OA413 Rounding on a Number Line Pages 80 81


 Reginald Whitehead
 3 years ago
 Views:
Transcription
1 OA413 Rounding on a Number Line Pages STANDARDS 3.NBT.A.1, 4.NBT.A.3 Goals Students will round to the closest ten, except when the number is exactly halfway between a multiple of ten. PRIOR KNOWLEDGE REQUIRED Number lines Concept of closer MATERIALS number cards, string or tape, rope, a ring or hoop (see Activity) The closest ten. Show a number line from 0 to 10 on the board: Circle the 2 and ask if the 2 is closer to the 0 or to the 10. When students answer 0, draw an arrow from the 2 to the 0 to show the distance. Repeat with several examples and then ASK: Which numbers are closer to 0? Which numbers are closer to 10? Which number is a special case? Why is it a special case? Tell students you want to round numbers to the nearest ten. ASK: Would you round 6 to 0 or to 10? (10) Why? (because it is closer to 10 than to 0) Exercises: a) 3 rounded to the nearest ten is. b) 2 rounded to the nearest ten is. c) 8 rounded to the nearest ten is. d) 9 rounded to the nearest ten is. Give students a minute to answer these questions, then take up the answers by having students signal rounding up to 10 with a thumbs up and signal rounding down to 0 with a thumbs down. Then draw an incorrect number line with numbers not equally spaced, so that 4 appears closer to 10 than to 0. ASK: Is 4 closer to 0 or to 10 on this number line? (closer to 10) Why? (because you drew the number line incorrectly) Explain that when mathematicians say that 4 is closer to 0 than to 10, they mean 4 is closer to 0 than to 10 on any number line where the numbers are equally spaced. The number line has to be drawn properly. For the same reason, graph paper is printed with equally spaced lines, and there is equal spacing between measurements on thermometers, measuring cups, rulers, and many other instruments. Operations and Algebraic Thinking 413 D1
2 Connection Real World Ask students whether they ve seen other number lines used to measure different things (e.g., on thermometers, measuring cups, radio stations). Ask students to identify cases where it s acceptable to round a measurement (e.g., indoor or outdoor temperature, percent of precipitation). Ask them to identify cases where it is important not to round numbers from a number line or measurement (e.g., body temperature, radio station, amount of medication). Conclude by saying that rounding on a number line or a measurement can be useful, but we should not do it in all situations. Then draw a number line from 10 to 30, with 10, 20, and 30 a different color than the other numbers Circle various numbers (not 15 or 25) and ask volunteers to draw an arrow showing which number they would round to if they had to round to the nearest ten. Repeat with a number line from 50 to 70, again writing the multiples of 10 in a different color. Then repeat with number lines from 230 to 250 or 370 to 390, etc. Ask students for a general rule to tell which ten a number is closest to. What digit should they look at? (the ones digit) How can they tell from this digit which multiple of ten a number is closest to? Then ask students to determine the closest multiple of ten given two choices instead of a number line. Example: Is 24 closer to 20 or 30? Is 276 closer to 270 or 280? ACTIVITY Write the numbers from 30 to 40 on cards. Use different colors to make the numbers 30 and 40 stand out from the rest. Attach the 11 cards to a rope using tape or by perforating the cards and attaching them with string. Make sure that the cards are equally spaced by 10 cm. Also, make sure that the entire line is centered on the rope. This is achieved most easily if the card labeled 35 is attached to the center of the rope and used as a reference for the placement of the rest of the cards. The ends of the rope will be longer than is indicated in the diagram below Take a ring or hoop and pull the rope through it. A hoop used for crossstitching would be a good size D2 Teacher s Guide for AP Book
3 Ask two volunteers to hold the number line taut. Ask a volunteer to find the middle number between 30 and 40. ASK: How do you know that this number is in the middle? What do you have to check? (the distance to the ends 30 of 31 the rope make a 35 volunteer do that) 38 Let 39 a 40 volunteer stand behind the line holding the middle number (35). Explain to students that the volunteers and the number line make a rounding machine. The machine will automatically round the number to the nearest ten. Put the ring on 32. Ask the volunteer holding the middle of the line to pull up from 35, so that the ring slides to Try more numbers. Ask students to explain why the machine works. You can repeat this activity with the multiples of 10 going up to 100 or with any other numbers. Do not include numbers that require rounding the digit 5. Operations and Algebraic Thinking 413 D3
4 OA414 Rounding on a Number Line Pages (Hundreds and Thousands) STANDARDS 4.NBT.A.4 Goals Students will round to the closest hundred or thousand, except when the number is halfway between a multiple of a hundred or a thousand. PRIOR KNOWLEDGE REQUIRED Number lines Concept of closer The closest hundred. Repeat the previous lesson with a number line from 0 to 100 that shows only the multiples of At first, ask students whether numbers that are multiples of 10 (30, 70, 60, and so on) are closer to 0 or 100. Example: Is 40 closer to 0 or 100? Draw an arrow to show this. Repeat with several examples, then ASK: Which multiples of 10 are closer to 0 and which multiples of 10 are closer to 100? Which number is a special case? Why is it a special case? Then ask students about numbers that are not multiples of 10. First ask them where they would place the number 33 on the number line. Have a volunteer show this. Then ask the rest of the class if 33 is closer to 0 or to 100. Repeat with several numbers. Repeat with a number line from 100 to 200 and another number line from 700 to 800. Ask students for a general rule to tell which multiple of a hundred a number is closest to. What digit should they look at? (the tens digit) How can they tell from this digit which multiple of a hundred a number is closest to? When is there a special case? Emphasize that the number is closer to the higher multiple of 100 if its tens digit is 6, 7, 8, or 9, and it s closer to the lower multiple of 100 if its tens digit is 1, 2, 3, or 4. If the tens digit is 5, then any ones digit except 0 will make it closer to the higher multiple. Only when the tens digit is 5 and the ones digit is 0 do we have a special case where it is not closer to either. Repeat the lesson for thousands, emphasizing the importance of considering the value of the hundreds digit. Extensions 1. Rounding to the nearest ten, how many numbers round down to... a) 20? (four: 21, 22, 23, 24) b) 200? (four: 201, 202, 203, 204) c) 2,000? (four: 2,001, 2,001, 2,003, 2,004) D4 Teacher s Guide for AP Book 4.1
