Journal+Prompts+3rd+grade

Suggested 3­rd Grade Math Journal Prompts

c = challenging, b = basic, r = relation with other topic


 * Chapter 1 || Chapter 2 || Chapter 3 || Chapter 4 || Chapter 5 || Chapter 6 ||
 * Chapter 7 || Chapter 8 || Chapter 9 || Chapter 10 || Chapter 11 || Chapter 12 ||

= Chapter 1 Top  = // 1-1 Ways to use numbers //


 * c ||  ||
 * b || How do you know when to use Ordinal Numbers? Describe the setting and give details. ||
 * r || What class might the teacher put you in order and use ordinal numbers? Why do you think she/he would do this? ||

// 1-2 Numbers in the Hundreds //


 * c || Explain why it is not okay to read the number 802 as eighty-2. ||
 * b || Explain how to write a number in expanded form. Give a step by step description. ||
 * r ||  ||

// 1-3 Place-Value Patterns //


 * c ||  ||
 * b || When you are using Base-Ten blocks what should you do when you get 10 ten sticks? Why? ||
 * r || Do you like using the Base-Ten blocks? What does it help you do? ||

// 1-4 Numbers in the Thousands //


 * c || What shape is the base-ten block that represents 1,000? Why is it this shape? How does the length of each side relate to the number it represents? ||
 * b || What place value do you think comes next after thousands? Explain your guess or why your answer makes sense. ||
 * r || What are some things that people count by thousands in real life? ||

// 1-5 Greater Numbers //


 * c ||  ||
 * b || Imagine your brother wants thirty-four thousand, one hundred fifty-three gumballs and your Mom aggress to buy thirty-four thousand, one hundred forty gumballs. Explain how you could decide which is the larger number? ||
 * r || Have you ever seen 100,000 of anything in your life? If so, what, and if not, why is it difficult to find 100,000 of something? ||

// 1-6 Read and Understand //


 * c ||  ||
 * b || If you read a word problem and are confused do you think it still makes sense to write down the information from the problem? Explain why or why not. ||
 * r || What strategies could you use to help you figure out a complicated word problem? Imagine it was a real situation, what might you do? ||

// 1-7 Comparing Numbers //


 * c ||  ||
 * b || Why is it important to line up two numbers by place value if you want to compare them? Why not just line the digits on the left? ||
 * r || What does a number line remind you of? How are they similar and different? ||

// 1-8 Ordering numbers //


 * c ||  ||
 * b || Is there ever a time when the tens digit in one number is higher than in a second number, but the second number is further right on a number line? Explain. ||
 * r || When you are putting words in alphabetical order you look at the first letter, then the second, and so on. How does this process compare to the way you order numbers? ||

// 1-9 Number patterns //


 * c ||  ||
 * b || How can you tell if a number pattern rule is addition or subtraction? Does a subtraction pattern ever end? Why or why not? ||
 * r || How is a number line different than and similar to a hundreds chart? ||

// 1-10 Rounding Numbers //


 * c || How is rounding a number to the nearest ten different than rounding to the nearest hundred? ||
 * b || Explain how to round 324 to the nearest ten. ||
 * r || When might you want to round numbers in real life? Why is addition and subtraction easier with rounded numbers? ||

// 1-11 Plan and Solve //


 * c || Explain how you choose a problem solving strategy? How do you know which will work best for you? ||
 * b || Will all the different problem solving strategies work with any problem? For example would you always be able to draw a picture of the problem? ||
 * r ||  ||

// 1-12 Counting Money //


 * c ||  ||
 * b || Suppose you have been saving money in your piggy bank since you were a little kid and now you have decided to count up what you have. In the bank are all different bills and coins. Explain how you would count this money up, step by step. ||
 * r || What does the decimal point do when we use it to write an amount of money? Is the decimal point different when it is used for money than for other numbers? ||

// 1-13 Making Change //


 * c || Explain why someone might give a cashier a 10 dollar bills and a quarter to pay for something that only costs $9.25? Why didn’t they just pay with the 10 dollar bill? ||
 * b || When you are making change do you always start with the same coin? For example, why might you want to start with a penny instead of a nickel or a nickel instead of a dime. ||
 * r ||  ||

// 1-14 Look back and Check //


 * c ||  ||
 * b || Is reading the question and doing your math work again the same as “looking back and check”? Explain ||
 * r ||  ||

