NumberSense-BemidjiStateUniversity数感-伯米吉州立大学.docx

Number SenseTravis Whittingtontwhittingtonclbs.k12.mn.usExecutive SummaryThis Number Sense unit will take about fifteen class days. The unit is composed of three parts: Part one will build students background on place value. Part two will build students understanding of fractions with a focus on representing them three ways. In part three students compare and find equivalency between decimals and fractions. The overall goal of the unit is for students to develop a greater understanding of fractions and decimals while meeting Minnesota state standards along the way. Minnesota Standards CoveredStandards utilized in the unit are highlighted.5Number & OperationDivide multi-digit numbers; solve real-world and mathematical problems using arithmetic.5.1.1.1Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. For example: Dividing 153 by 7 can be used to convert the improper fraction to the mixed number.5.1.1.2Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. For example: If 77 amusement ride tickets are to be distributed equally among 4 children, each child will receive 19 tickets, and there will be one left over. If $77 is to be distributed equally among 4 children, each will receive $19.25, with nothing left over.5.1.1.3Estimate solutions to arithmetic problems in order to assess the reasonableness of results.5.1.1.4Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.For example: The calculation 117 9 = 13 can be checked by multiplying 9 and 13.5Number & OperationRead, write, represent and compare fractions and decimals; recognize and write equivalent fractions; convert between fractions and decimals; use fractions and decimals in real-world and mathematical situations.5.1.2.1Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. For example: Possible names for the number 0.0037 are: 37 ten thousandths 3 thousandths + 7 ten thousandths;a possible name for the number 1.5 is 15 tenths.5.1.2.2Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number.5.1.2.3Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. For example: Which is larger 1.25 or ? Another example: In order to work properly, a part must fit through a 0.24 inch wide space. If a part is inch wide, will it fit?5.1.2.4Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts. For example: When comparing 1.5 and, note that 1.5 = = = , so 1.5 .5.1.2.5Round numbers to the nearest 0.1, 0.01 and 0.001. For example: Fifth grade students used a calculator to find the mean of the monthly allowance in their class. The calculator display shows 25.80645161. Round this number to the nearest cent. Add and subtract fractions, mixed numbers and decimals to solve real-world and mathematical problems.5.1.3.1Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. 5.1.3.2Model addition and subtraction of fractions and decimals using a variety of representations. For example: Represent and by drawing a rectangle divided into 4 columns and 3 rows and shading the appropriate parts or by using fraction circles or bars.5.1.3.3Estimate sums and differences of decimals and fractions to assess the reasonableness of results.For example: Recognize that is between 8 and 9 (since ).5.1.3.4Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data.For example: Calculate the perimeter of the soccer field when the length is 109.7 meters and the width is 73.1 meters.PretestBy the end of this unit, students should be able to answer the following questions correctly. MCA III sampler questions relating to the unit are included.1. Which number has a 5 in the ten-thousandths place? A. 0.20815B. 0.30256C. 0.40571D. 0.500982. Draw an area model to show the fraction 2 / 53. Johans race time was 45.03 seconds. Kyles race time was 0.1 second less than Johans time. What was Kyles race time?A. 44.03 secondsB. 44.93 secondsC. 45.13 secondsD. 45.14 seconds4. What is 0.45831 rounded to the nearest thousandth? A. 0.45 B. 0.458 C. 0.459 D. 0.4583 5. Use the set model to show the fraction.5 / 66. Compare, fill in the box.3 / 5 5 / 6A. C. =7. Compare, fill in the box.2 / 4 4 / 8A. C. =8. Compare, fill in the box.73 3 / 4A. C. =9.10.11.Table of Contents/Pacing GuidePart 1Day 1 Pre-test. Day 2 MillionaireDay 3 Dare to Compare MillionaireDay 4 Rational Number Project #9Day 5 Decimal DramaDay 6 Rounding RacesPart 2Day 7 Fractions: Area modelDay 8 Fractions: Set modelDay 9 Fractions: Length modelDay 10 Fractions: The big threeDay 11 Equivalent FractionsPart 3Day 12 Mixed and Improper FractionsDay 13 Fractions to DecimalsDay 14 Fractions Compared to DecimalsDay 15 Review DayDay 16 Post-test.Note: All materials are ordered and attached as referenced in the plan.Day 1(Pre-test)Standards Covered:5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 5.1.2.5 - Round numbers to the nearest 0.1, 0.01 and 0.001. 