Journal+Prompts+4th+grade

 Suggested 4th Grade Math Journal Prompts c = challenging, b = basic, r = relation with other topic

Click on the chapter you are on: Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9  Chapter 3 Multiplication and Division Concepts and Facts // 3-1 Meanings for Multiplication //


 * c || What does the word factor mean? Why do you think “factor” was chosen to identify these types of numbers? Think of how the word “factor” might be used in other subjects. ||
 * b || Explain how multiplication is like adding on many times. ||
 * r || When might you want to multiply in real life? Think of a time when you have a lot of equal groups together. ||

3-2 Patterns in multiplying by 0, 1, 2, 5, and 9


 * c ||  ||
 * b || Why do you think it might be important to notice multiplication patterns on a hundreds chart ||
 * r || Do you think there could be fact families for multiplication and division like there are for addition and subtraction? Explain why or why not. ||

3-3 Using known fact to find unknown facts


 * c || Explain how the “distributive property” breaks apart facts to find the product. ||
 * b || What numbers do you think you might want to break up when multiplying, why? ||
 * r ||  ||

3-4 Multiplying by 10, 11, and 12


 * c ||  ||
 * b || Explain how memorizing the multiples of ten might help you find the multiples of eleven. ||
 * r || Explain when you might need to multiply by ten or twelve (think about money, coins, feet, inches, etc.) ||

3-5 Make a table


 * c ||  ||
 * b || How can you tell making a table might help you solve a problem? What type of information might exist in the problem that may help you infer to make a table? ||
 * r || When do you think teacher, builders, and scientists make tables? Why, how does it help them? ||

3-6 Meanings for division


 * c || Is it possible to divide one thing into parts? What might you call these parts? ||
 * b || Explain what division has to do with sharing? ||
 * r || Imagine you were making dinner for your family, what might you need to share equally between everyone at the table? Why? ||

3-7 Relating multiplication and division


 * c || Why are multiplication and division related? If you multiply by a number, how do you change the product back to the original number? ||
 * b || Explain how you could use your 10 by 10 multiplication chart to help you solve division problems. ||
 * r ||  ||

3-8 Division facts


 * c ||  ||
 * b || Why is it important to say a division problem in the correct order? In other words why is saying “6 divided by 12” different than saying “12 divided by 6?” ||
 * r || Explain how knowing the multiples of numbers under ten might help you divide? Remember what factors are. ||

3-9 Special quotients


 * c || Explain why a number can’t be divided by 0? ||
 * b || Explain why zero divided by anything is zero? ||
 * r || Could you divide by 0 in real life? What might this look like? ||

3-10 Multiplication and division stories


 * c || What would happen if you had more groups than objects to divide? Like, for example if you needed to divide 4 slices of pizza between 8 people.v ||
 * b || What information is necessary for a division story? Why? ||
 * r || What kind of multiplication stories do you think your teacher encounters every day? ||

3-11 Multiple-step problems


 * c ||  ||
 * b || What is a “hidden question?” How do you identify a hidden question? ||
 * r || Usually you underline the important information and circle the question when doing work problems, what else might you want to do before you start to solve? Why? ||

3-12 Writing and evaluating expressions


 * c || Should you treat a variable different than other numbers? Why or why not? ||
 * b || Define the word “variable” in math. Why do you think this word is used? ||
 * r ||  ||

3-13 Find a rule


 * c || Write a problem that would require the solver to find a rule. ||
 * b || What strategy seems to go with finding a rule? Why ||
 * r || How is an in/out table different than a pattern? How are the “rules” different? ||

3-14 Solving multiplication and division equations


 * c || How can you prove your answer is correct when dividing? What if someone doesn’t believe that 18 divided by 9 is 2? ||
 * b || What is necessary when explaining your work? ||

 Chapter 4 Time, Data, and Graphs

4-1 Telling time


 * c || How could you use just the hour hand to tell about what time it is? ||
 * b || Why does the hour hand move slower than the minute hand on a clock? ||
 * r || Explain how you could use the sun to tell the time? ||

4-2 Units of time


 * c ||  ||
 * b || Using counting by fives can help you start to read the clock, but why use fives, why not count by threes or tens? ||
 * r || Explain how you can use multiplication to help you change between units of time. For example how could you multiply to figure out how many months are in 5 years? ||