= Chapter 2 Top  = // 2-1 //


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// 2-2 //


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// 2-3 //


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// 2-4 //


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// 2-5 //


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// 2-6 //


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// 2-7 //


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// 2-8 //


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// 2-9 //


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// 2-10 //


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// 2-11 //


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// 2-12 //


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// 2-13 //


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= Chapter 3 Adding and Subtracting Top   = // 3-1 Adding two-digit numbers //


 * c || Explain how you know when you must regroup? Is it possible to have a sum greater than ten in the ones place? ||
 * b || Explain how to set up a two-digit addition problem. Why is this important? ||
 * r || How does regrouping tens compare to regrouping with coins and dollar bills? ||

// 3-2 Models for Adding Three-Digit Numbers //


 * c || Explain why it makes sense for a hundreds tile to be a square 10 by 10. ||
 * b || How many times might you need to regroup when adding three-digit numbers? Why? ||
 * r ||  ||

// 3-3 Adding three-digit numbers //


 * c ||  ||
 * b || Explain the steps you take to add three-digit numbers ||
 * r || How is adding three-digit numbers the same of different than adding two-digit numbers? ||

// 3-4 Adding three or more numbers //


 * c ||  ||
 * b || What are some strategies to add up numbers in a particular place value column? Explain how you would use this strategy. ||
 * r ||  ||

// 3-5 Draw a picture //


 * c ||  ||
 * b || What details may help you to infer that drawing a picture is a good strategy to use. ||
 * r || Explain how picking a strategy to solve a problem fits in with UPSL or Story Grammar Marker. ||

// 3-6 Regrouping //


 * c ||  ||
 * b || Why do you think regrouping is called “regrouping”? What does regrouping have to do with groups? ||
 * r || Could you regroup with money? For example if you have 12 pennies why and how would you regroup them? ||

// 3-7 Subtracting two-digit numbers //


 * c || Explain step by step how you would subtract two two-digit numbers. ||
 * b || Explain how to check your work after you subtract two two-digit numbers. ||
 * r ||  ||

// 3-8 Models for subtracting three-digit numbers //


 * c ||  ||
 * b || How can you tell if you will need to regroup when you are subtracting? Might you ever have to regroup twice? ||
 * r || What is a strategy you can use if you were subtracting three-digit numbers and you got stuck? Why does this help you? ||

// 3-9 Subtracting three-digit numbers //


 * c || Do you think the rules for regrouping would be any different if you were subtracting four-digit numbers instead of three-digit numbers. ||
 * b || What are some words that help you infer that you should subtract when solving a word problem? ||
 * r ||  ||

// 3-10 Subtracting across zero //


 * c ||  ||
 * b || Explain why subtracting across zero is different than just regrouping? What looks different, what do you do differently, why is it different? ||
 * r || When might you need to subtract across zero in real life? What objects come in sets of hundreds or thousands? Why would you need to subtract? ||

// 3-11 Exact Answer or estimate //


 * c || Do you always need to round to find an estimate? What are some other ways you might estimate the sum of two numbers? ||
 * b || What about a problem lets you infer whether to estimate or find an exact answer? ||
 * r || Explain how and why you would estimate when you are shopping. ||

// 3-12 Adding and Subtracting Money //


 * c ||  ||
 * b || When you subtract amounts of money is regrouping different? Does the decimal point mean you have to do things differently? ||
 * r || Why do we use a decimal point when writing amounts of money? What does the decimal point do? ||

// 3-14 Equality and inequality //


 * c || If you know that a missing number is less than 8 what could be your missing number? How could you write a numerical expression showing that a missing number is less than 8? ||
 * b || Why do you think we talk about comparing numbers? When do we compare numbers in math, science, or reading? ||
 * r || Why do you think we can use a balance to talk about equality and inequality? Explain how this can help you figure out if an expression is true or not? ||

= Chapter 4 Time, Data, and Graphs Top   = // 4.1 Time to the half hour and quarter hour //


 * 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 || Why is 30 minutes past the hour called “half past” and 15 minutes past the hour called “quarter past”? When have you heard words like that before? ||

// 4.2 Time to the Minute //


 * c || If you just use the hour hand to read a clock, what does each line between two numbers mean? For example there are lines between the 5 and 6, what do these lines tell us? ||
 * 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 || How can using” half past” and “quarter past” help you begin to read time to the minute? ||

