structured curriculum lesson plan day: 044 subject: mathematics grade level:
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STRUCTURED CURRICULUM LESSON PLAN
Day: 044 Subject: Mathematics Grade Level: 4
Correlations (SG,CAS,CFS): 6C2; 6D1; 8D2
ITBS/TAP:Solve single-step problems using multiplication or division with whole numbers
ISAT:
Unit Focus/Foci
Multi-digit Multiplication
Instructional Focus/Foci
Understanding multiplication as it relates to the power of 10
Materials
Six-Group Activity: Multiplication (Multiply by tens)Math journalsPlay moneyBase ten blocksPlace value blocks
Educational Strategies/Instructional Procedures
Warm-up Activity:
Ask the students that if they would rather have 5 dollars, 50 dimes, or 500 pennies if given thechoice. (Answers may vary, but all three choices have the same value.)
Mental Math:
Have students respond to the following problems using mental math.
100 x 7 = (700) 1000 x 7 = (7,000)100 x 9 = (900) 1000 x 9 = (9,000)
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100 x 3 = (300) 1000 x 3 = (3,000)100 x 8 = (800) 1000 x 8 = (8,000)100 x 5 = (500) 1000 x 5 = (5,000)
Lesson:
Guide the students through multiplying by powers of 10. Explain the strategy that is applied inthe examples given.
In the following problem have students count how many zeros there are in the power of 10 andwrite that many zeros after the other factor.
1. 100× 7=n 2. 1000× 7=n
3. 1000× 6=n 4. 1000× 65=n
5. 100× 73=n 6. 10× 583=n
7. 583× 10=n 8. 68× 100=n
9. 10,000× 583=n 10. 657× 10=n
11. 10× 392=n 12. 497× 1000=n
13. 16× 1000=n 14. 709× 10=n
15. 200× 1000=n 16. 503× 10=n
17. 100× 783=n 18. 649× 1000=n
19. 594× 1000=n 20. 86× 100=n
21. How many years are there in ten centuries?
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Say: When you write 0 after 4, are you adding or multiplying? You are multiplying 4 x 10. Youcan show the product of 4 x 100 by writing 2 zeros after the 4. How can you write the product of4 x 10,000 (by writing 4 zeros after the 4.)
Have students write the following rule in their math journals.
A rule for multiplying numbers ending in zero, would be to count how many zeros there are inthe power of 10 and write that many zeros after the other factor.
Using the rule, review these problems with the students at the chalkboard.
10× 7=n 68× 100=n 100× 496=n
Example 1: Ask the students how many zeros there are in the power of 10.10 x 7 = 70# of 0 = 17 followed by one zero = 70one zero in power of ten = the factor followed by one 0 = 70
Example 2:68 x 100 = 6800# of zeros = 268 followed by two zeros = 6800two zeros in the power of ten = the factor followed by two 0’s = 6800
Example 3:100 x 496 = 49,600The factor 496 followed by two 0’s from the power of 10 equals 49,600.
Using the examples demonstrated as a reference, have the students complete the problemswritten on the chalkboard. Ask students to write a written explanation for solving the wordproblem.
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Ten Statements
Review the ten statements and have the students write yes if they heard it in today’s lesson andno, if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.
1) The rule for multiplying numbers ending in zero, would be to count how many zeros thereare in the power of 10. (yes)
2) One of the rules for determining power of 10 is to count the number of zeros in the powerand write that number of zeros after the factor. (yes)
3) In example 1 from the chalkboard, the example is not really adding a zero, it is multiplyingthe factor times ten. (yes)
4) The purpose of multiplying two-digit numbers by one-digit numbers is to teach the standardalgorithm for multiplying a two-digit number by a one-digit number. (no)
5) Place value is important when calculating math problems that are multiplied by the power of10. (yes)
6) 50 dimes, 500 pennies, and 5 dollars are all equal in value. (yes)7) In this example: 3 followed by one 0 (30) – 30, we used the term add, but in actuality we
multiplied. (yes)8) In the problem 10,000× 10,000, there are 8 zeros, when you count by power of 10 there are 7.
Rationale: the factors contained a zero. (no)9) To find product of 3 by 10,000 write 4 zeros after the 3. (yes)10) Function machines can perform multiplication, subtraction and addition if programmed to do
so. (no)
Free-Choice Lesson
Have the students choose a lesson from the Free-Choice Activity sheet (one box per day).
Six-Group Activity
Have a group of six students, two from each ability level, complete the teacher-directed activitysheet: Multiplication (Multiply by tens).
Math Workshop
Have the students work in the Math Workshop after completing their Free-Choice Lesson.
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Integration with Core Subject(s)
LA: Understanding explicit, factual informationUnderstanding the meaning of words in context
SC: Apply scientific method to solve problemsAnalyze and interpret data
SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose
Connection(s)
Enrichment: Have students design an area of five square feet and a perimeter of ten feet.
Suggest that students use the following questions to guide them.How many tiles will it take?How many measure around the perimeter?How should you arrange the tiles?
Fine Arts:
Home:
Remediation: See attached Six-Group Activity sheet: Multiplication (Multiply by tens).
Technology:
Assessment
Informally assess students’ class participation, and computations. Check for 80% accuracy.
Homework
Have students write the steps and rationale for the solution to the following problem: The Moonfamily made a patio using bricks. There are 20 rows of bricks with 100 bricks in each row. Howmany bricks are there all together?
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Dictate these problems to the students. Have them write the problems, then solve the problemsfor homework.
1. 503× 10 = n2. 800× 100 = n3. 657× 10 = n4. 10× 392 = n5. 1000× 7 = n
Teacher Notes
Stress knowledge of place value and multiplication facts. Make manipulatives available forpractice.
Answer to Enrichment problem:
Or any combination of three tiles in one row and two in another.
Answers to Homework:
1. 50302. 80,0003. 6,5704. 3,9205. 7,000
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STRUCTURED CURRICULUM LESSON PLAN
Day: 045 Subject: Mathematics Grade Level: 4
Correlations (SG,CAS,CFS): 6A2; 6C2
ITBS/TAP:Perform arithmetic operationsUnderstand number systems
ISAT:
Unit Focus/Foci
Multi-digit Multiplication
Instructional Focus/Foci
Multiplying by multiples of 10
Materials
Six-Group Activity: Multiplication (Multiply by 10’s)Math journalsMulti-color chalk
Educational Strategies/Instructional Procedures
Warm-up Activity:
Write the following problems on the chalkboard. Instruct students to copy the problems in theirjournals. Have students estimate and solve problems 1-5.
1. 6 8 4 2. 4 0 3 3. 8 1 3 7 4. 5 0 0 5. 9 0 7 - 2 6 9 -1 0 7 2 9 1 9 - 2 6 8 - 3 8 6
6. The answer to a subtraction problem is called the ______________ .7. A number from which another number is subtracted is called the ______________ .8. What is a subtrahend?
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Lesson:
Review multiplication terms: product (the result of multiplying two numbers) and factor (oneof the numbers multiplied to give a product).
Review multiplying by powers of 10.
Write 48 x 100 on the chalkboard. Tell students that they can determine the answer to thisproblem using mental math. Have students start by looking at 48, then count the zeros in 100.There are two. Have students put two zeros after the 48 (4800). (The zeros may be written incolor in both the 100 and 4,800 to emphasize this.) Tell students that the final step is to placecommas where needed (4800).
Write these three problems on the chalkboard:1) 7 x 10 2) 22 x 100 3) 451 x 1000.
Have students go to the chalkboard to solve the problems while the others work their problems intheir math journals. Ask students to explain how they got their answers.
Introduce powers of 10. Write 103 on the chalkboard. Tell students that this is read 10 to thethird power. Write 105 and tell students that this is read 10 to the fifth power. Write 104 and aska student to read it.
Repeat with more examples.
Write 100, 101, 102, 103, 104, 105, and 106 in a column on the chalkboard. Tell students that theyare now going to write these powers of 10 as standard numerals. Next have them write an equalsign followed by a one next to the 100. Ask what the power is for this number (0). Tell studentsthat the power tells how many zeros will be written after the one, in this case, 0. Therefore 100 isequal to 1.
Next look at 101. Have students write an equal sign and a 1 next to it. Ask what the power is. 1)Ask how many zeros should be written after the 1. 2) Therefore, 101 is equal to 10. Do thesame with the remaining numbers in the column.
Write 10,000 on the chalkboard. Tell students that they will now change a standard numeral to apower of 10. Write an equal sign and 10 next to the 10,000. Have students count the zeroes inten thousands. (4) Tell them that this is the power they will write next to the 10. (104) Writemore multiples of 10 and have students change them to powers of 10. Try a few numbers greaterthan 1,000,000.
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Write 7 x 50 on the chalkboard. Tell students to think of 50 as 5 x 10. So 7 x 50 = 7 x (5 x 10)7 x (5 x 10) = (7 x 5) x 10. This is an example of the Associative Property of Multiplication.Instruct students to work the problem from left to right: 7 x 5 = 35, 35 x 10 = 350.
Write the problems 1) 8 x 70, 2) 7 x 900, and 3) 500 x 3 on the chalkboard. Have students go tothe chalkboard to solve while others work in their journals. Have students at the chalkboardexplain how they solved their problems.