5 2. a) Rounding to the nearest ten, how many numbers round down to 30? (four: 31, 32, 33, 34) b) Rounding to the nearest hundred, how many numbers round down to 300? (fortynine: 301, 302, 303,, 349) c) Rounding to the nearest thousand, how many numbers round down to 3,000? (four hundred ninetynine: 3,001, 3,002, 3,003,, 3,499) Operations and Algebraic Thinking 414 D5
6 OA415 Rounding Pages STANDARDS 3.NBT.A.1, 4.NBT.A.3 Goals Students will round whole numbers to the nearest ten, hundred, or thousand. PRIOR KNOWLEDGE REQUIRED Knowing which multiples of ten, a hundred, or a thousand a number is between Finding which multiple of ten, a hundred, or a thousand a given number is closest to Review rounding 2digit numbers. Have students round 2digit numbers to the nearest ten. Do not at first include numbers that have ones digit 5. Ask students how they know which multiples of ten the number is between. ASK: How many tens are in 37? How many would be one more ten? So 37 is between 3 tens and 4 tens; that means it s between 30 and 40. Which multiple of ten is it closer to? ASK: How many tens are in 94? How many would be one more ten? What number is ten tens? So 94 is between what two multiples of 10? Which multiple of ten is it closer to? Repeat this line of questioning for 97. Connection Real World Rounding 2digit numbers when the ones digit is 5. Tell students that when the ones digit is 5, a number is not closer to either the smaller or the larger ten, but we always round up. Give students many examples to practice with: 25, 45, 95, 35, 15, 5, 85, 75, 55, 65. If some students find this hard to remember, you could share the following analogy: I am trying to cross the street, but there is a big truck coming, so when I am partway across I have to decide whether to keep going or turn back. If I am less than halfway across, it makes sense to turn back because I am less likely to get hit. If I am more than halfway across, it makes sense to keep going because I am again less likely to get hit. But if I am exactly halfway across, what should I do? Each choice gives me the same chance of getting hit. Have students discuss what they would do and why. Remind them that they are, after all, trying to cross the street. So actually, it makes sense to keep going rather than to turn back. That will get them where they want to be. Here is another way to help students remember which way to round: Write out all the 2digit numbers that have the same tens digits, for example, 3 (30, 31,..., 39). ASK: Which numbers should we round to 30 because they re closer to 30 than 40? Which numbers should we round to 40 because they re closer to 40 than to 30? How many are in each list? Where should we put 35 so that the lists are equal? Rounding 3digit numbers to the nearest ten. SAY: To round 3digit numbers to the nearest ten we look at the ones digit, the same way we do when we round 2digit numbers to the nearest ten. The difference is that there is now a digit we need to ignore (the hundreds digit). D6 Teacher s Guide for AP Book 4.1
7 Write on the board: SAY: The ones digit is less than 5, so we round down. Round 372 to 370. Exercises: Round each number to the nearest ten. a) 174 b) 885 c) 341 d) 936 Bonus e) 3,456 f) 28,712 Answers: a) 170, b) 890, c) 340, d) 940, e) 3,460, f) 28,710 Rounding 3digit numbers to the nearest hundred. Write on the board: 240, 241, 242, 243, 244, 245, 246, 247, 248, 249 ASK: What do these numbers all have in common? (3 digits, hundreds digit 2, tens digit 4) Are they closer to 200 or 300? (200) How do you know? PROMPT: On a number line, what number is halfway from 200 to 300? (250) Point out that all these numbers are less than halfway from 200 to 300, so they are closer to 200 than to 300. ASK: Did you need to look at the ones digit to check that these numbers are closer to 200 than to 300? (no) What digit did you look at? (the tens digit) Summarize by saying that, to round to the nearest hundred, we need to look at the tens digit. Then tell students to look at these numbers: 250, 251, 252, 253, 254, 255, 256, 257, 258, 259. ASK: Which hundred are these numbers closest to? Are they all closest to 300 or is there one that s different? Why is that one a special case? If you saw that the tens digit was 5 but you didn t know the ones digit, and you had to guess if the number was closer to 200 or 300, what would your guess be? Would the number ever be closer to 200? Tell students that when rounding a number to the nearest hundred, mathematicians decided to make it easier and say that if the tens digit is a 5, you always round up. It doesn t make any more sense to round 250 to 200 than to 300, so you might as well round it up to 300 like you do all the other numbers that have hundreds digit 2 and tens digit 5. Then ASK: When rounding a number to the nearest hundred, what digit do we need to look at? (the tens digit) Write on the board: Round to the nearest hundred: Have a volunteer underline the hundreds digit because that is what they are rounding to. Then ask another volunteer to draw an arrow to the digit that determines whether to round up or round down, so the board now looks like: ASK: Where is that digit compared to the underlined digit? (It is the next one to the right.) How do you know when to round down and when to round up? Have another volunteer decide in each case whether to round up or down and write the correct rounded number. Operations and Algebraic Thinking 415 D7
8 Repeat with 4digit numbers, having students again round to the nearest hundred. Examples: 5,439, 2,964, 8,249. Then round 4digit and 5digit numbers to the nearest thousand. Examples: 4,520, 73,618, 2,388, 28,103, 87,093, 9,843. To help ensure that students round correctly, suggest that they always underline the digit they are rounding to, then point their pencil tip at the digit to the right of the one they underlined. This digit will tell them whether to round up or down. If any students are having trouble with rounding, teach them to round on a grid as shown on AP Book 4.1 p (Lesson OA46). Extension Another way to round a number to the nearest ten. First, add 5. Then, replace the ones digit in the answer with 0. Example: = = To round to the nearest hundred, add 50 instead of 5. The rounded number will be the answer with the ones and tens digits replaced with 0. Example: = = You can explain why this works as follows: The number 842 is between 800 and 900. Any number between 800 and 900 will round up to 900 if it is at least halfway to 900. When you add half of 100 to a number that is less than halfway to 900, you get a number still in the 800s; when you add half of 100 to a number that is at least halfway to 900, you get a number that is in the 900s. You can liken this to pouring liquid into a container that is half full. If the amount you are pouring is at least half a container, you will reach the top, and maybe overflow. If the amount you are pouring is less than half a container, you will not reach the top. Challenge students to make up a rule for using this method to round to the nearest thousand. D8 Teacher s Guide for AP Book 4.1