4-3 Elapsed time


 * c || Explain some ways that calculating elapsed time would be different if there were 100 minutes in each hour, and 20 hours in a day? ||
 * b || When adding up elapsed time, should you start with the hours or minutes first? Why? ||
 * r || Subtracting times can sometimes help you calculate elapsed time, give some ways this type of subtraction is different or similar to subtraction you have done earlier. ||

4-4 Writing to Compare


 * c ||  ||
 * b || How can you tell if you’ve written a good comparison? How could this be graded? ||
 * r ||  ||

4-5 Calendars


 * c || Explain the relationships between weeks, months, years, decades, and centuries. For example, if someone has been alive for many decades what does this tell you about their age in weeks or centuries? ||
 * b || What is the average number of weeks in a month? Why is there sometimes more or less? ||
 * r || Some cultures used clocks that moved only once per day and had a line for each day of the year. How many lines would there be on that clock? Why? ||

4-6 Pictographs


 * c || Why are the labels so important for a Pictograph or Bar Graph? Remember what all the different labels are, including the key. ||
 * b || Compare and contrast Pictographs and Bar Graphs. ||
 * r || Why do Pictographs always have keys while Line Plots do not? ||

4-7 Line plots


 * c || How is a number line different than a Line Plot? How are they related? ||
 * b || How is a large “range” different from a small “range”, what does this tell you about your data? ||
 * r || When might you want to use a Line Plot to show your data? What kind of question might you have asked? ||

4-8 Bar graphs


 * c || How should you decide on a scale for a bar graph, does it always make sense to count by ones? ||
 * b || How can you tell how many bars you will have on your graph? What does this tell you about the space your graph will take up on the page? ||
 * r || Compare a Bar Graph to Line Plot. ||

4-9 Graphing ordered pairs


 * c || Why are there two numbers in an Ordered Pair? Why isn’t there three or four numbers? If there were 3, what would that mean? ||
 * b || Why is the order important for Ordered Pairs? What does each number tell you about the point on the graph? ||
 * r || If you look at a street map, usually it is divided by lines to form a grid. Why do you think maps are drawn this way, and how does this relate to Ordered Pairs? ||

4-10 Line graphs


 * c || Explain how you could look at a list of Ordered Pairs and create a Line Graph. ||
 * b || What might a line graph of shoe size compared to age look like for a person’s life? Would it start small and get big or big and then small? Would the lines connecting the points be steep or flat? ||
 * r || Why do we connect the points of a line graph with lines? Think about the space between points. ||

4-11 Make a graph (problem solving strategy)


 * c || How can you decide which type of graph to make when solving a problem? ||
 * b || Explain how you know when to make a graph to help you solve a problem? What information is given or asked for? ||
 * r ||  ||

4-12 Median, Mode, and Range


 * c || Why is it possible for there to be two modes? Give an example. ||
 * b || Explain, step by step, how to find the median for a given set of data. ||
 * r ||  ||

4-13 Data from surveys

 Chapter 5 Multiplying by One-Digit Numbers
 * c || What kinds of questions may not allow you to use a tally chart for your data? Why? ||
 * b || If you are going to use a tally chart, why should you allow on certain answers, and why should ask your question the same way every time? ||
 * r || If you were to survey the school about their favorite season, how many tallies do you think you would have for each answer? Think first about how many students there are in the school? ||

5.1 Multiplying by Multiples of 10, 100, or 1,000


 * c || How could remembering multiples of 10, 100, and 1,000 help you estimate other problems, like 4 x 505? ||
 * b || Why does a problem like 4 x 500 give an answer with more than two zeros? Explain. ||
 * r || When might you have to solve a problem using multiples? How about at the supermarket, bank, or soccer practice? ||

5.2 Estimating Products
 * c || When estimating products why is it possible for people to have different answers? How can we know which is correct? ||
 * b || How is the use of compatible numbers different than rounding? ||
 * r || How does the use of compatible numbers relate to multiplying by multiples? ||

5.3 Mental Math


 * c || Would the break-apart method or compatible numbers method work for other operations. Such as division, adding, subtracting, etc.? ||
 * b || Explain how and why we can break apart a number to multiply. ||
 * r || Which method of mental math do you think you may use in real life some time? Why? ||