Write 500 x 7000 = ______ on the chalkboard. All of the zeros should be written in a differentcolor. Ask students to name the digits which are not in color (5 and 7). Tell students to multiplythe 5 x 7 and write the 35 on the blank line: 500 x 700 = 35___ . Next have students count thezeros in 500 (2) and the zeros in 700. (2) Ask how many there are altogether. (4) Havestudents add 4 zeros to the right of 35: (500 x 700 = 350,000). Ask students what they shoulddo next add commas 350,000.
Write the following on the chalkboard: 1) 200 x 600 2) 4000 x 80 3) 500 x 800Have students go to the chalkboard while others solve problems in their math journals. Makesure students understand why there are five zeros at the end of problem 3. (because 5 x 8 = 40and there are two zeroes in 500 and two zeros in 800
Ten Statements
Review the ten statements and have the students write yes if they heard it in today’s lesson andno, if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.
1) In the answer for 4000 x 80 there are 4 zeros. (yes)2) 24 is divisible by 6. (no)3) When mentally solving 6 x 40, you should think of 40 as 4 x 10. (yes)4) 900 + 50 + 4 is the expanded form of 954. (no)5) To find the value of 105 write a one followed by five zeros. (yes)6) When multiplying 57 x 100, you will write the 57 first and then count the zeros in 100. (yes).7) 1000 is equal to 103. (yes)8) 6 feet = 2 yards. (no)9) In the problem 500 x 700, you will multiply 5 x 7 to get 35 and then add 4 zeros. (yes)10) The numbers multiplied to give a product are called factors. (yes)
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Free Choice Lesson
Have the students choose a lesson from the Free Choice Activity sheet (one box per day).
Six-Group Activity
Have a group of six students, two from each ability level, complete the teacher-directed activitysheet: Multiplication (Multiply by tens).
Math Workshop
Have the students go into the Math Workshop after completing their Free Choice Lesson.
Integration with Core Subject(s)
LA: Understanding explicit, factual informationUnderstanding the meaning of words in context
SC: Apply scientific method to solve problemsAnalyze and interpret data
SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose
Connection(s)
Enrichment:
Fine Arts:
Home:
Remediation:
Technology:
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Assessment
Review students’ responses in the in lesson, and the Ten Statements activity to formally assesstheir understanding of key concepts presented
Homework
Teacher Notes
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STRUCTURED CURRICULUM LESSON PLAN
Day: 046 Subject: Mathematics Grade Level: 4
Correlations (SG,CAS,CFS): 6B3; 6C2; 6D1
ITBS/TAP:Solve single-step problems using multiplication or division with whole numbers
ISAT:
Unit Focus/Foci
Multi-digit Multiplication
Instructional Focus/Foci
Practicing multiplication with multiples of 10
Materials
Six-Group Activity: Multiplication (1-digit by 3-digit)Meter sticksCoinsCentimeter rulerBugs Island (handout)Math journals
Educational Strategies/Instructional Procedures
Warm-up Activity:
Write the following on the chalkboard.
Tesha can buy barrettes in packs of two, four, six, and ten. Using all possible combinations ofpacks, how many different ways can she buy 20 barrettes? (19 ways)
Perform a drill in which numbers are presented to be added or multiplied. All answers should bebetween 100 and 200. Show thumbs up if the answer falls within the range or thumbs down if itfalls outside the range.
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Have students review the directions for the mental math activity. Play the Thumbs Up-ThumbsDown game according to the pre-set rules.
1. 38 + 32 (up) 2. 23 x 10 (down)3. 58 + 43 (down) 4. 7 x 40 (down) 5. 75 + 85 (down)
Vocabulary Review
1. Centimeter: a unit of measure, one hundredth of a meter2. Millimeter: one thousandth of a meter3. Kilometer: metric measure equal to one thousand meters
Lesson:
Explain to the students the importance of understanding metric conversions and measurements.Explain to the students that this lesson is intended to assess mastery of multiplication skills usingmultiples of 10 and powers of 10.
Example: 3200 (two zeroes here) x 200 (two zeroes here)
640,000 (write four zeroes here)
Then multiply 32 x 2.
Ask a student to explain the problem. (Possible answer/reply: For each zero in the factor, thereis also one in the product.)
Instruct the students to take out paper and pencil and solve problems that you assign from thetextbook or present the problems listed below. When students complete this assignment, havethem submit it for grading.
Problems:
1. 10 x 10 (100) 2. 100 x 10 (1,000) 3. 10 x 1,000 (10,000)4. 1,000 x 1,000 (1,000,000) 5. 90 x 30 (2,700) 6. 300 x 50 (15,000)7. 100 x 100 (10,000) 8. 200 x 70 (14,000) 9. 60 x 60 (3,600)10. 70 x 20 (1,400) 11. 150 x 10 (1,500) 12. 30 x 300 (9,000)13. 30 x 40 (1,200) 14. 50 x 50 (2,500) 15. 90 x 80 (7,200)16. 50 x 800 (40,000) 17. 90 x 900 (81,000) 18. 20 x 60 (1,200)
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19. 20 x 600 (12,000) 20. 480 x 10 (4,800) 21. 60 x 500 (30,000)22. 35 x 100 (3,500) 23. 35 x 1,000 (35,000) 24. 5,000 x 900 (4,500,000)25. 480 x 100 (48,000)
(Allow students to use centimeter rulers, meter sticks, play money and scratch paper to completethe assignment.)
When the students have completed the assignment, ask them to put a problem on the chalkboardand explain the steps they used to solve it.
Next, have the students read the story problem The Treasure of Bugs Island, answer thequestions, and draw the map according to the directions given in the story.
Bugs Island
Bugs Island. The south shore of Bugs Island is straight and about 2 kilometers long. On the eastside, the shore goes straight north for 3 kilometers. Then the shore goes west for 1 kilometer.Then the shore turns south for a short distance. Then there is a large bulge of land, about 1kilometer across, sticking out toward the west. After the bulge, the shore goes straight southagain until it meets the south shore. In the middle of the bulge is a small round lake. Out of thelake comes a stream, which flows eastward to the sea. The stream makes a line like a humanface, with a pointy nose pointing south.
Assemble students in groups of four. Instruct them to describe the task of drawing a map fromwritten directions in their math journals after having discussed as a class what he/she perceivesas the most difficult part of the assignment.
Ten Statements
Review the ten statements and have the students write yes if they heard it in today’s lesson andno, if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.
1) Bugs Island, is a story requiring students to draw a map following a verbal description.(yes)
2) The purpose of drawing the map was to try and find a royal treasure that supposedly hadbeen stolen. (yes)
3) It was necessary to have some knowledge of metric measurement in order to construct themap. (yes)
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4) When multiplying with multiples of 10 it is a helpful to remember to count the zeros and thenmultiply the non zero digits. (yes)
5) Distance is defined as space in between. (no)6) Problem solving can use money as a part of the problem. (no)7) Solving problems like 5000 x 900 = 4,500,000 gives practice with powers of 10 and
multiples of 10. (yes)8) Centimeter rulers were used to solve problems in this lesson. (yes)9) Using multiples of 10 is one way to practice multiplication skills. (yes)10) When multiplying decimals you don’t need to line the decimals up to complete the problem.
(no)
Free Choice Lesson
Have the students choose a lesson from the Free Choice Activity sheet (one box per day).
Six Group Activity
Have a group of six students, two from each ability level, complete the teacher-directed activitysheet: Multiplication (1-digit by 3-digit).
Math Workshop
Have the students work in the Math Workshop after completing their Free Choice Lesson.
Integration with Core Subject(s)
LA: Understanding explicit, factual informationUnderstanding the meaning of words in context
SC: Apply scientific method to solve problemsAnalyze and interpret data
SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose
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Connection(s)
Enrichment: Have students solve the following problem: One day, a new plant had only 7 open leaf buds. The next day there were 10 more new open buds. The following day, 14 more new buds opened, and the next day, 19 more new ones opened. At the end of the week, if the pattern continued, how many leaf buds had opened on the plant?
Fine Arts:
Home:
Remediation: See attached Six-Group Activity sheet: Multiplication (1-digit by 3-digit).
Technology:
Assessment
Homework
Instruct the students to draw a map, label the parts, and use the vocabulary that was introduced intoday’s lesson in the measurements for your map. The map can give directions which lead toanything you choose.
Teacher Notes
Make a note of those students that still need special help.
Answer to Bugs Island: The Island map should look roughly like this:
Answer to Enrichment:
Day 1 2 3 4 5 6 7New 7 10 14 19 25 32 40Total 7 17 31 50 75 107 147
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Bugs Island Worksheet
Work in groups. Discuss your answers and how you figured them out. Then compare youranswer with those of other groups.
1. Draw a map of Bugs Island. Try to use every fact that the story givesyou.
2. How would you decide the shape of Bugs Island?
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STRUCTURED CURRICULUM LESSON PLAN
Day: 047 Subject: Mathematics Grade Level: 4
Correlations (SG,CAS,CFS): 7A1; 8B1
ITBS/TAP:Estimate, make, and determine acceptable levels of accuracy
ISAT:
Unit Focus/Foci
Multiplication and Division
Instructional Focus/Foci
Rounding and approximating
Materials
Six-Group Activity: Multiplication (Rounding)
Educational Strategies/Instructional Procedures
Warm-up Activity:
Write the following problems on the chalkboard.