5.1.2.2 - Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number.5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. 5.1.2.4 - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts. Materials: MCA Pre-test, Wrap It Up activity.Launch: Question of the day activity, (students are given five minutes to gather their notebooks, pencils, and answer the following question on the smart board daily before class starts, at the end, we discuss and talk about a few answers/solutions.) “What is a number?” Discuss results and student answers.“Today were going to be taking a pre-test to see how much you all know about our next unit. Remember this helps us measure where we are starting at and where we are ending up, so be honest with yourself and try your hardest.”Explore: Hand out MCA Pre-Test. Once students complete the pretest they can work on the Wrap It Up activity.Share: Save five minutes at the end for students to share their wrap it up surveys with a neighbor.Summarize: Use information turned in from Wrap It Up survey to pinpoint on areas that need work.Day 2(Millionaire)Standards Covered:5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Materials: Smartboard, paper, playing cards.Launch: Question of the day activity, “My I pod has a battery length 86,400 seconds per charge. How would I write that number with words?” Discuss results and student answers.“Who wants to be a multimillionaire? Great then I have a game for you.”Rules: In pairs (to develop social / speaking-listening skills) Students draw 7 joined boxes in a horizontal line. I have a standard pack of playing cards with the face cards removed. Ill shuffle them, turn over the top card and call out the number. Students must choose a box to write this number in. The teacher also does this in secret. The cards are turned and called until all 7 boxes are filled.Students and teacher then display / say their number. Students who get a higher number than the teacher get 5 points. Equal to the teacher gets 3 points. Lower than the teacher 1 point. The teacher gets 10 points if he / she beats all the students!Note - a ten playing card is called as a zero.Explore: After each round, student pairs will write out the number they created on their place value cards using a chart created as a group on the Smartboard after the first round. This way there may be some confusion/teachable moment when students arent quite sure on how to read their number aloud. IF this is too easy, no points for incorrect number sentences.Share: Students must share/play the game against someone at home; bring in a game card for homework.Summarize: “In the game, what was the importance of place value? Did any groups have a strategy? Do you think place value is important?”Day 3(Dare to Compare Millionaire)Standards Covered:5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 5.1.2.5 - Round numbers to the nearest 0.1, 0.01 and 0.001. 5.1.2.2 - Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number.Materials: Smartboard, paper, spinner, and brass fastener.Launch: Question of the day activity, “How did your homework go last night? What strategies did your opponent use? Who won?” Discuss results and student answers.“How did we know yesterday who got points when we revealed our numbers? Comparing numbers helps us see which one is greater, or which one is less. So Im switching our game up a little today, do any of you dare to compare?”Have students create this format (two boxes, decimal, two boxes, space, two boxes, decimal, two boxes). . . They will also need the attached spinner cut out and assembled.Explore: Students will play this game in pairs and rotate when they complete a match. Before the game starts players get to choose their opponents symbol for the middle, (greater than or less than). Depending on the group, model a game before. Once a match is complete, students must write the number sentence WITH greater than or less than in the sentence.Share: Students need to take this game home and share/play with someone at home. Bring in one gamecard as homework.Summarize: Did your strategy change from yesterday? How did the added rule of greater than or less than change how you decided where to place your numbers?Day 4(Rational Number Project #9)Standards Covered:5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 5.1.2.2 - Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number.Materials: Smartboard, paper, Rational Number Project Lesson #9, Lesson #9 worksheets, coloring supplies.Launch: Question of the day activity, “How could you show how much a decimal is?” Discuss results and student answers.Work through the Rational Number Project Lesson #9Explore: Students work on their own to finish pages C and