5.4 Using Arrays to Multiply


 * c || After you multiply each part of the array why do the parts need to be added together? What does each part tell you? ||
 * b || What do you do if you have more than 10 ones after you multiply? Why? ||
 * r || How does the use of arrays relate to the break-apart method from last chapter? ||

5.5 Multiplying Two-Digit and One-Digit Numbers


 * c || How many times might you need to regroup if a 3-digit number was being multiplied? Why? ||
 * b || Why is regrouping sometimes necessary when multiplying? ||
 * r || How is regrouping in multiplication similar and/or different than in adding? ||

5.6 Multiplying Three-digit and one-digit numbers


 * c || How is this method related to the breaking apart method you previously used? ||
 * b || How can we tell if an answer is reasonable? Why is this important? ||
 * r || How might you use multiplication of 3-digit numbers in the future? What about when you have a job and earn money? ||

5.7 Try, Check, and Revise
 * c || How would you know to add or multiply to find the answer to a word problem? ||
 * b || What does it mean to you to “Try, check, and revise”? ||
 * r || Could you use “Try, check, and revise” for any math problem? Why or why not? ||

5.8 Choose a Computation Method


 * c || Explain how you can tell if a problem will require more than one regrouping step? ||
 * b || Describe how you know when to use each method? What do the problems look like? ||
 * r || What part of “Try, check, and revise” would a calculator help with? Why? ||

5.9 Multiplying money
 * c || How much do you think it would cost for your teacher to take the whole class out to dinner? How much does a meal usually cost? Explain your answer. ||
 * b || How do you know when to regroup to the ones place past the decimal point? What does this mean in terms of money? ||
 * r || When you are finished shopping and getting rung up, why would you want the cashier to remember to add a decimal point to your bill. ||

5.10 Multiplying Three Factors


 * c || Would the associative property stay true is four factors were multiplied? Why or why not? ||
 * b || Explain both the commutative and associative properties for multiplication. ||
 * r || Would the commutative property work for adding, subtraction, or division? Why or why not? ||

5.11 Choose an Operation

 Chapter 6 Multiplying by two-digit numbers
 * c || What makes problems such as these so challenging for you? Try to explain your own understanding of how you know what operation to use. ||
 * b || What are some of the key words that tell you which operation to use? How do they do this? ||
 * r || How might “Try, Check, Revise” help you choose the right operation? ||

6-1 Multiplying Multiples of Ten


 * c || Explain why when you multiply by a multiple of ten you simply add on the number of zeros in the factors to the product. ||
 * b ||  ||
 * r || How do rounding and the rules for multiplying multiples of ten relate? Why might you use them together. ||

6-2 Estimating Products


 * c || Which method of estimation, rounding or compatible numbers, would give you a closer estimate to the actual product? Why? ||
 * b || How do you know whether to use compatible numbers or rounding to estimate? What types of numbers works best for each method? ||
 * r || Describe what 5 X 100 would look like if you represented it with base-ten blocks. ||

6-3 Using Arrays to Multiply


 * c || How does an array represent multiplication? Is something being measured? ||
 * b || Explain the steps for drawing an array on graph paper to show and solve a multiplication problem. ||
 * r ||  ||

6-4 Make an organized list


 * c || How is an organized list different than a table? When might you want to use a list instead of a table, or a table instead of a list? ||
 * b || Why does a list have to be organized? How does this help you solve problems? How can you tell if it is organized or not? ||
 * r ||  ||

6-5 Multiplying two-digit numbers


 * c || What is a partial product? Why do you think we call it a partial product? ||
 * b || Explain each step of multiplying two digit numbers. Remember to include why you make certain choices. ||
 * r || How do the partial products relate to the array you draw when multiplying two-digit numbers? What parts of the array go with what parts of your written work? ||

6-6 Multiplying greater numbers


 * c ||  ||
 * b || Explain each step of multiplying a three-digit number by a two-digit number. Remember to include any choices you make and why and how you made your decision. ||
 * r || Do you think the rules for multiplying greater numbers are any different than the rules for multiplying two-digit numbers? What is different and what is the same? ||

6-8 Multiplying Money


 * c || Is there ever a time that you multiply two amounts of money? What would this situation look like in real life? ||
 * b || How do you deal with the decimal point in the money? Is it any different than multiplying without a decimal point? ||
 * r || What does the decimal point tell you about the amount of money you have? How come we need to write it at all? ||