Find the pattern. Then fill in the missing numbers.a. 14, 15, 16, 17, ___, ___, ___b. 3, 5, 7, ___, 11, ___, ___
What do the following numbers have in common?
c. 48, 80, 8, 72, 16, 32, 88
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Lesson:
Say to the students: At times we use numbers to mean about how many. You might say thatabout 3 and one half million people(3,500,000) live in Chicago, or your math book has about300 pages. We are going to practice the skill known as rounding.
Rounding has to do with numbers that are easier to work with. Example: 72 or 70; 32, or 300;4981 or 5,000
Say: Multiples of 10, 100, and 1,000 are easier to work with than other numbers.
Sometimes when we say, write, or use numbers, we do not have to be exact.
We can replace a number by the nearest multiple of 10 or 100 or 1,000. We call this processrounding.
How exact we need to be depends on what the numbers will be needed for.
Have students decide which answer matches each description.
I. a. School starts at 1. 7:14b. We eat dinner 2. around 6:00c. The plane leaves at 3. 8:30
II. a. The trip from here to St. Louis 1. every 6 monthsb. From here to the loop 2. about 6 hoursc. visit to the dentist 3. about 20 minutes
Tell students: Rounding is also useful when you do not need an exact answer to a problem.
Example: Robin wants to buy 3 CDs at $7.99 each. She has $25, does she have enough for theCD’s?
The answer is yes. You can figure that out without finding the exact amount. ($7.99 rounds to$8.00 x 3 = $24. $25 is larger than $24 so Robin has enough to buy 3 CDs.)
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Activity: Write the following on the chalkboard.
1. James sells hot dogs at the football games for $.95 each. If he sells 285 hot dogs, will hemake $300? (no)
2. Dwayne wants to buy 25 pencils. The pencils costs $.15 each. Dwayne has $3.00. Does hehave enough money to buy the pencils. (no)
3. At the party, Ashley said her guests consumed more than 1,000 cans of soda pop. A case ofsoda pop contains 24 cans. Ashley’s party guests consumed almost 42 cases of pop. (yes)
4. Brandi is nine years old. She wants to know if she is more than 2400 days old. Is she? (yes)
Ten Statements
Review the ten statements and have the students write yes if they heard it in today’s lesson andno if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.
1) Sometimes we use numbers to mean about how many. (yes)2) When you use the word about, that is a skill called rounding. (yes)3) Rounding has to do with numbers that are easier to work with. (yes)4) To find the area of a rectangle, you multiply the length by the width. (no)5) A line of symmetry in a figure cuts the figure into two parts that are mirror images of each
other. (no)6) Multiples of 10, 100, and 1,000 are easier to work with than other numbers. (yes)7) Sphere, cylinder, pyramid, and prism are mathematical names for many of the objects we see
and use in our everyday lives. (no)8) Sometimes when we say, write, or use numbers, we do not have to be exact. (yes)9) The number 7000 is easier to work with than 6,899. (yes)10) Rounding is also useful when you do not need an exact answer to a problem. (yes)
Free Choice Lesson
Have the students choose a lesson from the Free Choice Activity sheet (one box per day).
Six Group Activity
Have a group of six students, two from each ability level, complete the teacher-directed activitysheet: Multiplication (Rounding).
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Math Workshop
Have the students work in the Math Workshop after completing their Free Choice Lesson.
Integration with Core Subject(s)
LA: Understanding explicit, factual informationUnderstanding the meaning of words in context
SC: Apply scientific method to solve problemsAnalyze and interpret data
SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose
Connection(s)Enrichment:
Fine Arts:
Home:
Remediation: See attached Six-Group Activity Sheet: Multiplication (rounding).
Technology:Assessment
Homework
Have students read a newspaper article to find examples of rounded numbers.
Teacher Notes
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Six-Group Activity
Multiplication (rounding)
Materials:10 index cards (5” x 7”)1 black marker1 pencil1 (9 ½” x 6 ½”) envelope
Prepare the following index cards using the black marker to write the problems on the front ofthe cards. Use the pencil to write the answers on the back of cards.
72
58×
75
322
×
51
27
×
61
79
×
28
52
×
82
491
×
77
223
×
32
586
×
57
46
×
28
512
×
Answers:
60 58
70 72
×× 80 75
003 223
×× 50 51
30 72
×× 60 61
80 79
×× 30 28
50 52
××
80 82
005 914
×× 80 77
002 232
×× 30 32
006 865
×× 60 57
50 64
×× 30 28
005 125
××
Copy the study board to use it with reteaching the lesson.
Rounding numbers
Say: Step 1: When rounding numbers, if no specific value of number has been given to round:Round the whole number. Example: 356 rounds to 400.
Step 2: When looking at the whole number, remember the rules. If the number next to thenumber before the last number to the left is 5 or above, round up.
Example: 356
A 5 or more round up. 400 and 100 hundred to the 300 + 100 = 400.
Step 3: Look at the number to the far left. If the number next to it on the right is 4 or less, rounddown.
Example: 427
A 2 is 4 or less; round down. The rounded number is 400
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Use these example problems to explain how to round numbers.Example: 563, 421
Ask these questions:
1) For the number 563, what is the last number to the left? (5)2) Which number are we rounding? (6)3) What is the rule for numbers that are 5 or higher? (round up if the number is 5 or higher)4) What will we round the number up to? (600)5) Look at the number 421. What number are we rounding? (4)6) What is the number next to the 4 on the right? (2)7) What is the rule for numbers that are 4 or less? (round down)8) What would the new number be? (400)
Tell the students that they are going to do an activity that involves rounding multiplicationproblems. Let the students know that they don’t have to multiply; they will just round bothnumbers in the problem. Tell the students that when a card is placed on the table, they have oneminute to write the answer before it will be revealed. When the minute has passed, turn the cardover to reveal the answer and say: The answer is… Complete the remaining cards in the sameway.
Store the index cards and study board in the (9½” x 6½”) envelope.
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STRUCTURED CURRICULUM LESSON PLAN
Day: 048 Subject: Mathematics Grade Level: 4
Correlations (SG,CAS,CFS): 6A1,2; 6C2; 6D1,2
ITBS/TAP:Perform arithmetic operations involving integers, fractions, decimals and percentsUnderstand number systems
ISAT:
Unit Focus/Foci
Multi-digit Multiplication
Instructional Focus/Foci
Formally assessing multiplication by powers and multiples of 10
Materials
Educational Strategies/Instructional Procedures
Formal Assessment (See attached.)
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Test
Write these numbers as powers of ten.
1) 1000 2) 100,000 3) 10
Multiply. Remember placement of commas.
4) 10 x 1000 5) 10,000 x 10,000 6) 1,000 x 1,000 7) 10,000 x10
8) 20 x 70 9) 300 x 800 10) 6,000 x 40 11) 500 x 400
Write as standard numerals.
12) 107 13) 104 14) 102
15) There are 3000 pens in a package. How many pens are there in 700 packages?
16) Bill wants to give 100 M & M’s to each of his classmates. There are 31 people in his class.How many M & M’s does he need to buy?
Approximate the answers to these questions.
17) Cathy delivers 46 newspapers each day. Will she deliver more than 200 newspapers in aweek?
18) Sara wants to buy 20 candy bars. Each candy bar costs $0.18. She has $4.00. Does she haveenough to buy the candy bars?
Solve.
19) 167 x 10 20) 48 x 1000
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Ten Statements
Review the ten statements and have the students write yes if they heard it in today’s lesson andno, if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.
No Ten Statements today.
Free Choice Lesson
Have the students choose a lesson from the Free Choice Activity sheet (one box per day).
Six Group Activity
No Six-Group Activity today.
Math Workshop
Have the students work in the Math Workshop after completing their Free Choice Lesson.
Integration with Core Subject(s)
LA: Understanding explicit, factual informationUnderstanding the meaning of words in context
SC: Apply scientific method to solve problemsAnalyze and interpret data
SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose
Connection(s)
Enrichment:
Fine Arts:
Home:
Remediation:
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Technology:
Assessment
Formal Assessment: Test (See attached.)
Homework
Teacher Notes
Answer Key
1. 103 2. 105 3. 101 4. 10,000 5. 100,000,0006. 1,000,000 7. 100,000 8. 140 9. 2,400 10. 24,00011. 2,000 12. 10,000,000 13. 10,000 14. 100 15. 2,100,00016. 3,100 17. Yes 18. Yes 19. 1,670 20. 48,000
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STRUCTURED CURRICULUM LESSON PLAN
Day: 049 Subject: Mathematics Grade Level: 4
Correlations (SG,CAS,CFS): 7A1
ITBS/TAP:Estimate and determine acceptable levels of
accuracy
ISAT:
Unit Focus/Foci
Multiplication and Division
Instructional Focus/Foci
Approximating answers
Materials
Six-Group Activity: Division (Estimating)
Educational Strategies/Instructional Procedures
Warm-up Activity:
Write the following on the chalkboard.
Larry’s club sold tickets to the dance. If he rounded the number of tickets sold to the nearest ten,they would have sold 150 tickets. If they rounded the number to the nearest hundred, they soldabout 200 tickets. Give all the possible exact numbers of dance tickets Larry’s club could havesold. (150, 151, 152, 153, 154)
Lesson:
Say to the class: When you approximate an answer, you do not have to give just one number.You can give two numbers and say that the answer is between those two numbers.