9 OA416 Rounding on a Grid Pages STANDARDS 4.NBT.A.3 Goals Students will round whole numbers to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. PRIOR KNOWLEDGE REQUIRED Knowing which multiples of ten, a hundred, or a thousand a number is between Finding which multiple of ten, a hundred, or a thousand a given number is closest to. Rounding on a grid (without regrouping). Show students how numbers can be rounded on a grid. Follow the steps shown below to round 12,473 to the nearest thousand. Step 1: As before, underline the digit you are rounding to and put your pencil on the digit to the right. If the digit under your pencil is 5, 6, 7, 8, or 9, you will round up; write round up beside (or above) the grid. If the digit under your pencil is 0, 1, 2, 3, or 4, you will round down; write round down. The hundreds digit here is 4, so we write round down. Round Down Step 2: To round up, add 1 to the underlined digit; to round down, keep the digit the same. In this case, we are rounding down, so we copy the Isolate Step 2. If any students are struggling with Step 2, make up several examples where the first step is done for them so that they can focus only on rounding the underlined digit up or down. Sample questions: Exercises: Round the underlined digit up or down as indicated: Round Down Round Up Round Up Once all students have mastered Step 2, move on Operations and Algebraic Thinking 416 D9
10 Step 3: Change all numbers to the right of the rounded digit to zeros. Leave all numbers to the left of the rounded digit as they were. The number 12,473 rounded to the nearest thousand is 12,000. Round Down Rounding with regrouping. When students have mastered rounding without regrouping, give them several examples that demand regrouping as well. Warn them that the digits to the left of the rounded digit might change now. Round the 9 up to 10 and then regroup the 10 hundreds as 1 thousand and add it to the 7 thousand. Round Up Regroup Another way to do this rounding. Do an example together: Underline the digit you want to round to and decide whether to round up or down, as before, then change all numbers to the right of the rounded digit to zeros. We obtain (for the same example as above): Round Up Then ASK: Which two hundreds is the number between? PROMPT: How many hundreds are in 17,978? (179 hundreds are in 17,978, so the number is between 179 hundreds and 180 hundreds) Remind students that we are rounding up (point to the picture) because the tens digit is 7 the number is closer to 180 hundreds than to 179 hundreds. Complete the rounding by writing 180, not 179, as the number of hundreds. Round Up Point out that both ways of rounding get the same answer. Rounding larger numbers. Show grids with larger numbers, where regrouping does not occur. Ask students to round 538,226 to the nearest ten thousand. Here is the result they should obtain: Round Up D10 Teacher s Guide for AP Book 4.1
11 Repeat with numbers where there is regrouping. Ask students to round 745,391 to the nearest ten. Here is the result they should obtain: Round Up Round three more large numbers that require regrouping as a class: a) round 439,889 to the nearest thousand b) round 953,219 to the nearest hundred thousand c) round 595,233 to the nearest ten thousand Students can round more such numbers individually. Exercises: Round each number to the given digit. a) thousands b) hundreds c) ten thousands d) hundreds Extensions 1. Regrouping twice when rounding. If you have an advanced class, you can try teaching this to the whole class. SAY: Sometimes rounding forces you to regroup two or more numbers. Let s see what to do when this happens. We want to round 3,999 to the nearest ten. First, we round 90 up to Then we regroup the 10 tens as 1 hundred and add it to the 9 hundreds. This gives 10 hundreds (1,000) Operations and Algebraic Thinking 416 D11
12 Now we regroup the 10 hundreds as 1 thousand and add it to the 3 thousands To finish, we complete the rounded number by adding any missing zeros SAY: Let s do another example with a bigger number, such as 799,994. We will round this number to the nearest hundred. First, we round 900 up to 1, Then we regroup the 10 hundreds as 1 thousand and add them to the 9 thousands in the original number. Now we have 10 thousands ASK: What s the next step? (We regroup the 10 thousands as 1 ten thousand and add it to the 9 ten thousands in the original number. Now we have 10 ten thousands, or 1 hundred thousand (100,000).) ASK: What s the next step? (We add 1 to the hundred thousands.) ASK: How do we finish the rounding? (We complete the rounded number by adding any missing zeros.) D12 Teacher s Guide for AP Book 4.1
13 Have students round 3,997 to the nearest hundred and to the nearest ten; 73,992 to the nearest hundred and to the nearest ten; and 39,997 to the nearest hundred and to the nearest thousand. 2. If 48,329 is rounded to 48,300, what digit has it been rounded to? (MP.1) 3. a) Write down all numbers that round to 40 when rounded to the nearest ten. How many such numbers are there? b) Write down all numbers that round to 800 when rounded to the nearest ten. How many such numbers are there? c) What is the smallest number that rounds to 800 when rounded to the nearest hundred? What is the largest number that rounds to 800 when rounded to the nearest hundred? How many numbers round to 800 when rounded to the nearest hundred? Hint: If you wrote down all the numbers from 1 to the largest number you found, and took away all the numbers that don t round to 800, how many numbers would still be in the list? Answers a) 35, 36, 37, 38, 39, 40, 41, 42, 43, 44; there are 10 such numbers b) 795, 796, 797, 798, 799, 800, 801, 802, 803, 804; again, there are 10 such numbers c) 750 is the smallest such number, and 849 is the largest. There are 849 numbers from 1 to 849. We don t want to include all the numbers from 1 to 749. So there are = 100 numbers in the list. Operations and Algebraic Thinking 416 D13
14 OA417 Estimating Sums and Differences Pages STANDARDS 4.OA.A.3 Goals Students will estimate sums and differences by rounding each addend to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. Vocabulary estimating the approximately equal to sign ( ) PRIOR KNOWLEDGE REQUIRED Rounding to the nearest ten, hundred, thousand, ten thousand, or hundred thousand Estimations in calculations. Show students how to estimate by rounding each number to the nearest ten: = 80. SAY: Since 52 is close to 50 and 34 is close to 30, will be close to, or approximately, Mathematicians have invented a sign to mean approximately equal to. It s a squiggly equal sign:. So we can write It would not be right to put = 80 because they are not actually equal; they are just close to, or approximately equal. Connection Real World Tell students that when they round up or down before adding, they aren t finding the exact answer, they are just estimating. They are finding an answer that is close to the exact answer. ASK: When do you think it might be useful to estimate answers? Sample answer: in a grocery store, estimating total price or change expected. Have students estimate the sums of 2digit numbers by rounding each to the nearest ten. Remind them to use the approximately equal to sign. Exercises: a) b) c) d) e) f) = 70 Then ASK: How would you estimate 93 21? Write the estimated difference on the board (see margin). Have students estimate the differences of 2digit numbers by again rounding each to the nearest ten. Exercises: a) b) c) d) e) f) Then have students practice estimating the sums and differences of 3digit numbers by rounding to the nearest ten. (Examples: , ) 3 and 4digit numbers by rounding to the nearest hundred. (Examples: , 4,501 1,511) 4 and 5digit numbers by rounding to the nearest thousand. (Examples: 7, ,278, 13,891 11,990, 3, ,984) 5 and 6digit numbers by rounding to the nearest ten thousand. (Examples: 54, ,447, 679, ,928) D14 Teacher s Guide for AP Book 4.1