// 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 Using a Calendar //


 * 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? ||

// 4.5 Using Tally Charts to Organize Data //


 * 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? ||

// 4.6 Using Line Plots to Organize Data //


 * 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? ||

// 4.7 Reading pictographs and Bar Graphs //


 * 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? ||

// 4.9 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 Reading 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 || When might you want to use a line graph in your own life? ||

// 4.11 Making Pictographs //


 * c || Why is choosing the right number for your Key so important? Describe how you might decide on this number. ||
 * b || How can you tell what information a Pictograph is displaying? When you make your own, how can you make sure people can understand the information? ||
 * r || Have you ever seen a pictograph in the newspaper? What types of things might be shown? Give an example of a Key they may use. ||

// 4.12 Making 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. ||

// 4.13 Making Line Graphs //


 * c || Why do you connect the points on a line graph? Does this line give you more information? Explain. ||
 * b || What might happen if you graph your ordered pairs backwards? Give an example where it may make the graph look different. ||
 * r || Each number in an Ordered Pair tells you where to move on the grid, Does a digital clock show something like ordered pairs? ||

// 4.14 Make a Graph //


 * c || How might you make a bar graph without making a tally chart first? Explain why this may be hard to do. ||
 * b || How can you decide what type of graph to use, what type of information works well with each type of graph? ||
 * r || When might you use a graph in Science class? Explain what type of data goes with each type of graph. ||

= Chapter 5 Multiplication Concepts and Facts Top   = // 5.1 Multiplication as repeated addition //


 * 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. ||

// 5.2 Arrays and Multiplication //


 * c || Explain the Commutative property of multiplication. Use the idea of arrays to explain why this property makes sense. ||
 * b || Do all of the rows in an array have to be the same length? Why? ||
 * r || Think about a time when you might see an array in real life. Imagine an array that looks like a grid, like graph paper or the tiles of the floor. Does this relate to area at all? ||

// 5.3 Writing Multiplication Stories //


 * c || What might the problem say to tell you to use multiplication? Give an example. ||
 * b || Write your own multiplication story. Think about a character and situation that will need multiplication to find the answer. ||
 * r ||  ||

// 5.4 Make a Table //


 * c ||  ||
 * b || When might you want to use a table to help you solve a problem? What may the problem to clue you to make a table? ||
 * r || Have you ever seen or made a table in real life? Think about times that you played a game or watched a sport ||

// 5.5 Two as a Factor //


 * c || How do using multiples of 2 relate to adding on? How does a multiplication problem where 2 is a factor relate to using “doubles” as a adding strategy? ||
 * b || How would you explain the definition of “multiples” to someone? Imagine you were telling a student who was new to the class and missed the lesson. Give an example. ||
 * r || How is the word factor used in other subject areas? Think about history class or social studies. Have you ever discussed the “factors” in why a war has started or why a law was passed? ||

// 5.6 Five as a Factor //


 * c || If you wrote out the multiples of five you may see a patterns in the ones column. What is the pattern, how could this help you later, and why do you think this pattern exists? ||
 * b || Why do you think you are learning about five as a factor? Why might learning the multiples of fives be helpful later on? Do you think multiples of five are more important than multiples of four? Why? ||
 * r || How does multiplying by five relate to counting with nickels? Think of what the array might look like when five is a factor. ||

// 5.7 Ten as a Factor //


 * c || How may memorizing your multiples of ten help you with other problems? What does it mean to be a multiple of ten? ||
 * b || How can you tell if a number is a multiple of ten? Why might you want to be able to identify these numbers easily? ||
 * r || How could you show the multiples of ten using money? Think about what the array might look like. ||

// 5.8 Multiple-Step Problems //


 * c || How could you use UPSL to help you with multiple-step problems? How do you know how many steps there will be? ||
 * b || What makes a multiple-step problem different than other problems? How do you know there will be multiple steps? ||
 * r || Think of your own multiple-step problem based on something that may happen in real life. ||

// 5.9 Multiplying with 0 and 1 //


 * c || Why does the zero property of multiplication make sense? Think about what the arrays look like if zero was a factor? ||
 * b || Define the identity and zero property of multiplication in your own words. How would you explain it to your friend in another class? ||
 * r ||  ||