318
Example: A mat is 56 inches by 27 inches long. About how long is the mat? The answer mustbe less than 60 x 30 square inches. So it must be less than 1800 square inches.
The answer must be greater than 50 x 20 square inches. So it must be greater than 1000 squareinches.
The answer must be between 1000 and 1800 square inches.Provide the following example problem. The music room is 28 feet long and 12 feet wide.Approximate the area by finding two numbers that the area must be between.
Ask:
1) Can the area be 600 square feet? (no)2) Could the answer be 278 square feet? (no)
(The answer must be greater than 280 square feet; 28 x 10)
Continue trying to find two numbers for the following.
1) 32 x 17 (30 x 10, 30 x 20)2) 28 x 195 (30 x 200, 20 x 200)3) 46 x 61 (40 x 60, 50 x 60)4) 206 x 38 (210 x 40, 200 x 30)
Say: Remember when approximating an answer, you can say that it is between two numbers.
A good method to use in approximation is to round the lesser factor. Rounding the lesser factoris likely to have a greater effect than rounding the greater factor.
When both factors are rounded up, the approximation is likely to be too high. When both arerounded down, the approximation is likely to be too low.
If two factors are rounded in appropriate directions the one that is rounded more is likely tohave the greater effect.
There is no single best approximation method.
319
Ten Statements
Review the ten statements and have the students write yes if they heard it in today’s lesson andno, if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.
1) To approximate an answer, the answer can be between two numbers. (yes)2) In approximation, you can round the greater or lesser factor. (yes)3) There is no single best approximation method. (yes)4) When both factors are rounded up, the approximation is likely to be too high. (yes)5) A probability is a number that tells what fraction of a time something is expected to happen.
(no)6) When both factors are rounded down, the approximation is likely to be too low. (yes)7) A fraction with a numerator greater than its denominator is called an improper fraction. (no)8) A decimal point is the dot between the ones place and the tenths place. (no)9) If two factors are rounded in appropriate directions, the one that is rounded more is likely to
have the greater effect. (yes)10) 32 x 8796 ≈ 30 x 9000 = 270,000. (yes)
Free Choice Lesson
Have the students choose a lesson from the Free Choice Activity sheet (one box per day).
Six Group Activity
Have a group of six students, two from each ability level, complete the teacher-directed activitysheet: Division (Estimating).
Math Workshop
Have the students work in the Math Workshop after completing their Free Choice Lesson.
Integration with Core Subject(s)
LA: Understanding explicit, factual informationUnderstanding the meaning of words in context
SC: Apply scientific method to solve problemsAnalyze and interpret data
320
SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose
Connection(s)
Enrichment:
Fine Arts:
Home:
Remediation: See attached Six-Group Activity sheet: Division (Estimating).
Technology:
Assessment
Homework
Have students create three word problems in which they ask a question that can be answered byrounding or approximation.
Teacher Notes
321
Six-Group Activity
Division (Estimating)
Materials:10 index cards (5” x 7”)1 black marker1 pencil1 envelope (9 ½” x 6 ½”)
Prepare the following index cards using the black marker to write the problems on the front ofthe cards. Use the pencil to write the answers on the back of the cards.
3 23 4 18 6 34 7 58 9 30 9 40 3 25 4 35 5 37 2 15
Answers:27
2
21
233
r 24
2
16
184
r 45
4
30
346
r 28
2
56
5875
r 33
3
27
309
r 44
4
36
409
r
3 25
24
8 1
1
R 38
3
32
354
r 27
2
35
375
r 17
1
14
152
r
Copy this study board and use this with the reteaching lesson.
Estimating
Say: Step 1: Estimate and divide. 5 39
Estimate the greatest number of 5’s in 39. Since 7 × 5 = 35, 7 is the greatest number of
5’s in 39. Write the 7 in quotient in the ones place. 5 397
.
Step 2: Multiply 7 × 5 = 35. Write 35 under 39. 5 397
35
Step 3: Subtract 39 - 35 = 4. The remainder must be less than the number you are dividing by;4 is less than 5. Write the remainder in the quotient.
322
Review the steps in the study board with the students using this example: 8 67
Ask these questions about this problem: What is the first step? (estimate how many 8’s are in37)? Can you use multiplication to estimate? (yes) What number would you multiply 8 by? (8)(8× 8 = 64)? What would you subtract 64 from? (67) What is the remainder? (3)
38
3
64
678
r
Tell the students that you want them to risk writing the answer to some division problems thatwill have remainders. Give the students time to write the answers to the questions. Whenrevealing the answer, say: The answer is…… Complete the rest of the problems the same way.Store the study board and index cards in the 9 ½” x 6 ½” envelope.
323
STRUCTURED CURRICULUM LESSON PLAN
Day: 050 Subject: Mathematics Grade Level: 4
Correlations (SG,CAS,CFS): 6C3
ITBS/TAP:Add, subtract, multiply, and divide single - and multi-digit whole numbers
ISAT:
Unit Focus/Foci
Multiplication and Division
Instructional Focus/Foci
Multiplying two-digit numbers by one-digit numbers
Materials
Six-Group Activity: Multiplication (2-digit by 2-digit)
Educational Strategies/Instructional Procedures
Warm-up Activity:
Write the following on the chalkboard. Have students solve each problem.
1) 9 x 8 2) 10 x 9 3) 8 x 7 4) 5 x 9 5) 7 x 9
Lesson:
Ask students to solve the following problem.
Christopher and Monique collect cans as a fundraising event. They collected cans in cartons of24. They filled 8 cartons with cans. How many cans have they collected?
After a few minutes, offer this solution.
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Monique said that if there were 20 cans in a carton, they would have 160 cans because 8 x 2 =16, so 8 x 2 tens is 16 tens and that is 160.
But 4 cans from each carton were left out. 8 x 4 = 32. So if we add 32 cans to 160 cans we have192 cans. Therefore: 24
x 8 32 (8 x 4)
+ 160 (8 x 20 or 8 x 2 tens) 192
This way may seem too confusing or too long. A shorter way to solve the same problem wouldbe as follows.
29 Start at the right. Multiply the ones digit by 8 (8 x 4 = 32) that is x 8 3 tens and 2. Write the 2 and remember the 3 tens for the next column. 2
24 Multiply the tens digit by 8. 8 x 2 = 16. 16 tens plus the 3 tens you x 8 remembered is 19 tens. 192
If you have trouble remembering the number that you saved from the previous column, you maywrite the number above the next digit of the top number. Cross it off when you use it.
However, if you write the numbers, be sure to make them small and neat so you do not getconfused.
Activity: Have students complete the answers to each of the following problems.
1. 24 2. 26 3. 43 4. 60 x 6 x 9 x 3 x 8
5. 90 6. 83 7. 73 8. 19 x 3 x 4 x 4 x 6
325
Ten Statements
Review the ten statements and have the students write yes if they heard it in today’s lesson andno, if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.
1) You can multiply two digits by one digit by multiplying first the ones and then the tens andadding. (yes)
2) In multiplying, you work from right to left. (yes)3) In the shorter method of multiplying, you must remember to add the number you saved.
(yes)4) If you cannot remember the number you saved, write it above the next digit of the top
number. (yes)5) You should cross the saved number off after you use it . (yes)6) You should write the saved number small and neatly to avoid confusion. (yes)7) 8 x 20 = 8 x 2 is 16 and 8 x 2 tens is 16 tens which equals 160. (yes)8) In finding multiples of 9, the sum of the digits will either be 9 or a multiple of 9. (no)9) All multiples of 5 end in 0 or 5. (no)10) Sometimes we use numbers to mean about how many. (no)
Free Choice Lesson
Have the students choose a lesson from the Free Choice Activity sheet (one box per day).
Six Group Activity
Have a group of six students, two from each ability level, complete the teacher-directed activitysheet: Multiplication (3-digit by 2-digit).
Math Workshop
Have the students work in the Math Workshop after completing their Free Choice Lesson.
Integration with Core Subject(s)
LA: Understanding explicit, factual informationUnderstanding the meaning of words in context
SC: Apply scientific method to solve problemsAnalyze and interpret data
326
SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose
Connection(s)
Enrichment:
Fine Arts:
Home:
Remediation: See attached Six-Group Activity sheet: Multiplication (3-digit by 2-digit).
Technology:
Assessment
Have students role play teaching each other how to multiply a two-digit number by a one-digitnumber.
Homework
Have students create six multiplication problems of their own to solve, each of which uses adifferent one-digit multiplier.
Teacher Notes
327
Six-Group Activity
Multiplication (2-digit by 2-digit)
Materials:5 index cards (5” x 7”)1 black marker1 pencilChart paper1 envelope (9 ½” x 6 ½”)
Prepare the following index cards using the black marker to write the problems on the front ofthe cards. Use the pencil to write the answers on the back of the cards.
62
23× 27
35× 33
62× 21
15× 42
34×
Answers:
62
186
1240
1426
×23
27
35
135
810
945
×
33
62
66
1980
2046
×
21
15
105
210
315
×
42
34
168
1260
1428
×
Copy the study board and use it with this reteaching activity.