15 6 digit numbers by rounding to the nearest hundred thousand. (Examples: 928, ,219, 467, ,234) Is the estimate too high or too low? Write on the board: SAY: I estimated to be 70. Do you think this is higher than the actual answer or lower? (lower) Why? PROMPT: Is 30 more or less than 33? (less) Is 40 more or less than 41? (less) SAY: I rounded both numbers down, so the sum I get will be less than the actual sum. Have students verify this by calculating the actual sum. (74; indeed, 70 is less than 74) (MP.8) Exercises: Calculate both the actual sums and the rounded sums. Circle the larger sum. a) b) c) Answers: a) 73, 70, b) 87, 80, c) 115, 110. The actual sum should be circled in all cases. ASK: Which sum is larger, the actual sum or the rounded sum? (always the actual sum) Why was the actual sum always larger? (because the rounded numbers were smaller than the actual numbers; we always rounded down) Exercises: Calculate both the actual sums and the rounded sums. Circle the larger sum. a) b) c) Answers: a) 84, 90, b) 115, 120, c) 93, 100. The rounded sum should be circled in all cases. ASK: Which sum is larger, the actual sum or the rounded sum? (always the rounded sum) Why was the rounded sum always larger? (because the rounded numbers were larger than the actual numbers) Point out that when both numbers are rounded up, the rounded sum is larger, and when both numbers are rounded down, the rounded sum is smaller. Exercises: Predict whether Ahmed s estimate is too high or too low, then check your prediction by calculating the actual sum. a) Ahmed estimates as = 130. b) Ahmed estimates as = 1,500. c) Ahmed estimates as = 940. d) Ahmed estimates 23, ,706 as 20, ,000 = 30,000. e) Ahmed estimates 65, ,964 as 66, ,000 = 90,000. Answers a) Too low because 60 is less than 63 and 70 is less than 71, so will be less than Indeed, = 134 is more than 130. Operations and Algebraic Thinking 417 D15
16 b) Too high because 800 is more than 752 and 700 is more than 689, so will be more than Indeed, = 1,441. c) Too low. Indeed, = 946. d) Too low. Indeed, 23, ,706 = 38,618. e) Too high. Indeed, 65, ,964 = 89,496. (MP.2) Recognizing when an answer is reasonable or not. For example, Daniel added 273 and 385, and got the answer 958. Does this answer seem reasonable? Students should see that even rounding both numbers up gives a sum less than 900, so this answer can t be correct. Do the following answers seem reasonable? Invite students to explain using estimates and perform the actual calculation to check their answers. a) Xian added 444 and 222 and got 888. b) Melissa added 196 and 493 and got 709. c) Enrico added 417 and 634 and got 951. (MP.8) Rounding to smaller place values is more accurate. SAY: Let s try estimating the sum by rounding to the tens and then to the hundreds. ASK: Which way do you think will give an answer closer to the actual sum? Write the sum on the board and get students to help you round the numbers to the given place value and then do the calculation. nearest ten: nearest hundred: ,180 1,200 Then calculate the sum of the two numbers and compare it with the two values we just obtained by estimating. ( = 1,181) ASK: The sum is closest to which answer, the one obtained by rounding the tens or the hundreds? (the tens) Explain that the lower the place value we round to in our estimation, the closer we get to the actual sum. Discuss how this is similar to measuring. Measuring to the nearest millimeter is more accurate and gives more information than measuring to the nearest centimeter because millimeters are smaller than centimeters. Do the same type of exercise with two 4digit numbers: 5, ,213. Round to the tens: hundreds: thousands: 5,938 5,940 5,938 5,900 5,938 6, ,213 8, ,213 8, ,213 8,000 14,150 14,100 14,000 The actual sum is 14,151, so again rounding to the closest ten is the most accurate. Now estimate the sum 2, ,432 by rounding each number to the nearest: a) ten b) hundred c) thousand d) ten thousand D16 Teacher s Guide for AP Book 4.1
17 Have students put their answers in order from closest to the actual answer to furthest from the actual answer. What do students notice? (rounding to smaller place values is more accurate) Point out that the answer to part d) above is = 0. Emphasize that rounding to too big a place value can become absurd. SAY: It would be like rounding the distance from my desk to your desk to the nearest mile. (MP.5) Choosing between speed and accuracy. ASK: Was adding more accurate when we rounded to the nearest tens, hundreds, or thousands? (tens) ASK: Was adding faster when we rounded to the nearest tens, hundreds, or thousands? (thousands) Why? (Adding 6,000 and 8,000 is as easy as adding 6 and 8, two 1digit numbers, but adding 5,900 and 8,200 is like adding 59 and 82, two 2digit numbers; 1digit numbers are easier to add than 2digit numbers.) Point out that we often need to choose between being fast and being more accurate. Sometimes we need more accuracy, and sometimes we need to be faster. Extensions 1. a) Estimate by rounding both numbers to the nearest hundred. Is your estimate higher or lower than the actual answer? b) Estimate by rounding both numbers to the nearest ten. Is your estimate higher or lower than the actual answer? Bonus: Make up another question where rounding to the nearest hundred is lower than the actual answer, but rounding to the nearest ten is higher than the actual answer. (MP.3) 2. Have students investigate when rounding one number up and one number down is better than rounding each to the nearest hundred by completing the following chart and circling the estimate that is closest to the actual answer: Actual Answer Round to the Nearest Hundred Round One Up and Round One Down 1, = 1, = 1,500 Operations and Algebraic Thinking 417 D17
OA413 Rounding on a Number Line
OA413 Rounding on a Number Line 1. Draw an arrow to show whether the circled number is closer to 0 or 10. 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 c) 0 1 2 3 4 5 6 7 8 9 10 d) 0 1 2 3 4 5 6 7 8 9
More informationUnit 6 Number and Operations in Base Ten: Decimals
Unit 6 Number and Operations in Base Ten: Decimals Introduction Students will extend the place value system to decimals. They will apply their understanding of models for decimals and decimal notation,
More informationUnit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.
Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L34) is a summary BLM for the material
More informationOA310 Patterns in Addition Tables
OA310 Patterns in Addition Tables Pages 60 63 Standards: 3.OA.D.9 Goals: Students will identify and describe various patterns in addition tables. Prior Knowledge Required: Can add two numbers within 20
More informationNF512 Flexibility with Equivalent Fractions and Pages 110 112
NF5 Flexibility with Equivalent Fractions and Pages 0 Lowest Terms STANDARDS preparation for 5.NF.A., 5.NF.A. Goals Students will equivalent fractions using division and reduce fractions to lowest terms.
More informationEE65 Solving Equations with Balances Pages 77 78
EE65 Solving Equations with Balances Pages 77 78 STANDARDS 6.EE.B.5, 6.EE.B.6 Goals Students will use pictures to model and solve equations. Vocabulary balance equation expression sides (of an equation)
More informationUsing Proportions to Solve Percent Problems I
RP71 Using Proportions to Solve Percent Problems I Pages 46 48 Standards: 7.RP.A. Goals: Students will write equivalent statements for proportions by keeping track of the part and the whole, and by solving
More informationUnit 7 The Number System: Multiplying and Dividing Integers
Unit 7 The Number System: Multiplying and Dividing Integers Introduction In this unit, students will multiply and divide integers, and multiply positive and negative fractions by integers. Students will
More informationMD526 Stacking Blocks Pages 115 116
MD526 Stacking Blocks Pages 115 116 STANDARDS 5.MD.C.4 Goals Students will find the number of cubes in a rectangular stack and develop the formula length width height for the number of cubes in a stack.
More informationNBT41 Place Value Ones, Tens, Hundreds, Page 24
NBT41 Place Value Ones, Tens, Hundreds, Page 24 and Thousands STANDARDS 4.NBT.A.2 Goals Students will identify the place value of digits in 2, 3, and 4digit numbers. Vocabulary hundreds ones place
More information1 ENGAGE. 2 TEACH and TALK GO. Round to the Nearest Ten or Hundred
Lesson 1.2 c Round to the Nearest Ten or Hundred Common Core Standard CC.3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100. Lesson Objective Round 2 and 3digit numbers
More informationNS650 Dividing Whole Numbers by Unit Fractions Pages 16 17
NS60 Dividing Whole Numbers by Unit Fractions Pages 6 STANDARDS 6.NS.A. Goals Students will divide whole numbers by unit fractions. Vocabulary division fraction unit fraction whole number PRIOR KNOWLEDGE
More informationMeasuring with a Ruler
Measuring with a Ruler Objective To guide children as they measure line segments to the nearest inch, _ inch, _ inch, centimeter, _ centimeter, and millimeter. www.everydaymathonline.com epresentations
More informationUnit 2 Number and Operations in Base Ten: Place Value, Addition, and Subtraction
Unit 2 Number and Operations in Base Ten: Place Value, Addition, and Subtraction Introduction In this unit, students will review the place value system for reading and writing numbers in base ten. Students
More information2 Mathematics Curriculum
New York State Common Core 2 Mathematics Curriculum GRADE GRADE 2 MODULE 3 Topic E: Model Numbers Within 1000 with Place Value Disks 2.NBT.A Focus Standard: 2.NBT.A Understand place value. Instructional
More informationTom wants to find two real numbers, a and b, that have a sum of 10 and have a product of 10. He makes this table.
Sum and Product This problem gives you the chance to: use arithmetic and algebra to represent and analyze a mathematical situation solve a quadratic equation by trial and improvement Tom wants to find
More informationEstimating Differences. Finding Distances on a Map
Estimating Differences Problem Solving: Finding Distances on a Map Estimating Differences How do we use rounding to estimate differences? Sometimes subtraction is like addition. There are times when we
More informationArea and Perimeter: The Mysterious Connection TEACHER EDITION
Area and Perimeter: The Mysterious Connection TEACHER EDITION (TC0) In these problems you will be working on understanding the relationship between area and perimeter. Pay special attention to any patterns
More informationChange Number Stories Objective To guide children as they use change diagrams to help solve change number stories.
Number Stories Objective To guide children as they use change diagrams to help solve change number stories. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game
More informationMathematics Navigator. Misconceptions and Errors
Mathematics Navigator Misconceptions and Errors Introduction In this Guide Misconceptions and errors are addressed as follows: Place Value... 1 Addition and Subtraction... 4 Multiplication and Division...
More informationRounding Decimals S E S S I O N 1. 5 A. Rounding Decimals
S E S S I O N 1. 5 A Math Focus Points Rounding decimals to the nearest one, tenth, and hundredth Today s Plan ACTIVITY DISCUSSION Rounding a 9 Up SESSION FOLLOWUP 45 MIN CLASS PAIRS INDIVIDUALS 15 MIN
More information5 Mathematics Curriculum
New York State Common Core 5 Mathematics Curriculum G R A D E GRADE 5 MODULE 1 Topic B Decimal Fractions and Place Value Patterns 5.NBT.3 Focus Standard: 5.NBT.3 Read, write, and compare decimals to thousandths.