// 5.10 Nine as a Factor //


 * c || Look at the list of multiples of nine; compare it to the list of multiples for ten. What differences and similarities do you see? Can memorizing one list help you with the other. ||
 * b || Explain the patterns you see when looking at the tens and ones digits for the multiples of nine. ||
 * r || Which strategy will you use to help you remember your multiples of nine? Why? ||

// 5.11 Practicing Multiplication Facts //


 * c || Give your own definition for each of the properties of multiplication you have heard about so far. ||
 * b || Do you feel comfortable using the different properties of multiplication? Which one do you understand the least? Why? ||
 * r ||  ||

= Chapter 6 More Multiplication Facts Top   = // 6.1 3 as a factor //


 * c || 3 multiplied by 10 equals 30, how might memorizing this help you remember what 3 times 9 is, or 3 times 8, or 3 times 11? Think about how multiplication relates to addition. ||
 * b || Explain what a factor is. How might it help to have the factors of a number memorized? For example why might you want to remember that the possible factors of 18 are 1 and 18, 2 and 9, and 3 and 6? ||
 * r || Imagine you have three friends and you are giving each pair of shoes to borrow. How many shoes are you lending out total? ||

// 6.2 4 as a factor //


 * c || Explain how the multiples of 4 relate to the multiples of 3. Write out both lists up to 10 as a factor, do you see any pattern? ||
 * b || Imagine you have 4 packages of hotdogs, in each package there are 8 hot dogs. How many hot dogs are there total? Explain how you choose which operation to use? ||
 * r || Think or a quilt made of square pieces of fabric. The quilt is 4 squares long and 8 squares wide. How many squares are there total? How does this relate to finding the area of the quilt? ||

// 6.3 6 and 7 as a factor //


 * c || 6 and 7 are one digit apart, how many digits apart is the product of 6 X 2 from 7 X 2? How about 6 X 3 and 7 X 3? Do you notice a pattern? Why do you think this is? ||
 * b || What multiple of 6 is easiest to remember? How might this help you remember other multiples of 6? ||
 * r ||  ||

// 6.4 8 as a factor //


 * c || What makes a number “square”? What does you answer have to do with array? ||
 * b || Why do you think we use the words “factor” and “multiple”? Think about how we use those words in other subjects. Think about parts of the words that sound familiar. ||
 * r ||  ||

// 6.5 Practicing Multiplication facts //


 * c || How might using doubles help you multiply numbers? Think about how you can break up a multiplication problem into parts. ||
 * b ||  ||
 * r || How do you practice your multiplication facts in school and/or at home? Why is important? What do you find challenging about studying? ||

// 6.6 Problem solving strategy (look for a pattern) //


 * c || How can you tell if a pattern might show up in your work? What are some words or numbers or clues to tell you this? ||
 * b || Describe what it means to look for a pattern when trying to solve a problem. How might this help you? ||
 * r || Have you noticed a multiplication pattern in real life or another subject outside of math? If so explain how it was a pattern. ||

// 6.7 Using multiplication to compare //


 * c ||  ||
 * b || When might you want to use multiplication to compare two things? What might a key word be to tell you to use multiplication to compare? ||
 * r || Have you ever hear someone talk about “parts”? Sometimes the word “parts” are used to explain a recipe, for example a recipe might say; the cake is 2 parts sugar, 6 parts flour, and 1 part butter. How do you think this might relate to multiplication? ||

// 6.9 Algebra: Multiplying with three factors //


 * c || Why does order not matter when you are multiplying three factors? ||
 * b || How can you tell which pair of factors to multiply first? What kinds of numbers are easier to multiply? ||
 * r || Write a problem that would require the solver to multiply three factors, make the problem relate to sometime in real life. ||

// 6.11 Problem solving skill (choose an operation) //


 * c ||  ||
 * b || What are some words that help you know which operation to use when solving a word problem? Why is it important to ask yourself if you answer makes sense? ||
 * r || Think of an example of when you might have to use addition, subtraction, and multiplication in real life. Explain why each example requires the operation you chose. ||

= Chapter 7 Division concepts and facts Top   = // 7.1 Division as sharing //


 * 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? ||

// 7.2 Division as repeated subtraction //


 * c || Since division is related to subtraction and subtraction is the opposite of addition, explain how division is related to addition? ||
 * b || Explain how division is related to subtraction? Give an example. ||
 * r || If you are dividing eggs into pans how do you know how many groups to share between? ||