6-9 Writing to Explain


 * c ||  ||
 * b || What should you include in your written explanation? ||
 * r || Why do think teachers ask you to write an explanation? Do you think it helps you understand math better? ||

 == Chapter 7 Dividing ==

7.1 Using Patterns to Divide Mentally


 * c ||  ||
 * b || Explain the rule that helps you divide a large number with many zeros by a single digit number. ||
 * r || How is dividing a large number with many zeros by a single digit number similar to multiplying a single digit number by a large number with many zeros. ||

7.2 Estimating Quotients


 * c ||  ||
 * b || Which method seems to work best for you to estimate a quotient; Compatible numbers or rounding? Why do you like this method? ||
 * r || How does multiplication help you identify compatible numbers? ||

7.3 Dividing with remainders


 * c || Why can’t your remainder be larger than the divisor? What would happen if ended up with a remainder larger than the divisor? ||
 * b || What is a remainder? What is an example of a remainder in real life? ||
 * r || Explain how you would make an array to show 22 divided by 4. What would the array look like? ||

7.4 Two-digit Quotients


 * c || After you divide and find your quotient, how can you check to see if your answer is correct? ||
 * b || Does it matter where you write your quotient when dividing two digit numbers using the “house?” Do any of the digits need to be lined up? ||
 * r ||  ||

7.5 Dividing two-digit numbers


 * c || Is it possible to get a quotient that is larger than the divisor? Explain why or why not. ||
 * b || Explain the step by step directions for multiplying a two-digit number by a one-digit number. ||
 * r || What is different about the order of division than subtraction and addition of 2-digit numbers? Think about what place value you look at first. ||

7.6 Interpreting Remainders


 * c ||  ||
 * b || Can a remainder be too large? How can you tell if a remainder is too large? How can you fix this issue? ||
 * r || What are some real life examples of division problems with remainders? Explain what the remainder is and if it would cause a problem in real life. For example a remaining person left after people are divided between vans would need a ride somehow. ||

7.7 Dividing three-digit numbers


 * c || How can estimating help you solve the first step of a three-digit by one-digit division problem? How can you tell if your estimate was a good one? ||
 * b || After the first subtraction you do when dividing, what do you need to compare? Explain why. ||
 * r || How is dividing three-digit numbers by one-digit numbers similar to dividing two-digit numbers by one-digit numbers? Explain. ||

7.8 Zeros in the quotient


 * c ||  ||
 * b || How can you tell that you will end up with a zero in the quotient? How can this help you finish the problem quicker? ||
 * r || Is 22 R3 a reasonable quotient for 560 divided by 5? Why or why not? ||

7.9 Dividing money amounts


 * c || 1 dollar equals 100 cents, if 1 dollar equaled 80 cents could we still use the decimal point to show dollars and cents? In other words, could we write 3 dollars and 40 cents as $3.40 if a dollar was worth 80 cents? ||
 * b || What does the decimal point tell us about the amount of money you have? ||
 * r || If you end up with a remainder when dividing money, what does the remainder represent in real life? ||

7.11 Divisibility rules


 * c ||  ||
 * b ||  ||
 * r || Which divisibility rules do you think are the most important to memorize? Why? ||

7.12 Finding Averages


 * c || Is it possible for the mean of a group of numbers to be same as the numbers in the group? How is this possible? ||
 * b || Explain the steps that you take to find the mean of a group of numbers. ||
 * r || Which type of average (mean, median, or mode) is the most useful for test scores? Why? ||

7.13 Dividing by Multiples of 10


 * c ||  ||
 * b || Explain the steps for dividing large numbers that are multiples of ten by other numbers that are multiples of ten. ||
 * r || How is dividing by multiples of 10 similar to multiplying by multiples of ten? ||

7.14 Dividing with two-digit divisors

 Chapter 8 Geometry and Measurement
 * c || Which method of estimation would you use to divide by a two-digit number, rounding or compatible numbers? Why? ||
 * b || Explain how the remainder can tell you if your estimate was too small? What does this mean in terms of groups? ||
 * r || How can you tell if your estimate is too large? What should you do if this happens? ||