Multiplying 2-digit by 2-digit
Say: Step 1: Multiply the ones first. (8 × 2 = 16. Rename the 16 as 1 ten + 6 ones. Write the 6in the ones column and write the 1 over the tens column.Example: 162 A × 48 6
Step 2: Multiply 8 times 6. (8 × 6 = 48). Add the renamed 1 to the8× 6 + 1 = 49. (49 tens = 4 hundreds + 9 tens.) Write the 9 in the tens place and the 4 in thehundreds place.
Step 3: Write zero under the 6 in the ones column. This is to hold the place because you arenow multiplying in the tens place.
328
Step 4: Multiply 4 times 2 (4 × 2 = 8). Write the 8 under the 9 in the tens place. 162 × 48 496 80
Step 5: Multiply 4 times 6 (4 × 6 = 24). Write the 4 in the hundreds column and the 2 in thethousands column. (24 hundreds = 2 thousands and 4 hundreds)
62
× 48 496 2480
Step 6: Add the totals.
62
× 48 496 + 2480 2976
Solve a sample problem with the students, showing step-by-step process. Use this example:25× 95. Write the problem on a large sheet of paper.
25
95×
Ask the following questions:
1. What two numbers are you going to multiply first? (5 × 5)2. What is the answer? (25)3. Do we have to rename? (yes)4. What are we renaming and to what? (25 to 2 tens and 5 ones)5. Where do we write the renamed numbers? (write the 5 in the ones place and the 2 over the
tens place)6. What are the next numbers being multiplied? (5 × 2 = 10 = one hundred and zero tens)7. Where do we write the 12? (write the 2 in the tens and the 1 in the hundreds)8. What is the next step? (place a 0 in the ones place)
329
9. Why do we write a zero in the ones place? (to serve as a place holder because we aremultiplying in the tens column)
10. What are the next two numbers to be multiplied? (9× 5 = 45)11. Do we rename the 45? (yes)12. To what? (4 tens and 5 ones)13. What do you do with the 2 already over the 2? (cross it out)14. Why? (because it was already used)15. What is the position of the numbers in 45? (write the 5 in the tens place and the 4 over the 2
in the tens column)16. What are the next two numbers to be multiplied? (9× 2)17. Do we need to rename? (no)18. Why? (because there are no other numbers to be multiplied in the hundreds place)19. What do we do with the 4? (add it to 9 × 2 = 18 + 4 =22; two thousands + 2 hundreds)20. Where do we put the 22? (write one 2 in the hundreds place and the other 2 in the thousands
place)21. What is the last step in this problem? (add)22. What two numbers are being added? (125 + 2250)23. What is the answer? (2375)
Tell the students that they are going to do five problems that are similar to the problem they justcompleted. Show the students a card and tell them there will be a one-minute time limit on eachproblem. Place a card on the table and give the students the time allotted to answer. When oneminute has elapsed, turn the card over to reveal the answer. While doing that say: The answeris… Complete the rest of the cards in the same manner.
Store the study board and index card in the 9 ½” x 6 ½” envelope.
330
STRUCTURED CURRICULUM LESSON PLAN
Day: 052 Subject: Mathematics Grade Level: 4
Correlations (SG,CAS,CFS): 6B3; 6C2; 8D4
ITBS/TAP:Solve single-step problems using
multiplication or division with wholenumbers
ISAT:
Unit Focus/Foci
Multi-digit Multiplication
Instructional Focus/Foci
Practice the multiplication of three digits by one digit
Materials
Six-Group Activity: Multiplication (writing steps to 1-digit by 3-digit multiplication problems)Number cubes 0-5/5-10Overhead projector (optional)Math journals
Educational Strategies/Instructional Procedures
Warm-up Activity:
Write the following problems on the chalkboard. Have the students copy and complete them.This will also provide mental math practice.
1. 50 x 50 2. 20 x 40 3. 30 x 504. 70 x 90 5. 80 x 200 6. 40 x 407. 30 x 600 8. 60 x 90 9. 80 x 400
331
Introduce the terms factors and product. Factors are the numbers being multiplied (8 x 8). Theproduct is the answer to a multiplication problem.
8 (factor) x 8 (factor) 64 (product)
Explain that multiplication is a fast way to add numbers. Example: 8 x 8 = 8 + 8 + 8 + 8 + 8 + 8+ 8 + 8.
Lesson:
Write the following problem on the chalkboard or transparency.413x 2
Step 1: Have students copy the problem in their journals. It is important that they keep thedigits in straight columns. Step 1: Tell students that they are going to multiply each digit in thenumber 413 times 2. Tell students that they will be multiplying from right to left starting withthe ones place of both factors. Have students look at 413 and identify the digit in the ones place(3). Rewrite the problem and write the 3 and 2 using a different color. The different color willindicate which digits are being multiplied.
413x 2
Ask students for the product of 3 x 2. Tell students that, because the digit 3 in 413 is in the onesplace, the product of 3 x 2 will be written in the ones place of the answer also. Write the 6 usingthe same color used for the 3 and 2.
413x 2 6
Step 2: Have students look at 413 and identify the digit in the tens place (1). Have students givethe value of the 1 (1 ten or 10). Rewrite the problem, writing the digits 1 and 2 using a differentcolor.
413x 2 6
332
Ask students for the product of 1 x 2. Tell students that, because the 1 is in the tens place, thatthe product of 1 x 2 will be written in the tens place of the answer also.
413x 2 26
Remind students again to keep their digits in straight columns. After writing the 2 in the tensplace of the product, ask students for the value of that 2 (2 tens or 20). Students shouldunderstand that they are multiplying 10 (1 ten) times 2 and not 1 x 2.
Step 3: Have students look at 413 and identify the digit in the hundreds place (4). Havestudents give the value of the 4 in 413 (4 hundreds or 400). Rewrite the problem, writing the 4and the 2, a different color.
413x 2 26
Ask students for the product of 4 x 2. Tell students that, because the 4 is in the hundreds place,the product of 4 x 2 will be written in the hundreds place of the answer also.
413x 2826
Students should understand that 4 hundreds times 2 equals 8 hundreds.
Write the following problem on the chalkboard.321x 3
Have a student go to the chalkboard to work the problem while the rest of the students solve theproblem in their journals. Remind students to keep digits in straight columns. Have the studentat the chalkboard tell how he/she arrived at the answer (963).
333
Ten Statements
Review the ten statements and have the students write yes if they heard it in today’s lesson andno if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.
1) When multiplying, you should keep all the digits in straight columns. (yes)2) The answer to a multiplication problem is called the product. (yes)3) 6 x 7 = 7 + 7 + 7 + 7 + 7 + 7. (yes)4) In the problem 5 x 3 = 15, 5 and 3 are factors. (yes)5) The sum of two negative numbers is negative. (no)6) A protractor is a math tool. (no)7) When multiplying two numbers, you work from left to right. (yes)8) A semi-circle is half a circle. (no)9) Factors are the numbers you multiply. (yes)10) When multiplying 3 x 6, write the 8 in the ones place and carry the 1 ten. (yes)
Free-Choice Lesson
Have the students choose a lesson from the Free Choice Activity sheet (one box per day).
Six-Group Activity
Have a group of six students, two from each ability level, complete teacher directed activitysheet: Multiplication (Writing the steps to 1-digit by 3-digit multiplication problems)
Math Workshop
Have the students work in the Math Workshop after completing their Free Choice Lesson.
Integration with Core Subject(s)
LA: Understanding explicit, factual informationUnderstanding the meaning of words in context
SC: Apply scientific method to solve problemsAnalyze and interpret data
SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose
334
Connection(s)
Enrichment:
Fine Arts:
Home:
Remediation: See attached Six-Group Activity sheet: Multiplication (Writing the steps to 1-digit by 3-digit multiplication problems).
Technology:
Assessment
Informally assess students’ responses during the lesson and Ten Statements review.
Homework
Have students write and solve the 10 problems on the chalkboard or choose 10 from the text.Problems should be similar to the ones presented in class.
Teacher Notes
335
Six-Group Activity
Multiplication (Writing the steps to 1-digit by 3-digit multiplication problems)
Materials:2 sheet of blank paper (8 ½” x 11”)1 black marker1 envelope (9 ½” x 6 ½”)2 index cards (5” x 7”)
Prepare the following index cards and the two pieces of paper (8 ½” x 11”) with these questionsand answers.
205
× 3
310
× 8
Say: Step 1: Multiply 3 × 5 = 15 ones. Rename the 15 ones as 1 ten + 5 ones. Write the 5 in theones place, and the 1 above the zero.
2 051
× 3
5
Step 2: 3 × 0 tens = 0 tens. Add the 1 ten. Write the 1 in the tens place.2 051
× 3
15
Step 3: 3 × 2 hundreds = 6 hundreds. Write the 6 in the hundreds place.
2 051
× 3
615
336
Writing the steps to 1-digit by 3-digit multiplication problems
Say: Step 1: 8 × 0 ones = 0 ones. Write 0 in the ones place.
310
× 8
0
Step 2: 8 × 1 ten = 8 tens. Write 8 in tens place.
310
× 8
80
Step 3: 8 × 3 hundreds = 24 hundreds. Rename 24 hundreds as 2 thousands + 4 hundreds.Write 4 in the hundreds place and 2 in the thousands place.
310
× 8
2480
Use this problem to review writing the steps to solve 1 digit-by-3 digit multiplication problems.