// 7.3 Writing 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. ||
 * b || What information do you need to include in a division story? ||
 * r || Why do you think it is important for you to be able to write division stories? Why is this different than just solving the number sentences? ||

// 7.5 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 ||  ||

// 7.6 Dividing with 2 and 5 //


 * c || Why do you think we began by learning to divide by 2 and 5? What makes 2 and 5 so important? ||
 * b || Dividing by two is the same as subtracting what? What types of numbers can always be divided by two? ||
 * r || When do you divide time by two? What kinds of words do we use to describe an hour divided by two, or a day divided by two? ||

// 7.7 Dividing with 3 and 4 //


 * c || How could we use what we know about dividing by 2 to help us divide by 4? ||
 * b || Does the order matter when you write a division sentence? For example is 24 divided by 3 the same as 3 divided by 24? Explain your answer. ||
 * r ||  ||

// 7.8 Dividing with 6 and 7 //


 * c || How can we use what we know about dividing by 3 to help us divide by 6? ||
 * b || What makes 7 a tough number to divide by? Do you see any patterns to help you? ||
 * r || If you divide 28 by 2 and then by 4 and then by 7 what do you notice about your answer? Why do you think this is the case? ||

// 7.9 Dividing with 8 and 9 //


 * c || How does dividing by 8 relate to dividing by 2 and 4? Does this work for dividing by 9? Why or why not? ||
 * b || Explain how you might be able to use your fingers to help your remember your 9’s division’s rules. Think about how you used your fingers to multiply by 9. ||
 * r ||  ||

// 7.10 Dividing with 0 and 1 //


 * c || Explain why 3 divided by 0 cannot be done? What makes 0 unique? ||
 * b || Explain why 8 divided by 8 equals 1? Use the word “groups” in your answer. ||
 * r || Could you divide by 0 in real life? What might this look like? ||

// 7.11 Remainders //


 * c || Is it possible for a remainder to be to big? How would you know? ||
 * b || Does a remainder form a new group? Why or why not? ||
 * r || What might a remainder look like in real life? If you had a remaining slice of pizza after you divided 5 between 4 people is this fair? ||

// 7.12 Division patterns with 10, 11, and 12 //


 * c || Explain how the word “multiple” is related to the word “factor”. ||
 * b || Is it true that any number that ends in a 0 is a multiple of 10? If a number ends in a 5 or 0 what is it a multiple of? ||
 * r ||  ||

= Chapter 8 Geometry and Measurement Top   = // 8.1 Solid figures //


 * c || What solid figure is a soda can? Why do you think it is shaped like this? ||
 * b || Explain what 2 dimensional (flat) shapes you would use to make a cube, pyramid, cone, and cylinder. ||
 * 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 Relating solids and shapes //


 * c || A pyramid and a cone look similar, but they are very different. Explain all the ways you can think of that make them different. ||
 * b || Imagine you traced a dime on a piece of paper and then cut out the shape. Now imagine you did this 100 times and then stacked up all your shapes, what solid shape would you have. Why? ||
 * r ||  ||

// 8.3 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? ||

// 8.4 Lines and line segments //


 * c || Are solid shapes made of lines or line segments? Are there “points” on a cube? What would you call them? ||
 * b || Explain the difference between a line and a line segment. Which do you think would be easier to make in real life? Why? ||
 * r || There are many examples of lines listed in the book but are these actually lines? Why or why not? ||

// 8.5 Angles //


 * c || Could you have a triangle made up of all right angles? Obtuse angles? Acute angles? Why or why not? ||
 * b || What time would look like an acute angle on an analog clock? What time would look like a right angle? Obtuse angle? ||
 * r || What type of angle is most common in the classroom? Why do you think this is? ||

// 8.6 Polygons //


 * c || What happens to the number of angles as a polygons gains more sides? Why is this the case? Could a triangle have four angles? ||
 * b || Is a circle a polygon? Why or why not? Could you make a circle on a geoboard? ||
 * r || What is true about the sides of most of the polygons you see in real life? Give some examples. ||

// 8.8 Quadrilaterals //


 * c || Is a rhombus also a prallelogram? Explain why or why not. ||
 * b || Is a square also a rectangle? Explain why or why not. ||
 * r || What does the beginning of the word “quadrilateral” remind you of? Have you heard the sound “quad” or “quar” before? What do you think this sound tells us? ||