DShare: Come together as a whole group and look at different students decimal/grid solutions. Talk about where the different place values are shown on the grid.Summarize: “Why would this tool be useful?” “What were we trying to find out?”Day 5(Decimal Drama)Standards Covered:5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 5.1.2.2 - Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number.5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. Materials: Smartboard, paper, spinners.Launch: Question of the day activity, “Whittingtons Waterpark uses chlorine tablets to kill bacteria in the pool. State standards say that there needs to be a chlorine level of 2.7651339 mL per liter of water. My pools are at 2.7651347 mL of chlorine per liter of water. Who has more chlorine in their pool? “Discuss results and student answers.Explore: “Using our place value chart we created on the Smartboard, Were going to add in a decimal place and start working through defining the various decimal place values. See if you and a partner can come up with names for seven places behind the decimal. Then as a group well fill in our chart.“Get out your spinners from yesterday and create three different decimal numbers out to the seventh decimal place, challenge yourself and write a number sentence for your three numbers. Write your three number sentences on the board when finished.Once everyone has their three sentences up, try to order them from least to greatest. Ask if this is different from ordering whole numbers and why. If students struggle, write it in standard form: example, two tenths = .2Share: “Where do we use decimals outside the classroom?” Generate a list on the Smartboard.Summarize: “How is ordering decimals different from ordering whole numbers? Why? Where do you see decimals outside of the math classroom?”Day 6(Rounding Races)Standards Covered:5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 5.1.2.5 - Round numbers to the nearest 0.1, 0.01 and 0.001. 5.1.2.2 - Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number.Materials: Smartboard, paper, spinnerLaunch: Question of the day activity, “What does it mean to round numbers? Do you think we could round decimals? Give me an example of where you think this does or doesnt work.” Discuss results and student answers.Have students create this format. . Similar to the games played on previous days (See day 1), choose a student to play against to model the game play for the class (great time to cover decimal rounding). Before starting pairs play paper rock scissors, one match, winner = player one. Player one decides whether were playing for the greatest value or the least value, player two decides to what place value they will round.Once rules are set, players use their spinners to fill their boxes, then they round according to the rules they have picked. Student that has either the greatest or least number (depending on the rules they picked wins that round)Explore: Let students play the game, rotating after each match.Share: Ask students to share their strategies with other pairs, “How do you get the greatest value?” “How do you get the least value?” “Has the game now changed since previous days?”Summarize: Did rounding affect anyones match? Is rounding different on the left side of the decimal compared to the right side? Day 7(Fractions: Area Model)Standards Covered:5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. 5.1.2.4 - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts. Materials: Smartboard, paper, inch grid paper, Navigating through Number and Operations in Grades 3-5 Lesson: “Fraction Models p.27”, fraction circles CD-rom, tiles,Launch: Question of the day activity, “I cooked a large pepperoni pizza, and I cut it into 31 pieces. If I ate 13 of those pieces, what would be the fraction of pizza I ate?” Discuss results and student answers.Review numerator and denominator. Remind them that denominator indicates the pieces of the whole,.Go through the engage activity from Navigating through Number and Operations in Grades 3-5 pg. 28-30.Explore: Introduce the area model for displaying fractions, work through the lesson using the fraction circles. Distribute manipulatives and have students start working on fraction model charts made from folding paper into fourths (2x2 array). Let them choose four fractions to represent on the charts. Challenge them to use different representations (circles, squares, etc.) for their area models/fraction pictures.Share: Select a few students to show their different area models on the Smartboard.Summarize: “What shapes or manipulatives did you use to represent fractions in your area models?” “Does the shape you choose change the value of the fraction?” “Could I use any shape to represent a fraction?”Day 8(