a division
problem? Explain your answer.
• Dad buys 6 cans of paint for $19 each. How much change
will he get from $150? Estimate your answer. Then solve
and compare your answer with your estimate.
• Mr. Estes wants to split his 30 students into 5 equal groups.
Explain if this is or is not possible.
• Lisa buys 6 packets of balloons for a party. Each packet
contains 28 balloons. 150 balloons are used at the party.
How many balloons will Lisa have left? Estimate your
answers and then solve.
• Solve to find the quotient and explain how you found your
answer: 63 divided by 7.
Operations and Algebraic Thinking
• Makira bought candy to share with her 8 friends for her
birthday. The package of candy from the store has 33 pieces
of candy in it. How many pieces of candy can each friend
get? Are there any left over? If there is a remainder, what
should Makira do with the remaining candy?
• Mrs. Fulkerson wants to spilt her 31 students into 4 equal
groups. Explain if this is or is not possible.
• I have 15 pencils and four tables to divide them between.
How many pencils will each table receive?
• At a movie theater there are 154 people in 7 rows. How
many people are in each row? Explain your steps for solving
this problem.
• How are prime and composite numbers different? Explain
your answer using mathematical terms.
Operations and Algebraic Thinking
• Are there more prime numbers or composite
numbers between 1 and 50?
• Sarah said that all prime numbers are odd, but
Jack disagreed with her. Who is correct? Explain
your thinking.
• Is 28 a prime or a composite number? Explain
your answer using mathematical vocabulary.
• What are the rules for a prime number? What are
the rules for a composite number?
• Is 2,136 a prime or a composite number? How do
you know?
Operations and Algebraic Thinking
• Are there more multiples of 6 or multiples of 7
between 1 and 100? How many more?
• Which of the following are prime numbers? 2, 3,
4, 5, 6, 7, 8
How did you figure it out?
• What is a factor? What is a multiple? How are
factors and multiples different?
• I added two prime numbers together and got a
sum that is less than 15. What might the two
numbers be? Show all possible solutions.
• What are the factor for 100? How did you find
them?
Operations and Algebraic Thinking
• Which of the following are composite numbers?
28,
29, 30, 31, 32, 33 How did you figure it out?
• Choose a number less than 10. Write the multiples of that
number up to 100 in your math journal and place counters
on a 100’s chart. Describe any patterns that you notice on
the chart.
• Select two 2-digit number between 20 and 100 and list all
of the factor pairs for each number. Which number has
more factor pairs? How many more?
• ____ x 3 = ____ ~ What factor can you use in this equation
to make a product that is even and between 20 and 50?
Show all possible solutions and explain your strategy.
• Consider the following sequence: 1, 4, 7, 10, 13. Is 100 a
member of this sequence? Explain your reasoning.
Operations and Algebraic Thinking
• Sam read for 5 minutes of Monday, 10 minutes on Tuesday, and 20
minutes on Wednesday. If the pattern continues, how long would
Sam have read for, in total, by the end of the week on Saturday?
Explain your thinking.
• 4 x ___ = ___ What factor can you use to make a product that ends
in zero and is between 199 and 301? Show all possible solutions
and explain your strategy.
• A man ate 100 cookies in 5 days. Each day he ate 6 more cookies
than the day before. How many cookies did he eat each day?
Explain your thinking.
• Record a number sequence where each number is eight more than
the previous number. You need 10 numbers. Take the last number
you recorded and create a pattern where each number is six les
than the previous pattern.
• Create a number patter that follows a rule and explain your rule.
Create a shape pattern that follows a rule and explain your rule.
Numbers and Operations: Fractions
• Describe a fraction using mathematical
vocabulary and representation.
• Use two different kids of fraction models to show
2 fractions that are equivalent to ½.
• Choose two fractions with the same numerator.
Which is greater? Justify your conclusions using a
fraction model.
• Brianna says that 2/5 is the same as 4/11. Is she
correct? Explain your conclusion and use a
representation.
• Write 1/6 in three different ways. Explain how
you did it, and why all three fractions are equal.
Numbers and Operations: Fractions
• Draw 2 pictures that show the same fraction. Explain
how you represented the same fraction in different
ways.
• Explain how you would create an equivalent fraction
for 1/4.
• Model two fractions with the same denominator.
Explain how you would compare them with a fraction
model.