// 8.9 Congruent figures and motion //


 * c || If you know two shapes are congruent, what does this tell you about the lengths of its sides and angles? ||
 * b || Explain how you can tell two shapes are congruent, what do you look for? ||
 * r || Do you think the Earth slides or turns around the sun? Consider why there are seasons. ||

// 8.10 Symmetry //


 * c || Is it possible for a shape to have more than one line of symmetry? How can this be? ||
 * 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? ||

// 8.11 Perimeter //


 * c || If you wanted to draw the perimeter of the school on a paper what might your scale be? Why? ||
 * b || What type of tool would you use to measure perimeter in real life? What might the units be? Feet, meter, liters, gallons, minutes, kilograms? ||
 * r || What do people use to represent perimeter in real life? Sometime people like to be able to show where the perimeter of their yard is. ||

// 8.12 Area //


 * c || If you knew the perimeter of square could you figure out the area of that square? If so how, if not, why not? ||
 * b || Explain how area relates to multiplication and arrays. ||
 * 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? ||

// 8.13 Volume //


 * 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. ||

= Chapter 9 Fractions and Measurement Top   = // 9.1 Equal parts of a whole //


 * c || If you fold a paper in half, what are you actually dividing in half? Length, area, volume, width, height? Explain. ||
 * b || If you want to make halves of a paper does it matter how you fold it? Why or why not? ||
 * r || If a shape has a line of symmetry what faction does each piece represent? ||

// 9.2 Naming fractional parts //


 * c || If you fold a paper in half over and over again what happens to the denominator of the fraction? ||
 * b || What does each part of a fraction mean? How do this relate to division? ||
 * r || On a clock, what fraction does the minute hand move every five minutes? ||

// 9.3 Equivalent Fractions //


 * c || Do you notice anything about the denominators of equivalent fractions? Try to remember what “multiples” are. ||
 * b || Explain what equivalent fractions are. ||
 * r || Think about equivalent fractions you see with money. Explain how you might show ½ equals 2/4 with change? ||

// 9.4 Comparing and Ordering Fractions //


 * c || Is it possible to have a number that is too big in the denominator? What does a large number mean? ||
 * b || What happens to the value of the fraction as the denominator gets smaller? ||
 * r || Does the word equivalent remind you of any other word? Explain what is similar about the words and their definitions. ||

// 9.5 Estimating fractional amounts //


 * c || How is estimating fractions similar to rounding numbers? ||
 * b || Explain how you would estimate a fraction in real life? ||
 * r || Imagine you are cutting a cake for 10 people why is it important to be able to estimate the size of each piece before cutting? ||

// 9.6 Fractions on the number line //


 * c || Can you put fractions with different denominators on the same number line? Explain why or why not. ||
 * b || If you wanted to put equivalent fractions on a number line would they be near each other? For example 4/8 and 2/4. ||
 * r || On a number line fractions are written at points of division, what measurement of the line is being divided? ||

// 9.7 Fractions and sets //


 * c ||  ||
 * b || Write a problem of your own that requires the solver to create sets and fractions. ||
 * r || What are some of the key words in a problem that tell you that you will need to create sets and fractions? ||

// 9.8 Finding a fractional part of a set //


 * c ||  ||
 * b || What might be the best strategy when trying to figure out a fractional part of a set? Why? ||
 * r || Take a problem from the book and rewrite it as a division problem. What did you need to change? ||

// 9.9 Adding and subtracting fractions //


 * c || Could you add or subtract fractions that had different denominators? How could you do it, or, why can’t you do it? ||
 * b || When you add fractions the denominator does not change, why? ||
 * r || How many cents are in a dollar? What might be the common denominator when adding different amounts of money in cents? ||

// 9.10 Mixed numbers //


 * c || Explain how you know when you need to create a mixed number? What is different about a mixed number than a regular fraction or whole number? ||
 * b || Explain how 5 slices of pizza can be divided equally between four people. ||
 * r ||  ||

// 9.12 Length //


 * c || How does length relate to perimeter? Does know the length of a shape maybe help you figure out its perimeter? ||
 * b || Explain how a ruler is similar to a number line. ||
 * r || Give some examples of objects you might measure in inches. Can you only measure length with inches? ||