More informationCHAPTER 4 DIMENSIONAL ANALYSIS
CHAPTER 4 DIMENSIONAL ANALYSIS 1. DIMENSIONAL ANALYSIS Dimensional analysis, which is also known as the factor label method or unit conversion method, is an extremely important tool in the field of chemistry.
More informationAim To help students prepare for the Academic Reading component of the IELTS exam.
IELTS Reading Test 1 Teacher s notes Written by Sam McCarter Aim To help students prepare for the Academic Reading component of the IELTS exam. Objectives To help students to: Practise doing an academic
More informationYour logbook. Choosing a topic
This booklet contains information that will be used to complete a science fair project for the César Chávez science fair. It is designed to help participants to successfully complete a project. This booklet
More informationMathematics Task Arcs
Overview of Mathematics Task Arcs: Mathematics Task Arcs A task arc is a set of related lessons which consists of eight tasks and their associated lesson guides. The lessons are focused on a small number
More information1 ST GRADE COMMON CORE STANDARDS FOR SAXON MATH
1 ST GRADE COMMON CORE STANDARDS FOR SAXON MATH Calendar The following tables show the CCSS focus of The Meeting activities, which appear at the beginning of each numbered lesson and are taught daily,
More informationMath Journal HMH Mega Math. itools Number
Lesson 1.1 Algebra Number Patterns CC.3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Identify and
More informationArc Length and Areas of Sectors
Student Outcomes When students are provided with the angle measure of the arc and the length of the radius of the circle, they understand how to determine the length of an arc and the area of a sector.
More informationUsing games to support. WinWin Math Games. by Marilyn Burns
4 WinWin Math Games by Marilyn Burns photos: bob adler Games can motivate students, capture their interest, and are a great way to get in that paperandpencil practice. Using games to support students
More informationSHELL INDUSTRIAL APTITUDE BATTERY PREPARATION GUIDE
SHELL INDUSTRIAL APTITUDE BATTERY PREPARATION GUIDE 2011 Valtera Corporation. All rights reserved. TABLE OF CONTENTS OPERATIONS AND MAINTENANCE JOB REQUIREMENTS... 1 TEST PREPARATION... 2 USE OF INDUSTRIAL
More informationMcKinsey Problem Solving Test Top Tips
McKinsey Problem Solving Test Top Tips 1 McKinsey Problem Solving Test You re probably reading this because you ve been invited to take the McKinsey Problem Solving Test. Don t stress out as part of the
More information2 Mathematics Curriculum
New York State Common Core 2 Mathematics Curriculum GRADE GRADE 2 MODULE 3 Topic G: Use Place Value Understanding to Find 1, 10, and 100 More or Less than a Number 2.NBT.2, 2.NBT.8, 2.OA.1 Focus Standard:
More informationObjective To introduce a formula to calculate the area. Family Letters. Assessment Management
Area of a Circle Objective To introduce a formula to calculate the area of a circle. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment
More informationCircumference of a Circle
Circumference of a Circle A circle is a shape with all points the same distance from the center. It is named by the center. The circle to the left is called circle A since the center is at point A. If
More informationDecomposing Numbers (Operations and Algebraic Thinking)
Decomposing Numbers (Operations and Algebraic Thinking) Kindergarten Formative Assessment Lesson Designed and revised by Kentucky Department of Education Mathematics Specialists Fieldtested by Kentucky
More informationLESSON 7 Don t Be A Square by Michael Torres
CONCEPT AREA GRADE LEVEL Measurement 56 TIME ALLOTMENT Two 60minute sessions LESSON OVERVIEW LESSON ACTIVITIES OVERVIEW LEARNING OBJECTIVES STANDARDS (TEKS) Students will learn the relationship between
More informationSession 7 Fractions and Decimals
Key Terms in This Session Session 7 Fractions and Decimals Previously Introduced prime number rational numbers New in This Session period repeating decimal terminating decimal Introduction In this session,
More informationEquations, Lenses and Fractions
46 Equations, Lenses and Fractions The study of lenses offers a good real world example of a relation with fractions we just can t avoid! Different uses of a simple lens that you may be familiar with are
More informationObjective. Materials. TI73 Calculator
0. Objective To explore subtraction of integers using a number line. Activity 2 To develop strategies for subtracting integers. Materials TI73 Calculator Integer Subtraction What s the Difference? Teacher
More informationFive daily lessons. Page 23. Page 25. Page 29. Pages 31
Unit 4 Fractions and decimals Five daily lessons Year 5 Spring term Unit Objectives Year 5 Order a set of fractions, such as 2, 2¾, 1¾, 1½, and position them on a number line. Relate fractions to division
More informationKristen Kachurek. Circumference, Perimeter, and Area Grades 710 5 Day lesson plan. Technology and Manipulatives used:
Kristen Kachurek Circumference, Perimeter, and Area Grades 710 5 Day lesson plan Technology and Manipulatives used: TI83 Plus calculator Area Form application (for TI83 Plus calculator) Login application
More informationSession 7 Bivariate Data and Analysis
Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table covariation least squares
More informationSubject: Math Grade Level: 5 Topic: The Metric System Time Allotment: 45 minutes Teaching Date: Day 1
Subject: Math Grade Level: 5 Topic: The Metric System Time Allotment: 45 minutes Teaching Date: Day 1 I. (A) Goal(s): For student to gain conceptual understanding of the metric system and how to convert
More informationVolume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.
Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game
More informationGrade 3: Module 1: Unit 1: Lesson 8 Paragraph Writing Instruction
Grade 3: Module 1: Unit 1: Lesson 8 This work is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 Unported License. Exempt thirdparty content is indicated by the footer: (name
More information4 Mathematics Curriculum
New York State Common Core 4 Mathematics Curriculum G R A D E GRADE 4 MODULE 1 Topic F Addition and Subtraction Word Problems 4.OA.3, 4.NBT.1, 4.NBT.2, 4.NBT.4 Focus Standard: 4.OA.3 Solve multistep word
More informationScience Grade 1 Forces and Motion
Science Grade 1 Forces and Motion Description: The students in this unit will use their inquiry skills to explore pushing, pulling, and gravity. They will also explore the different variables which affect
More informationTime needed. Before the lesson Assessment task:
Formative Assessment Lesson Materials Alpha Version Beads Under the Cloud Mathematical goals This lesson unit is intended to help you assess how well students are able to identify patterns (both linear
More informationMathematics Success Grade 6
T276 Mathematics Success Grade 6 [OBJECTIVE] The student will add and subtract with decimals to the thousandths place in mathematical and realworld situations. [PREREQUISITE SKILLS] addition and subtraction
More informationPushes and Pulls. TCAPS Created June 2010 by J. McCain
Pushes and Pulls K i n d e r g a r t e n S c i e n c e TCAPS Created June 2010 by J. McCain Table of Contents Science GLCEs incorporated in this Unit............... 23 Materials List.......................................
More informationProperty of the Salvadori Center ~ not for reproduction
Outline Salvadori AfterSchool: Skyscrapers In this 12week module, students identify the characteristics that make skyscrapers unique. They learn how columns and beams work together to support tall structures;
More informationA Drop of Water A Lesson for Sixth, Seventh, and Eighth Graders
A Drop of Water A Lesson for Sixth, Seventh, and Eighth Graders By Jennifer M. BayWilliams and Sherri L. Martinie From Online Newsletter Issue Number 1, Winter 2004 200 In Walter Wick s picture book A
More information1. I have 4 sides. My opposite sides are equal. I have 4 right angles. Which shape am I?
Which Shape? This problem gives you the chance to: identify and describe shapes use clues to solve riddles Use shapes A, B, or C to solve the riddles. A B C 1. I have 4 sides. My opposite sides are equal.
More informationPaper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 4 6
Ma KEY STAGE 3 Mathematics test TIER 4 6 Paper 1 Calculator not allowed First name Last name School 2007 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You
More informationUnit 8 Angles, 2D and 3D shapes, perimeter and area
Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest
More informationRubber Band Race Car
Rubber Band Race Car Physical Science Unit Using LEGO Mindstorms NXT Copyright 2009 by Technically Learning 1 of 17 Overview: Through a series of handson activities, students will design a rubber band
More informationInteraction at a Distance
Interaction at a Distance Lesson Overview: Students come in contact with and use magnets every day. They often don t consider that there are different types of magnets and that they are made for different
More informationLesson 1: Linear Measurement
Lesson 1: Linear Selected Content Standards Benchmarks Addressed: M1M Applying the concepts of length, area, surface area, volume, capacity, weight, mass, money, time, temperature, and rate to realworld
More informationUnit 2 Number and Operations Fractions: Multiplying and Dividing Fractions
Unit Number and Operations Fractions: Multiplying and Dividing Fractions Introduction In this unit, students will divide whole numbers and interpret the answer as a fraction instead of with a remainder.
More informationBar Graphs and Dot Plots
CONDENSED L E S S O N 1.1 Bar Graphs and Dot Plots In this lesson you will interpret and create a variety of graphs find some summary values for a data set draw conclusions about a data set based on graphs
More informationGRADE 8 English Language Arts Proofreading: Lesson 6
GRADE 8 English Language Arts Proofreading: Lesson 6 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information
More informationLocal Government and Leaders Grade Three
Ohio Standards Connection: Government Benchmark A Identify the responsibilities of the branches of the U.S. government and explain why they are necessary. Indicator 2 Explain the structure of local governments
More informationLesson 4: Solving and Graphing Linear Equations
Lesson 4: Solving and Graphing Linear Equations Selected Content Standards Benchmarks Addressed: A2M Modeling and developing methods for solving equations and inequalities (e.g., using charts, graphs,
More informationCommutative Property Grade One
Ohio Standards Connection Patterns, Functions and Algebra Benchmark E Solve open sentences and explain strategies. Indicator 4 Solve open sentences by representing an expression in more than one way using
More informationPLANT TECHNICIAN SKILLS AND ABILITIES PRACTICE TEST
PLANT TECHNICIAN SKILLS AND ABILITIES PRACTICE TEST OVERVIEW Welcome to the Plant Technician Skills and Abilities Practice Test. The purpose of this Practice Test is to help you get used to the questions
More informationBecause the slope is, a slope of 5 would mean that for every 1cm increase in diameter, the circumference would increase by 5cm.
Measurement Lab You will be graphing circumference (cm) vs. diameter (cm) for several different circular objects, and finding the slope of the line of best fit using the CapStone program. Write out or
More informationHidden Treasure: A Coordinate Game. Assessment Management. Matching Number Stories to Graphs
Hidden Treasure: A Coordinate Game Objective To reinforce students understanding of coordinate grid structures and vocabulary. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM
More informationPERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
More informationThree daily lessons. Year 5
Unit 6 Perimeter, coordinates Three daily lessons Year 4 Autumn term Unit Objectives Year 4 Measure and calculate the perimeter of rectangles and other Page 96 simple shapes using standard units. Suggest
More informationGrade 7 Circumference
Grade 7 Circumference 7.SS.1 Demonstrate an understanding of circles by describing the relationships among radius, diameter, and circumference of circles relating circumference to PI determining the sum
More informationPlace Value (What is is the Value of of the the Place?)
Place Value (What is is the Value of of the the Place?) Second Grade Formative Assessment Lesson Lesson Designed and revised by Kentucky Department of Education Mathematics Specialists Fieldtested by
More informationAtomic Structure OBJECTIVES SCHEDULE PREPARATION VOCABULARY MATERIALS. For each team of four. The students. For the class.
activity 4 Atomic Structure OBJECTIVES Students are introduced to the structure of the atom and the nature of subatomic particles. The students are introduced to the properties of protons, neutrons, and
More informationImperial Length Measurements
Unit I Measuring Length 1 Section 2.1 Imperial Length Measurements Goals Reading Fractions Reading Halves on a Measuring Tape Reading Quarters on a Measuring Tape Reading Eights on a Measuring Tape Reading
More informationReview: Comparing Fractions Objectives To review the use of equivalent fractions
Review: Comparing Fractions Objectives To review the use of equivalent fractions in comparisons. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters
More informationStudent Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes)
Student Outcomes Students give an informal derivation of the relationship between the circumference and area of a circle. Students know the formula for the area of a circle and use it to solve problems.