• Grace can have either 7/8 or 3/4 of a candy bar. Which
fraction of the candy bar should she pick to get the
most? Explain your answer and use a representation.
• How would you compare 2/4 and 5/8? Are they
equivalent or is one larger than the others? Use words
and representations to justify your conclusion.
Numbers and Operations: Fractions
• Choose two fractions with different denominators. Explain
how you would compare them. Is it easier to compare
fractions that have the same or different denominators?
Why?
• Place these fractions on a number line: 5/6, 2/3, 1/8, 1/2.
How did you figure out how to place them?
• Which is larger, 2/4 or 5/8? Explain and represent your
comparison.
• There are 2 pizzas on the table that are the same size. The
first pizza has ½ left and the second pizza has 5/12 left.
Which pizza has more left? Justify your conclusion with
words and representations.
• Matthew is trying to explain to Ben that 7/7is larger than
8/10. Is Ben correct? Explain your thinking.
Numbers and Operations: Fractions
• Addy wants to compare 2/3 and 3/4. Describe how she
can write an inequality with these fractions using <, >,
or =
• Rob fills four pitchers ¾ full of water. How many
pitchers could he have filled to the top? Write an
equation and explain your thinking.
• How many different ways can you decompose 4/8 into
a sum of fractions with the same denominator? Record
an equation and a fraction model for each
decomposition.
• Write 8/4 as a mixed number. How did you come to
your answer?
• When added together two mixed numbers equal 7.
What might the two mixed numbers be?
Numbers and Operations: Fractions
1
8
• Write 2 as an improper fraction. Explain how you made
this conversion.
1
• The difference between two mixed numbers is 5 . What
4
might the two mixed numbers be?
• Fiona said that 4/6 was a larger fraction that 3/2 because 4
is larger than 3. What is her mistake? How would you
explain it to her?
• A cake recipe needs 1/3 cup of vegetable oil, ¾ cup of
water, and ½ cup of milk. How much liquid is needed to
make the cake?
• Zach added two fractions with the same denominator and
got a sum of 7/8. What might the two fractions be?
Numbers and Operations: Fractions
5
4
8
• Tony has pounds of potatoes and 9/8 pounds of carrots.
How many pounds of vegetables does he have? Write the
directions to solve this problem and solve it.
1
2
5
• Draw a representation to write the mixed number as an
improper fraction. Explain how you created your
representation.
• Write the directions to change the improper fraction 33/7
into a mixed number.
• Fred says that 5/8 is the same as 5 x 1/8. Is he correct?
Draw a model to prove your answer.
• Show how you would used a fraction model to find 5 x 1/6.
Use the same strategy to multiply another fraction by a
whole number.
Numbers and Operations: Fractions
• Danielle drew 12 pictures at school. 1/3 of them were for her Mom.
How many pictures did she draw for her Mom. How would you
solve this problem?
• Would you rather have 7/8 or a pie or 4 x ¼ of one? Explain your
answer and use a representation.
1
8
4
• David is making lemonade. Each gallon takes pounds of lemons.
How many pounds of lemons does he need to make 3 gallons? Use
representations, equations, and words to justify your conclusion.
• Mary has 5 people in her family. If each person will eat 3/8 of a
pizza for dinner how many pizzas does she need to order? Use a
fraction model to show your thinking.
• Jeremy is having a party. He wants each guest to have 1/3 cup of
cheese dip. If there will be 7 friends at his party, how much cheese
dip does he need? Draw a representation to solve this problem and
explain how you solved it.
Numbers and Operations: Fractions
• Write a word problem for 3/8 x 6 and solve the problem.
• Mrs. Galloway runs ½ a kilometer and then stops to drink
water. If she repeats this 4 times, how many kilometers did
she run in total? Use a fraction model to show your
thinking.
• Max bought 12 apples and ate 1/3 of them. Melody bought
12 apples and ate ¼ of them. Amelia bought 12 apples and
ate ½ of them. How many apples did they each eat? Draw a
model to justify your conclusion.
• 4/10 and 40/100 have unlike denominators. Are they
equivalent fractions? How do you know?
• Find an equivalent fraction for 8/10 with a denominator of
100. Explain your answer.
Numbers and Operations: Fractions
• 7/10 = /100. Solve and explain your answer.
• Why are 2/10 and 20/100 equal?
• Jennifer said that she would rather have 30/100
of something than 4/10 since 30 is more than 4
and 100 is more than 10. Is she correct? Why or
why not?