// 9.13 Measuring to the nearest ½ and ¼ inch //


 * c || Which a more exact measurement, ½ inch or ¼ inch? Explain. ||
 * b || Explain how to use a ruler to measure length, which number do you start at? ||
 * r || If you look a ruler the lines are all different lengths, why do you think this is so? ||

// 9.14 length in Feet and Inches //


 * c || Why is it better to measure some objects in feet not inches? Is there any difference between 12 inches and 1 foot? ||
 * b || Write 6 inches as a fraction. Explain how you knew what the denominator should be. ||
 * r || Do you think most people’s height is a mixed number or a whole number? Is height the same as length? ||

// 9.15 Feet, yards, and Miles //


 * c || What is 1/3 or a yard? What about 2/3 of a yard? Explain how you figured out your answer. ||
 * b || Explain how to convert a measurement in feet to inches? Why do you use this operation and not another? Explain. ||
 * r || How many feet long do you think the school is? How many yards is that? How many miles is that? ||

= Chapter 10 Decimals and Measurement Top   = // 10.1 Tenths //


 * c || If 2/10 is the same as 0.2 what do you think the fraction would look like for 0.02? Explain. ||
 * b || Explain what a decimal point is, what does it tell us about the number? ||
 * r ||  ||

// 10.2 Hundredths //


 * c || Is 20/100 the same as 2/10? Why or why not? ||
 * b || Why do we use the names tenths and hundredths? How come these names sound similar to the other place values we’ve already heard of? ||
 * r || What do you carry around with you in your pocket that has to do with decimals? Think about when you want to buy something. ||

// 10.3 Comparing and ordering decimals //


 * c || If a number has a lot of zeros between a digit and the decimal point is the number large or small? Which is closer to zero, 0.02 or 0.002? How do you know? ||
 * b || What strategy might work best to help you compare decimals? Why is this strategy the most helpful? ||
 * r ||  ||

// 10.4 Adding and subtracting decimals //


 * c || Explain how you might be able to estimate the answer when adding decimals, what pairs of number might you look for? ||
 * b || Explain how you could add two decimals and get a whole number. ||
 * r || Give an example of when you might need to add to decimals in real life. Think about a job where people might do that every day. ||

// 10.6 Centimeters and Decimeters //


 * c || Explain what is similar about the words decimeter and decimal. Why do you think these two words sound similar? ||
 * b || Why do you think the word centimeter sounds like cents? Think about what piece of a whole each is. ||
 * r ||  ||

// 10.7 Meters and kilometers //


 * c || If a meter is 100 centimeters and a kilometer is a 1000 meters, how many centimeters is 1 kilometer? Explain how you found your answer. ||
 * b || Explain how you could measure the length of the school in meters, what tools would you use, and why might it be difficult? ||
 * r || If you were a carpenter which unit do you think would be more useful to you, a meter or a kilometer? Why? ||

= Chapter 11 Multiplying and Dividing Greater Numbers Top   = // 11.1 Mental Math: Multiplication Patterns //


 * c || Explain how a number can have no tens or ones but have 5 hundreds. ||
 * b || If a number has no tens and is multiplied by a number with no tens will the product have any tens? Why or why not? ||
 * r ||  ||

// 11.2 Estimating products //


 * c || What does rounding and estimating have to do with the patterns we explored earlier? ||
 * b || Why is it usually easier to find the product of a rounded number than the original number? ||
 * r || Give an example of a time you would not want to overestimate a product in real life. Why would you want to avoid an overestimation? ||

// 11.3 Mental Math: Division patterns //

10 x 10 can help you divide larger numbers. ||
 * c || Explain how finding division patterns are similar to finding multiplication patterns. ||
 * b || Explain why knowing your basic division and multiplication facts up to
 * r ||  ||

// 11.4 Estimating quotients //


 * c || Are the steps for estimating a quotient the same as estimating a product? Explain. ||
 * b || To estimate a quotient is it best to round to the closest ten all the time? Why or why not? ||
 * r || When might estimating a quotient but okay even though it is not exact? Explain. ||

// 11.5 Multiplication and arrays //


 * c ||  ||
 * b || Does it matter if you multiply the tens first and then the ones? Explain. ||
 * r || Why do you think the authors of the book put a picture of a traffic jam on page 626? What does this have to do with arrays? ||