462
× 2
4Say: Step 1: Multiply the numbers in the ones column. 2 × 2 = 4. As you explain the problem,write the answers down so the students can see them.
Step 2: Multiply 2 ones times 6 tens. 2 × 6 = 12. Rename 12 to 1 ten and 2 ones. Put 2 underthe tens place and place 1 over the 4.Example:
1462
× 2
24Step 3: Multiply 2 ones times 4 tens and add the renamed ten. So 2× 4 + 1 = 9. Write the 9under the hundreds place.
337
Example:
1462
× 2
924
Tell the students that they are going to do two problems the same way, writing in words the stepsto solving the problems. Lay one card on the table and give the students four to five minutes towrite the answer to the question. When the time is up, show the students the written answer.This paper may not be exact as to the right answer: use teacher judgement. Say: The answeris…… Store the index card and written answer key in the 9 ½” x 6 ½” envelope. Repeat thisprocess with the second card.
338
STRUCTURED CURRICULUM LESSON PLAN
Day: 053 Subject: Mathematics Grade Level: 4
Correlations (SG,CAS,CFS): 6C2; 6D1,2
ITBS/TAP:Solve single-step problems using multiplication with whole numbers
ISAT:
Unit Focus/Foci
Multi-digit Multiplication
Instructional Focus/Foci
Assessing multiplication of 2- and 3-digit numbers by 1-digit numbers
Materials
Teacher-prepared test
Educational Strategies/Instructional Procedures
Test (See attached.)
339
Test
Multiply
1) 24 2) 83 3) 97 4) 65 5) 43 x 7 x 4 x 5 x 8 x 6
6) 385 7) 409 8) 620 9) 487 10) 248 x 3 x 7 x 4 x 6 x 5
11) 400 12) 93 13) 322 14) 153 15) 48 x 7 x 6 x 3 x 5 x 9
16) 523 17) 74 18) 207 19) 59 20) 457 x 8 x 4 x 6 x 8 x 9
21. A T-shirt costs $18. How much will 8 T-shirts cost?
22. An auditorium has 39 rows. Each row has 7 seats. How many seats are there?
23. Dave planted 9 rows of corn. Each row had 253 plants. How many plants did Dave have?
Estimate to get the approximate answers to solve these problems.
24. Ken had 27 boxes of baseball cards. He had 319 cards in each box. His goal was to save10,000 cards. Has he reached his goal?
25. The zoo bought 3832 kilograms of bananas. Each month the zoo uses 479 kilograms of thebananas. Will they have enough bananas for 7 months?
340
Ten Statements
Review the ten statements and have the students write yes if they heard it in today’s lesson andno if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.
No Ten Statements for this lesson.
Free Choice Lesson
Have the students choose a lesson from the Free Choice Activity sheet (one box per day).
Six- Group Activity
No Six-Group Activity today.
Math Workshop
Have the students work in the Math Workshop after completing their Free Choice Lesson.
Integration with Core Subject(s)
LA: Understanding explicit, factual informationUnderstanding the meaning of words in context
SC: Apply scientific method to solve problemsAnalyze and interpret data
SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose
Connection(s)
Enrichment:
Fine Arts:
Home:
Remediation:
341
Technology:
Assessment
Formal assessment: Teacher-prepared test.
Homework
Teacher Notes
Answer key for test:
1. 168 2. 332 3. 485 4. 520 5. 258
6. 1,155 7. 2,863 8. 2,480 9. 2,922 10. 1,240
11. 2,800 12. 558 13. 966 14. 765 15. 432
16. 4,184 17. 296 18. 1,242 19. 472 20. 4113
21. $144 22. 273 seats 23. 2,277 24. no 25. yes
342
STRUCTURED CURRICULUM LESSON PLAN
Day: 054 Subject: Mathematics Grade Level: 4
Correlations (SG,CAS,CFS): 6B3; 6C2; 8D4
ITBS/TAP:Solve single-step problems using multiplication or division with whole numbers
ISAT:
Unit Focus/Foci
Multi-digits Multiplication
Instructional Focus/Foci
Multiplying two-digit numbers by two-digit numbers
Materials
Six-Group Activity: Multiplication (2-digit by 2-digit)Coins and nickelsQuarters
Educational Strategies/Instructional Procedures
Warm-up Activity:
Write the following problem on the chalkboard. Have students solve the problem.
Jamal is the best basketball player on the team. He made 156 two-point goals, 47 three-pointgoals and 132 free throws for one-point each. What is Jamal’s total number of points scored?(585)
Next try a mental math game. List several items on the chalkboard and have students voluntarilyprice the items. The first set of items should be items popular with the age group doing thepricing. The second group of items should be from the basic needs group. Compare theaccuracy of the pricing of the two groups of items. (Ask how the answers were derived.)
343
Present the following multiplication rules.
Multiplication Rules 3 6 Say: Start at the right, multiply the top number by the digit in thex 1 8 ones column, 8 x 36 = 288. Write 288 so that the digit on the right2 8 8 (8) is in the ones column.
3 6 Multiply the top number by the tens digit. x 1 8 1 x 36 = 36. There are 36 tens. Write 36 so that the digit in the 2 8 8 right (6) is in the tens column. 3 6
3 6 Add to get the answer. x 1 8 2 8 8 3 6 6 4 8
Lesson:
H students read and discuss ways to recognize if a problem is correct or incorrect. Take this timeto point out clues to indicate if an answer is correct or not. By now the students should have agood grasp of how to multiply by two-digit numbers. Explain that the process of elimination isone way to determine the correctness of a given answer. Looking at the last digit in a productmay be an indicator. Example: 42 x 16 = 672. When you multiply the digits in the ones place, 6x 2 = 12, there will be a 2 in the last digit of the product. No other answer has a 2 in the onesplace.
After explaining some strategies that can be used to determine students complete the problemsassigned individually. Have students check the problems to make sure they are correct. Collectstudents’ papers for evaluation. Once the papers have been collected, ask for volunteers to solveproblems of the teacher’s choice. (Do not allow more than 5 to 10 minutes for this activity.)When a student solves a problem, have him/her explain the reasoning or rationale used, and why.
Have the students turn to a page in their textbook with multiplication problems, 2-digit by 2-digitmultiplication.
344
Ten Statements
Review the ten statements and have the students write yes if they heard it in today’s lesson andno if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.
1) The first step in multiplying 2-digit by 2-digit numbers is to start at the far right of theproblem and multiply the digits in ones place first. (yes)
2) Always multiply from right to left. (yes)3) When the first row has been multiplied, you must move over one place under the tens column
and place your next answer. (yes)4) The last step in multiplying 2-digit by 2-digit numbers is to add the partial products. (yes)5) Approximating is a way to find the upper or lower boundaries when solving problems. (no)6) When using multiple guess to solve multiplication problems, the digit in the ones place in the
product can sometimes be the clue needed to solve. Example: 42 x 16 = 672 a) 720b) 255 c) 672. (yes)
7) Knowledge of the metric system helps when we shop. (no)8) When multiplying by zero, write the answer 0 directly under the 0 in the problem. (no)9) 27 x 58 is an example of a two-digit number multiplied by a two-digit number. (yes)10) There are three parts to a division problem: quotient, divisor, and dividend. (no)
Free- Choice Lesson
Have the students choose a lesson from the Free Choice Activity sheet (one box per day).
Six- Group Activity
Have a group of six students, two from each ability level, complete the teacher-directed activitysheet: Multiplication (2-digit by 2-digit).
Math Workshop
Have the students work in the Math Workshop after completing their Free Choice Lesson.
Integration with Core Subject(s)
LA: Understanding explicit, factual informationUnderstanding the meaning of words in context
345
SC: Apply scientific method to solve problemsAnalyze and interpret data
SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose
Connection(s)
Enrichment:
Fine Arts:
Home:
Remediation: See attached Six Group Activity sheet: Multiplication (2-digit by 2-digit).
Technology:
Assessment
Homework
Teacher Notes
346
Six-Group Activity
Multiplication (2-digit by 2-digit)
Materials:5 index cards (5” x 7”)1 black marker1 pencilChart paper1 envelope (9 ½” x 6 ½”)
Prepare the following index cards using the black marker to write the problems on the front ofthe cards. Use the pencil to write the answers on the back of the cards.
62
23× 27
35× 33
62× 21
15× 42
34×
Answers:
62
186
1240
1426
×23
27
35
135
810
945
×
33
62
66
1980
2046
×
21
15
105
210
315
×
42
34
168
1260
1428
×
Copy the study board and use it with this reteaching activity.
Multiplying 2-digit by 2-digit
Say: Step 1: Multiply the ones first. (8 × 2 = 16. Rename the 16 as 1 ten + 6 ones. Write the 6in the ones column and write the 1 over the tens column.Example: 162 A × 48 6
Step 2: Multiply 8 times 6. (8 × 6 = 48). Add the renamed 1 to the8× 6 + 1 = 49. (49 tens = 4 hundreds + 9 tens.) Write the 9 in the tens place and the 4 in thehundreds place.
Step 3: Write zero under the 6 in the ones column. This is to hold the place because you arenow multiplying in the tens place.