More informationStandard 1: Students can understand and apply a variety of math concepts.
Grade Level: 4th Teacher: Pelzer/Reynolds Math Standard/Benchmark: A. understand and apply number properties and operations. Grade Level Objective: 1.A.4.1: develop an understanding of addition, subtraction,
More information1. The Fly In The Ointment
Arithmetic Revisited Lesson 5: Decimal Fractions or Place Value Extended Part 5: Dividing Decimal Fractions, Part 2. The Fly In The Ointment The meaning of, say, ƒ 2 doesn't depend on whether we represent
More informationLab 11. Simulations. The Concept
Lab 11 Simulations In this lab you ll learn how to create simulations to provide approximate answers to probability questions. We ll make use of a particular kind of structure, called a box model, that
More informationGrade 7 Mathematics. Unit 2. Integers. Estimated Time: 15 Hours
Grade 7 Mathematics Integers Estimated Time: 15 Hours [C] Communication [CN] Connections [ME] Mental Mathematics and Estimation [PS] Problem Solving [R] Reasoning [T] Technology [V] Visualization Grade
More informationRepresenting Vector Fields Using Field Line Diagrams
Minds On Physics Activity FFá2 5 Representing Vector Fields Using Field Line Diagrams Purpose and Expected Outcome One way of representing vector fields is using arrows to indicate the strength and direction
More informationAddition of Multidigit Numbers
Addition of Multidigit Numbers Objectives To review the partialsums algorithm used to solve multidigit addition problems; and to introduce a columnaddition method similar to the traditional addition
More information5 Mathematics Curriculum
New York State Common Core 5 Mathematics Curriculum G R A D E GRADE 5 MODULE 1 Topic C Place Value and Rounding Decimal Fractions 5.NBT.4 Focus Standard: 5.NBT.4 Use place value understanding to round
More informationUnit 4 Measures time, mass and area
Unit 4 Measures time, mass and area Five daily lessons Year 4 Spring term (Key objectives in bold) Unit Objectives Year 4 Estimate/check times using seconds, minutes, hours. Page 98 Know and use the relationships
More informationMathematical goals. Starting points. Materials required. Time needed
Level N of challenge: B N Mathematical goals Starting points Materials required Time needed Ordering fractions and decimals To help learners to: interpret decimals and fractions using scales and areas;
More informationUnit 5 Length. Year 4. Five daily lessons. Autumn term Unit Objectives. Link Objectives
Unit 5 Length Five daily lessons Year 4 Autumn term Unit Objectives Year 4 Suggest suitable units and measuring equipment to Page 92 estimate or measure length. Use read and write standard metric units
More informationPhases of the Moon. Preliminaries:
Phases of the Moon Sometimes when we look at the Moon in the sky we see a small crescent. At other times it appears as a full circle. Sometimes it appears in the daylight against a bright blue background.
More informationG C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Performance Assessment Task Circle and Squares Grade 10 This task challenges a student to analyze characteristics of 2 dimensional shapes to develop mathematical arguments about geometric relationships.
More informationLesson 26: Reflection & Mirror Diagrams
Lesson 26: Reflection & Mirror Diagrams The Law of Reflection There is nothing really mysterious about reflection, but some people try to make it more difficult than it really is. All EMR will reflect
More informationSolving Rational Equations
Lesson M Lesson : Student Outcomes Students solve rational equations, monitoring for the creation of extraneous solutions. Lesson Notes In the preceding lessons, students learned to add, subtract, multiply,
More informationIntegers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern.
INTEGERS Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern. Like all number sets, integers were invented to describe
More informationLearn How to Revise 1
Learn How to Revise 1 SCHOOL EXAM DATES 2016 END OF YEAR EXAMS FOR YEARS 79 BEGIN ON MONDAY 6 TH JUNE THEY WILL TAKE PLACE IN LESSONS DURING THIS WEEK AND IF NECESSARY THE WEEK AFTER. Some subjects are
More informationThe Key to Keywords LESSON PLAN UNIT 1. Essential Question Which keywords will give you the best search results?
LESSON PLAN The Key to Keywords UNIT 1 Essential Question Which keywords will give you the best search results? Lesson Overview Students learn strategies to increase the accuracy of their keyword searches.
More informationObjective To introduce the concept of square roots and the use of the squareroot key on a calculator. Assessment Management
Unsquaring Numbers Objective To introduce the concept of square roots and the use of the squareroot key on a calculator. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts
More informationFigure 1. A typical Laboratory Thermometer graduated in C.
SIGNIFICANT FIGURES, EXPONENTS, AND SCIENTIFIC NOTATION 2004, 1990 by David A. Katz. All rights reserved. Permission for classroom use as long as the original copyright is included. 1. SIGNIFICANT FIGURES
More information3rd Grade Lesson Fractions
3rd Grade Lesson Fractions Lesson planning team: Tracey Carter, Rebecca Kotler, Tom McDougal Instructor: Tracey Carter Focus Question Sixth Annual Lesson Study Conference DePaul University Chicago, Illinois
More informationTranslating between Fractions, Decimals and Percents
CONCEPT DEVELOPMENT Mathematics Assessment Project CLASSROOM CHALLENGES A Formative Assessment Lesson Translating between Fractions, Decimals and Percents Mathematics Assessment Resource Service University
More informationRefining Informational Writing: Grade 5 Writing Unit 3
Unit Title: Refining Informational Writing Concepts: 1. Writers read mentor texts to study informational writing. 2. Writers generate ideas and experiment with notebook entries. 3. Writers learn strategies
More informationSquaring, Cubing, and Cube Rooting
Squaring, Cubing, and Cube Rooting Arthur T. Benjamin Harvey Mudd College Claremont, CA 91711 benjamin@math.hmc.edu I still recall my thrill and disappointment when I read Mathematical Carnival [4], by
More informationDecimals and other fractions
Chapter 2 Decimals and other fractions How to deal with the bits and pieces When drugs come from the manufacturer they are in doses to suit most adult patients. However, many of your patients will be very
More information