8.1 Relating Solids and Plane Figures


 * c || What shape do you get when you cut a sphere with a plane? Is there different shapes you can get? ||
 * b || What is the “base” or a pyramid? What kinds of shapes can it be? How would the shape of the “base” change the number of faces the pyramid would have? ||
 * r || If you dig in sand or dirt what solid shape does you pile look like? Why do you think it is that shape and not another? Explain why it would impossible for sand to make a pile shaped like one of the other solid shapes. ||

8.2 Polygons


 * c || Is a circle a polygon? Why or why not? Could you make a circle on a geoboard? ||
 * b || What happens to the number of angles as a polygons gains more sides? Why is this the case? Could a triangle have four angles? ||
 * r || List three reasons a shape might be a square. ||

8.3 Lines, Line Segments, Rays, and Angles


 * c ||  ||
 * b || Are solid shapes made of lines or line segments? Are there “points” on a cube? What would you call them? ||
 * r || Explain the difference between a line and a line segment. Which do you think would be easier to make in real life? Why? ||

8.4 Triangles and Quadrilaterals


 * c || Can you make a triangle whose angles add up to more than 180o? Why or why not? ||
 * b || Can you make a triangle with two obtuse angles in it? Why or why not? ||
 * r ||  ||

8.5 Circles


 * c || What happens to the Radius or a circle as the diameter gets bigger? Explain. ||
 * b || Describe the steps you take to make a circle. What tools do you use and how do you use them? ||
 * r ||  ||

8.6 Congruent Figures and Motions


 * c || Explain how you can tell if two shapes are congruent. What has to be true and what can you do to prove it to be true? ||
 * b || What shape might it be difficult to tell whether it had been flipped, slid, or turned? What about this shape makes it difficult? ||
 * r || The earth revolves around the sun. What point does it revolve around? Explain. ||

8.7 Symmetry


 * c || How many lines of symmetry does a circle have? Explain. ||
 * b || Explain how you can tell if a shape is symmetric? ||
 * r || Do you think painters usually make their paintings symmetrical? Why or why not? ||

8.8 Similar figures


 * c || How can you prove that two triangles are similar? What needs to be measured? ||
 * b || If two triangles are similar what is true about their angles? What is different about the triangles? ||
 * r || Why does the book use nesting dolls as an example of similar figures? Explain ||

8.10 Perimeter


 * c || Is it possible for two different rectangles to have the same perimeter? Give an example and explain. ||
 * b || If you wanted to draw the perimeter of the school on a paper what might your scale be? Why? ||
 * r || What type of tool would you use to measure perimeter in real life? What might the units be? Feet, meter, liters, gallons, minutes, kilograms? ||

8.11 Area


 * c || Explain how you can find the area of a shape if it not drawn on a grid? For example how you find the area of a L-shaped object if you know all its dimensions? ||
 * b || What tools do people usually use to measure area? Do they use grid paper, square tiles, or something else? Explain why. ||
 * r || What units are usually used for area, ft, square ft, gallons, or miles? What would you estimate the area of your classroom to be? ||

8.12 Act it Out


 * c ||  ||
 * b || Explain why acting out a problem might help you find a solution. When/why would you not want to act it out? ||
 * r || Do you think adults “act out” problems at their jobs? If so what types of questions would they act out? If not, why? ||

8.13 Volume

 ** Chapter 9 Fraction Concepts  **
 * c || Could you use blocks to measure the volume of a cylinder? Why or why not? ||
 * b || Pretend you have to explain volume to a friend, who missed class, write what you would say. ||
 * r || What types of things do you think people measure the volume of? Think about what you eat and/or drink. ||

9.1 Parts of a Region


 * c || If you ate half of a pizza and your friend ate half of a different pizza, did you both eat the same amount of pizza? How could you tell? ||
 * b || Explain how to draw a picture of a fraction. ||
 * r || Where have you heard people use fractions before? When do people use words like half or quarter? Why do they use these words? ||

9.2 Parts of a set


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 * r ||  ||

7.1 Using Patterns to Divide Mentally


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7.1 Using Patterns to Divide Mentally


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7.1 Using Patterns to Divide Mentally


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7.1 Using Patterns to Divide Mentally


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7.1 Using Patterns to Divide Mentally


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Chapter 12 Graphing and Probability Top

Understanding probability


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Listing outcomes


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Finding Probability


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Making Predictions


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