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Step 4: Multiply 4 times 2 (4 × 2 = 8). Write the 8 under the 9 in the tens place. 162 × 48 496 80
Step 5: Multiply 4 times 6 (4 × 6 = 24). Write the 4 in the hundreds column and the 2 in thethousands column. (24 hundreds = 2 thousands and 4 hundreds)
62
× 48 496 2480
Step 6: Add the totals.
62
× 48 496 + 2480 2976
Solve a sample problem with the students, showing step-by-step process. Use this example:25× 95. Write the problem on a large sheet of paper.
25
95×
Ask the following questions:
1. What two numbers are you going to multiply first? (5 × 5)2. What is the answer? (25)3. Do we have to rename? (yes)4. What are we renaming and to what? (25 to 2 tens and 5 ones)5. Where do we write the renamed numbers? (write the 5 in the ones place and the 2 over the
tens place)6. What are the next numbers being multiplied? (5 × 2 = 10 = one hundred and zero tens)7. Where do we write the 12? (write the 2 in the tens and the 1 in the hundreds)8. What is the next step? (place a 0 in the ones place)
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9. Why do we write a zero in the ones place? (to serve as a place holder because we aremultiplying in the tens column)
10. What are the next two numbers to be multiplied? (9× 5 = 45)11. Do we rename the 45? (yes)12. To what? (4 tens and 5 ones)13. What do you do with the 2 already over the 2? (cross it out)14. Why? (because it was already used)15. What is the position of the numbers in 45? (write the 5 in the tens place and the 4 over the 2
in the tens column)16. What are the next two numbers to be multiplied? (9× 2)17. Do we need to rename? (no)18. Why? (because there are no other numbers to be multiplied in the hundreds place)19. What do we do with the 4? (add it to 9 × 2 = 18 + 4 =22; two thousands + 2 hundreds)20. Where do we put the 22? (write one 2 in the hundreds place and the other 2 in the thousands
place)21. What is the last step in this problem? (add)22. What two numbers are being added? (125 + 2250)23. What is the answer? (2375)
Tell the students that they are going to do five problems that are similar to the problem they justcompleted. Show the students a card and tell them there will be a one-minute time limit on eachproblem. Place a card on the table and give the students the time allotted to answer. When oneminute has elapsed, turn the card over to reveal the answer. While doing that say: The answeris… Complete the rest of the cards in the same manner.
Store the study board and index card in the 9 ½” x 6 ½” envelope.
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STRUCTURED CURRICULUM LESSON PLAN
Day: 055 Subject: Mathematics Grade Level: 4
Correlations (SG,CAS,CFS): 6A3; 6C2; 6D1
ITBS/TAP:Solve single-step problems using
multiplication or division with wholenumbers
ISAT:
Unit Focus/Foci
Multi-digits Multiplication
Instructional Focus/Foci
Multiplying three digit numbers by two-digit numbers
Materials
Six-Group Activity: Multiplication (Multiplying tens)Meter sticks
Educational Strategies/Instructional Procedures
Warm-up Activity:
Write the following problems on the chalkboard. Have students solve each problem.
1) 43 2) 84 3) 53 4) 81 5) 57 x 29 x 76 x 36 x 93 x 42
Lesson:
Have students open their textbooks to a page that shows multiplication of three-digit numbers bytwo digit numbers. Using the text example, walk the students through the algorithm formultiplying a three-digit multiplicand by a two-digit multiplier. (This may be a good time toreview estimation.) Emphasize the importance of the correct placement of each partial product.Once you have reviewed the regular algorithm, show the students how to use a shorter method.
350
Demonstrate the following problems.
312 Multiply the top number by the ones digit. x 30 0 x 312 = 0 (next)
0 Write the zero in the ones column.
312 Multiply by the digits in the tens place x 30 3 x 312 = 936 There are 936 tens. 0 936 Write 936 with the 6 placed in the 10’s column.
Next: Add 312 x 30
0 + 936 9360Shorter way:
312 Multiply the top number by the ones digit. x 30 0 x 312 = 0 0 Write the 0 in the ones column.
312 Multiply by the tens digit. x 30 3 x 312 = 936 9360 Write the 936 next to the 0.
Now that the students have a long and short way to multiply, allow the students to solveproblems one through 26 within 15 minutes. This timed activity may be used as a mini-assessment. Introduce the term perimeter. Ask if a student can define the term.
Perimeter: The distance around a figure is called the perimeter. (Give a few examples.) Then ask the student what area is.
Area: the number of square units inside a figureLength: the measurement from end to end. (the longer length)Width: the measurement from side to side
After reviewing terms and working through the examples, the students should be ready to solveproblems that the teacher assigns. When students complete the assignment, have them writeanything that seemed difficult to them in the math journals. (Before introducing the next lesson,have students read their entries and review what is necessary to clarify any deficiencies.)
351
Ten Statements
Review the ten statements and have the students write yes if they heard it in today’s lesson andno if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.
1) The area is the number of square units inside a figure. (yes)2) In this lesson, we were taught to solve multiplication problems with a three-digit
multiplicand and a two-digit multiplier. (yes)3) Multiplication can be done using the short or long methods to solve. (yes)4) The perimeter is found by adding the length and the width of all sides of a square or
rectangle. (yes)5) 7 is a prime number. (no)6) The area of a square is found by multiplying the length times the width. (yes)7) A rectangle can have measurements of 2 inches in length and 5 inches in width. (yes)8) The opposite of multiplying is dividing. (no)9) In the problem 60 x 70 = 4200, the product is an example of a power of 10. (no)10) When multiplying 3-digit numbers by 2-digit numbers multiplication and addition are used to
solve the problem. (yes)
Free Choice Lesson
Have the students choose a lesson from the Free Choice Activity sheet (one box per day).
Six-Group Activity
Have a group of six students, two from each ability level, complete the teacher-directed activitysheet: Multiplication (Multiplying tens).
Math Workshop
Have the students work in the Math Workshop after completing their Free Choice Lesson.
Integration with Core Subject(s)
LA: Understanding explicit, factual informationUnderstanding the meaning of words in context
SC: Apply scientific method to solve problemsAnalyze and interpret data
352
SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose
Connection(s)
Enrichment:
Fine Arts:
Home:
Remediation: See attached Six Group Activity sheet: Multiplication (Multiply tens)
Technology:
Assessment
Assess students’ ability to apply the algorithm to multiply two-and-three digit numbers correctly.
Homework
Teacher Notes
353
Six-Group Activity
Multiplication (Multiply by tens)
Materials:1 black marker1 pencil1 envelope (9 ½” x 6 ½”)5 index cards (5” x 7”)
Prepare the following index cards using the black marker to write the problems on the front ofthe cards. Use the pencil to write the answers on the back of the cards.
35
10× 62
10× 80
10× 255
10× 380
10×
Tell the students that when you lay a card on the table they are going to multiply by tens.Answers:
350
10
380
× 62
10
×
620
80
10
×
800
255
10×
2550
380
10×
3800
Copy the study board and use it with the lesson to reteach.
Multiply by Tens
Do the following sample problem with the students.
Say: Step 1: Think of 40 as 4 tens or 4 × 10.
268
40×
Say: Step 2: Write a zero in the ones place because 0 × any number equals zero.
268
40
0
×
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Say: Step 3: Multiply by 4.
268
40
10720
×
Ask these questions:
1) What should we think of 90 as? (9 tens or 9 × 10)2) What do we write in the ones place? (0)3) Why not multiply 0 times all the numbers? (because 0 × any number is 0)4) What is the next step? (multiply 9 × 3)5) What is the answer? (27)6) What do we do with the 27? (rename it as 2 tens and 7 ones.)7) What goes in the tens column? (7)8) What is done with the 2? (renamed over the 2)9) What is the last step? (multiply 9 × 2 + 2)10) What is the final answer? (2070)
Tell the students that they are going to do an activity, Multiplying by Tens. When a card isdisplayed on the table, tell the students they have one minute to complete the problem. When thetime is up, turn over the card to reveal the answer and say: The answer is… Complete the rest ofthe cards the same way. Store the study board and index cards in the 9 ½” x 6 ½” envelope.
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STRUCTURED CURRICULUM LESSON PLAN
Day: 056 Subject: Mathematics Grade Level: 4
Correlations (SG,CAS,CFS): 6A2; 6C2; 6D1
ITBS/TAP:Solve single-step problems using addition or subtraction with whole numbers
ISAT:
Unit Focus/Foci
Multi-digits Multiplication
Instructional Focus/Foci
Exploring multiplication uses
Materials
Six-Group Activity: Division (Word problems)Centimeter rulersMeter stickCruncherOne 0-5 cube
Educational Strategies/Instructional Procedures
Roll a Problem Game
Players: 2 or moreMaterials: one 0-5 cubeObject: To get the greatest productFocus: Multi-digits multiplication, place value and mathematical reasoning
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Rules
Discuss these rules with the students:
1. Use blanks to outline a multiplication problem on your paper. _____ _____x _____ __________________
2. The first player rolls the cube four times.3. Each time the cube is rolled, write that number in one of the blanks in your outline.4. When all the blanks have been filled, find the product of the two numbers.5. The player with the greatest product wins the round.
Write the following on the chalkboard. Have students solve each problem.