• How would you combine 6/10 and 20/100?
Provide an explanation.
• Add 3/10, 4/10, and 2/10 together and write the
fraction with 100 as the denominator. Explain
how you did this.
Numbers and Operations: Fractions
• Jack wrote the fraction 7/100 and 0.7. Brian wrote
7/100 as 0.07. Who is correct? Justify your conclusion.
• Create a number line from 0 to 1. Change the fractions
45/100 and 8/10 to decimals and mark them on the
number line. Explain your reasoning.
• Paige told Elizabeth that the fraction 5/10 is the same
as the fraction 50/100. Elizabeth asked her to explain
but Paige could not. Help Paige by explaining how they
are the same.
• Compare 0.9 and 0.13. Explain your reasoning.
• How would you write ½ as a decimal?
Numbers and Operations: Fractions
• Draw a number line and place 4/10 and 0.9 on it.
Write about how you were able to do this.
• Explain the steps for solving 5/10 + 0.25.
• 0.45 = 0.4 + 0.05. Write this problem with
fractions and explain how you did this.
• Draw a 10 by 10 grid. Shade in the fraction 7/10.
How would you write this fraction as a decimal?
Describe how you shaded in 7/10.
• Explain how fractions and decimals are related.
Numbers and Operations: Fractions
• How could you write 0.68 in expanded form?
• Eric says that .23 is larger than .9 because 23 is larger
than 9. John disagrees. Who is correct? Justify your
conclusion.
• How much larger is .75 than .7? How do you know?
• Place the following numbers in order from least to
greatest: 4.92, 5.86, 7.23, 7.43, 5.68, 4.29. Explain how
you placed them in order.
• How many different decimals can you write using the
digits 7, 0, and 8? Order the numbers from greatest to
smallest.
Numbers and Operations: Fractions
• Scarlett at 0.3 pounds of grapes, Vivian at 0.38
pounds of grapes, and Melanie ate an amount
between Scarlett and Vivian’s. How many pounds
of grapes might Melanie have eaten? Explain your
thinking.
• Explain how 0.1 is equal to 0.10.
• Compare 6.21 and .621 using an inequality.
• What decimal is equivalent to ¾?
• Classify the following decimals as: Near to 0,
About ½, or Close to 1; 0.4, .15, 0.8, .47, 0.94.
Name 3other decimals that belong in each group.
Measurement and Data
• Would you be more likely to measure the length of a bus in liters,
meters, or kilometers? Explain your reasoning6,000 ml is equal to
___ L. Solve and write to explain how to solve this problem.
• If you were to measure how much water was in a pool, would you
use cups, pints, or gallons? Explain your answer.
• Kristin is helping her mom make macaroni and cheese. What is the
most appropriate unit of measure for her to measure the milk:
cups, pints, quarts, or gallons?
• Explain how the following units of measurement are related:
– Foot, yard, mile
– Pint, quart, gallon
• What is the length of your desk in: millimeters, centimeters,
decimeters, meters? If you find one measurement, how can you
find the others without measuring?
Measurement and Data
• It takes Jim 75 minutes to get to school every day. Write
that number in hours and minutes. How did you figure this
out?
• Tracy took 3 days to get to Chicago, Illinois. How many
hours was that?
• James took 150 seconds to go to his friend’s house. How
many minutes and seconds is that? Write the steps to solve
this problem.
• What is the most appropriate unit to measure the length of
a football field? Explain why you chose this unit
• What is the most appropriate unit of measure to find out
the width of the Smart Board? Explain your answer using
mathematical terms.
Measurement and Data
• Which is larger, 1 gallon, or 4 pints? Explain how you figured
this out.
• Sam’s dog weighs 8 pounds. Victoria’s dog weighs 125 ounces.
Whose dog is heavier? Explain your thinking.
• There are 11 players on a football team. If each football player
weighed 250 pounds, how many pounds would the whole
team weigh? Explain how you figured out your answer.
• Brad says the best unit of measure to weigh his dog is ounces.
Is he correct? Explain your answer using mathematical terms.
• Heather poured 2 pints of soda, Joe poured 4 cups, and Grace
poured 1 quart. Who poured the most soda? How do you
know?
Measurement and Data
• You are creating a 3 ½ yard Lego model train. The Lego pieces come
in 6” lengths. How many Lego pieces do you need to create the 3 ½
yard train? Use an addition and a multiplication equation, along
with a diagram to show your solution.