// 11.6 Breaking numbers apart to multiply //


 * c || When multiplying a two digit number by a one digit number why can you multiply by the tens and the ones separately? ||
 * b || If you multiply a two digit number by a one digit number will the product always be a two digit number? Explain ||
 * r ||  ||

// 11.7 Multiplying two digit numbers //


 * c || Do you think it is easier to multiply by breaking numbers apart or by regrouping? Why? ||
 * b || Explain how breaking numbers apart is different than regrouping. ||
 * r || We use the word “regrouping” when we multiply, add, subtract, and divide, does “regrouping” always mean the same thing? ||

// 11.8 Multiplying Three-digit numbers. //


 * c || When you are regrouping while multiplying why do you regroup after you multiply the two numbers? ||
 * b || Explain when you might have to regroup when multiplying 3-digit numbers. ||
 * r ||  ||

// 11.9 Multiplying Money //


 * c || Multiplying 0.5 by 4 is the same as doing what division problem? Why? ||
 * b || After you multiply money, how can you tell if your answer is reasonable? ||
 * r || What has to be true about the groups for you to be able to multiple them? ||

// 11.12 Using objects to divide //


 * c || Explain how using objects to divide is related to using groups to multiply. ||
 * b || Explain what to do if you need to split two tens between 8 groups. What is this called? ||
 * r || Is there a time in real life when you would not be able to regroup? In other words is there a time when something cannot be divided? ||

// 11.13 Breaking Numbers Apart to Divide //


 * c || Explain when Breaking Numbers apart to divide would help you divide easier, when might it not make it easier? ||
 * b || What are the steps to breaking a number apart to divide? Is it okay to forget a step? ||
 * r || Does breaking numbers apart to divide seem similar to regrouping when you multiply or add? How so? ||

// 11.14 Dividing //


 * c || Is it possible for the larger number to be outside of the little house? If so what might your answer look like? ||
 * b || After you divide two numbers, how can you check your answer? Explain. ||
 * r || Jim thinks the dividing the tens first is strange compared to adding and subtraction, what do you think? ||

= Chapter 12 Measurement and Probability Top   =

// 12.1 Customary Units of Capacity //


 * c || How many 2 liter soda bottles do you think it would take to equal a gallon of milk? ||
 * b || Why do you think people started measuring capacity? What does it help us do? ||
 * r || At the movie theater you can get a small, medium, or large soda. Which one of these sizes do you think is closest to 1 cup? ||

// 12.2 Milliliters and Liters //


 * c ||  ||
 * b || Explain how you could remember that there are 1,000 milliliters in one liter? ||
 * r || Which would be easier to drink a gallon of water or 2 liters of water? Why? ||

// 12.4 Customary Units of Weight //


 * c || People say you are weightless in space, how is that possible? ||
 * b || Explain how you can convert a weight in ounces to a weight in pounds. ||
 * r || Is it possible for some object to have a large capacity and a small weight? Give an example? What about the other way around? ||

// 12.5 Grams and Kilograms //


 * c || People say you are weightless in space, does this also mean you are massless? Explain. ||
 * b || What is the basic unit of mass in the metric system? DO you think we would measure our own mass with this or something else? ||
 * r ||  ||

// 12.6 Temperature //


 * c || How do you think people decided what temperature should be labeled zero degrees Celsius? ||
 * b || Which change in temperature feels bigger, from 20 to 50 degrees Celsius, or from 20 to 50 degrees Fahrenheit? Why? ||
 * r || Is it possible for the temperature outside to be below zero? What do we call these types of temperatures? ||

// 12.7 Describing Chances //


 * c || Explain what an “event” is. ||
 * b || Explain the difference between an event being likely or unlikely. ||
 * r || If some things in real life are impossible, why do people sometimes say, “nothing is impossible?” ||

// 12.8 Fair and Unfair //


 * c ||  ||
 * b || Explain how the terms “Fair, unfair, likely, and unlikely” are related. What do they have to do with each other? ||
 * r || Is it possible for people to have a different idea of “fair” in real life? What about in math? ||

// 12.9 Probability //


 * c || Explain how probability relates to “likely” and “unlikely.” ||
 * b || Explain how you know which number should be the numerator and which should be the denominator when you are figuring out probability. ||
 * r || When might you want to know the probability of something happening? ||