• Rachel, Kim, and Lori each measure the length of a rope. Rachel
says the rope is 15 feet long. Kim says it’s 180 inches long. Lori says
that it is 5 yards long. Do all of the girls agree? Explain and justify
your conclusion.
• Jerry, Barry, and Harry went fishing and they each caught a giant
fish. Jerry’s fish is 62 inches long. Barry’s fish is 7 feet long. Harry’s
fish is 2 yards long. Who caught the longest fish?
• Write the steps to find the area and perimeter of a rectangle that is
10 cm long and 6 centimeters wide. Find the perimeter and the
area.
• The 3 sides of a triangle are 4 inches, 5 inches, and 7 inches. Find
the perimeter and the area of the triangle.
Measurement and Data
• You and your dad are building a tree fort. The floor will
be 40 square feet. One side is 8 feet long. How long is
the other side? Solve and explain your answer.
• An truck can hold 1200 pounds. About how many
bricks could the truck hold at one time?
• Jerry wants to know how many square feet his room is.
Write directions that would explain to Jerry how to find
the square feet of his room.
• How is area different from perimeter?
• Which has a great area? A 100 yards × 53 yards football
field, or a 90 feet × 30 feet basketball court? Solve the
problem and explain how you solved it.
Measurement and Data
• The area of a rectangle is 36 square inches. What might the
width and length be? Which possibility gives the smallest
perimeter?
• Tara is designing a run for her ferret. The run must be
rectangular with whole number dimensions. If she wants to
enclose 48 square feet how many options does she have?
• Draw 3 different shapes with the same area. Compare their
perimeter.
• Write the steps to find the area and perimeter of a 10cm by
6 cm rectangle.
• Write the steps to find the area and perimeter of a triangle
with the sides measuring 4 in, 5 in, and 7 in.
Measurement and Data
• Draw and label the three types of angles.
• A circle has 360 degrees. A half circle has 180 degrees.
How many degrees are in a quarter circle? Draw and
explain your answer.
• What is the difference between a line, a line segment,
and a ray?
• You and your friend are going to race up a hill. Would
you rather run up a hill with a 45 degree angle or a 25
degree angle. Use mathematical terms to explain your
answer.
• What angle would you have to add to a 50 degree
angle to create a straight line?
Measurement and Data
• If you know that two angles together equal 90 degrees
and one of the angles is 30 degrees, how can you
determine the other angle without measuring?
• Explain how an obtuse angle is different from a right
angle. Use mathematical terms.
• Look around the room. Find examples of acute, obtuse,
and right angles.
• Draw the three different types of angles and measure
them with a protractor.
• What angle would you need to add to a 50 degree
angle to equal 18 degrees?
Geometry
• Draw a 7-sided object. What is the name for this
shape?
• Find a cylinder in our classroom. Describe what
the object is and how you know it is a cylinder.
• What is a parallelogram? How would you know if
you saw one in our classroom?
• Describe the properties of a square.
• How are rectangles and squares similar? How are
they different? Be specific and use geometric
terms.
Geometry
• When students line up with their classmates, is this a
line, line segment, or ray? Does this change as the class
starts walking somewhere?
• How many different shapes can you draw and name
that have at least one set of parallel sides?
• Draw a pair of perpendicular line segments. Describe
how you know they are perpendicular and line
segments.
• Select 8 different polygons and sort them in two
different ways. Describe your sorting criteria.
• Draw a quadrilateral that has two pairs of parallel sides
and exactly four right angles. What shape did you
draw?
Geometry
• Marshall drew a right triangle and marked the right
angle. What might the measures of the second and
third angles be?
• Create a rhombus. Explain how you know it is a
rhombus.
• What is the name of a six sided polygon? Draw and
describe how you figured out its name.
• What is a line of symmetry? Describe it using
geometric terms.
• How could you find the lines of symmetry for an object
if you could not draw or fold the object? Explain your
thinking
Geometry
• Draw a shape that has more than one line of symmetry.
• Can a figure have more than one line of symmetry?
Explain your answer using geometric terms and
examples.
• Do all objects have a line of symmetry? Explain your
answer.
• Create a shape that has no lines of symmetry. Explain
how you created it.
• How are rectangles and squares similar? How are they
different? Be specific and use geometric terms.