1. Mrs. Jones ordered 10 boxes of pencils. There are 120 pencils in each box. How manypencils did she order? (1,200)
2. There 50 rows of seats in the auditorium. There are 30 seats in each row. How many seatsare in the auditorium? (1,500)
Lesson:
Have the students attempt to solve the following problem. Say: You have a piece of cloth 10centimeters long and 7½ centimeters wide. Do you have enough cloth to make a pencil box thatrequires a piece of cloth 20 centimeters long and 15 centimeters wide? (yes/no) How muchmore cloth do you need to make 3 pencil boxes?
One box requires a piece of cloth 20 centimeters long and 15 centimeters wide. The piece I haveis only 10 centimeters long and 7½ centimeters wide. I only have enough to make ½ a box, Ineed to get a piece of cloth 50 centimeters long and 37½ centimeters wide. If one box requires apiece of fabric 20 centimeters by 15 centimeters 20c x 15x = 1 pencil box.
x 2 x 2 40 by 30c 40 by 30 = 2 pencil boxes
I already have a piece 10 centimeters long and 7½ centimeters wide. (½ + ½ = 1)7½cm + 7½cm = 15cm 10cm + 10 cm = 20cm.
Answer any questions that will clarify the algorithms used to solve the problem.
357
Students may play the “Roll a Problem” Game. Allow students to engage in the Roll a ProblemGame for about 10 minutes longer. Allow students about five minutes to start on the homeworkassignments. Select a problem from the assignment and solve on the chalkboard to explainunclear algorithms.
Ten Statements
Review the ten statements and have the students write yes if they heard it in today’s lesson andno if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.
1) Multiplication is a faster way of adding. (yes)2) In the problem 5× 3 the 5 is the multiplicand. (yes)3) The product is the result of multiplying two numbers together. (yes)4) The problems using algorithms for constructing pencil boxes is a good example of
application of multiplication. (yes)5) A triangle is a polygon that has three sides. (no)6) Using multiples of ten is one way to practice multiplication. (no)7) Multiples of 4 can be found by doubling multiples of 2. (yes)8) 3 × 7 = 14 + 7 = 21 (yes)9) The number being divided is called the dividend. (no)10) The mental math approximation exercise is helpful when students need practice with
approximation. (yes)
Free Choice Lesson
Have the students choose a lesson from the Free Choice Activity sheet (one box per day).
Six-Group Activity
Have a group of six students, two from each ability level, complete the teacher-directed activitysheet: Division (Word problems).
Math Workshop
Have the students work in the Math Workshop after completing their Free Choice Lesson.
358
Integration with Core Subject(s)
LA: Understand ing explicit, factual informationUnderstanding the meaning of words in context
SC: Apply scientific method to solve problemsAnalyze and interpret data
SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose
Connection(s)
Enrichment:
Fine Arts:
Home:
Remediation: See attached Six-Group Activity sheet: Division (Word problems).
Technology:
Assessment
Assess students’ understanding informally by monitoring classroom participation.
Homework
Teacher Notes
Have students review their math journals and classroom activities to prepare for the formalassessment/test.
359
Six-Group Activity
Division (Word problems)
Materials:5 index cards (5” x 7”)1 black marker1 pencil1 envelope (9 ½” x 6 ½”)
Prepare the following index cards using the black marker to write the problems on the front ofthe index cards. Use the pencil to write the answers on the back of the index cards.Tell the students that when you lay an index card on the table they are going to solve the problemusing their problem solving skills.
1) The students plan to rent boats at the lake. How many boats will the 20 students need if eachboat holds 4 students?
2) James cut a glass 12 feet long into 4 equal pieces. How long was each piece?
3) Ms. Giles made 7 telephone calls. She spent 35 minutes on the telephone. What was theaverage length of each call?
4) Ray received a free festival ticket for every 6 tickets he sold. How many free tickets did hereceive if he sold 36 festival tickets?
5) Jordan scored 72 points in the last 8 basketball games he played. What was the averagenumber of points he scored in each game?
Answers: (5 boats), (3 feet), (5 minutes), (6 free tickets), (9 points)
Copy this study board to use with the reteaching of this lesson.
360
Word problems
Review the following key words which indicate that a word problem requires division.
Division key words:
divided (evenly) averagesplit everyeach out ofcut ratioequal pieces shared
Review the study board with the students and use this sample word problem:
Mrs. Alfred has 20 candles to use for table decorations. She wants to decorate 5 tables. Howmany candles can she put on each table? Ask: What are the key words that let you know this is adivision problem? Can you use multiplication to solve this problem? (yes) If so, what wouldthe problem be? (5× 4 = 20)
Tell the students that they are going to do five word problems the same way they did theexample. Tell them they have a minute to solve each problem. While revealing the answer say,The answer is…… Store the index cards and study board in the 9 ½” x 6 ½” envelope.
361
STRUCTURED CURRICULUM LESSON PLAN
Day: 057 Subject: Mathematics Grade Level: 4
Correlations (SG,CAS,CFS): 7A2,3; 7B6; 7C2; 8D2
ITBS/TAP:Solve single-step problems using multiplication or division with whole numbers
ISAT:
Unit Focus/Foci
Multiplication Skills
Instructional Focus/Foci
Reviewing mixed skills
Materials
Six-Group Activity: Multiplication (Multiply tens and ones by ones)Graph paperPencilsMath journalsThe Cruncher
Educational Strategies/Instructional Procedures
Warm-up Activity:
Present this problem and provide graph paper for students to work on. Have students draw acapital letter on the graph paper that has a perimeter of 38 units. (Answers will vary.) Draw theletter H.
4 + 4 2 2 2 + 4 + 4 + 11 + 4 + 4 + 11 + 2 + 2 + 2 11 + 2 + 2 + 2 = 50 11 + 2 2 2 4 + 4
362
Discuss students’ response. Review the definition of perimeter. (perimeter = the distancearound a surface.)
Lesson:
This lesson is designed to give practice for the basic arithmetic operations learned by thestudents.
Algebra preparatory problems: (A timed review)Have students solve for n:
1. n = 15 + 3 2. 27 ÷ n = 3 3. n ÷ 8 = 32
4. n x 9 = 72 5. n - 9 = 9 6. 8 + n = 30
7. n = 72 ÷ 9 8. n = 12 + 23 9. n ÷ 10 = 80
10. 48 ÷ 6 = n 11. n = 10 x 8 12. 10 x 7 = n
Watch for the (x, ÷ , +, -, =, n) signs.
13. 257 × 30 = n 14. 100 x 864 = n 15. 504 + 321 = n
16. 88 x 1000 = n 17. 484 x 25 = n 18. 418 - 405 = n
19. 56 ÷ 7 = n 20. 52 - 7 = n 21. n - 84 = 7
22. Joy and Bobby toured the Grady Caves. The path was marked so that the tourists could tellhow far they had traveled. Joy and Bobby decided to make a graph to show how far they hadtraveled. Look at their graph.
0
2
4
6
8
10
12
6A.M
8A.M.
10A.M.
12P.M.
2P.M.
4P.M.
6P.M.
8P.M.
10P.M.
12A.M.
Dis
tanc
e fr
om c
abin
Miles
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Answer these questions.
a. How far had they gone by 9:00 A.M.?b. How far had they gone 3 hours later?c. At what time were they farthest from the cabin?d. How fast do you think they traveled?e. What was the farthest distance they could have traveled?
Say: Write a journal entry using the data from the graph. Make sure the story/narrative agreeswith the graph data.
Ten Statements
Review the ten statements and have the students write yes if they heard it in today’s lesson andno if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.
1) This lesson reviewed addition and subtraction skills. (yes)2) Solving for “n” is an example of pre-algebra readiness. (yes)3) In order to correctly solve this problem: 61 x 1000 = n correctly, one needs to know how
place value is utilized. (61,000). (yes)4) The problems in the pre-algebra section of this lesson can be used in function machines. (no)5) Problem #22 was an example of graphing. (yes)6) The journal entry was an example of integrating writing with math. (yes)7) In order to correctly answer questions about the graphs in this lesson, one needs to be able to
read graphs. (yes)8) There are many different kinds of graphs: , circle, bar & line are just a few. (no)9) In this lesson, addition, subtraction, multiplication, and division skills were needed to solve
problems. (yes)10) Multiples of 10 powers of 10 are algorithms used in multiplication skills. (no)
Free-Choice Lesson
Have the students choose a lesson from the Free Choice Activity sheet (one box per day).
Six- Group Activity
Have a group of six students, two from each ability level, complete the teacher-directed activitysheet: Multiplication (multiply tens and ones by ones).
364
Math Workshop
Have the students work in the Math Workshop after completing their Free Choice Lesson.
Integration with Core Subject(s)
LA: Understanding explicit, factual informationUnderstanding the meaning of words in context
SC: Apply scientific method to solve problemsAnalyze and interpret data
SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose
Connection(s)
Enrichment:
Fine Arts:
Home:
Remediation: See attached Six Group Activity sheet: Multiplication (Multiply tens and ones byones).
Technology:
Assessment
Assess students’ understanding using classroom participation and journal entries.
Homework
365
Teacher Notes
Answer key
1. 18 2. 9 3. 256 4. 8
5. 18 6. 22 7. 8 8. 35
9. 800 10. 8 11. 80 12. 70
13. 7,710 14. 86,400 15. 825 16. 88,000
17. 12,100 18. 13 19. 8 20. 45
21. 91
22. a. Approximately 4 miles from the cabin b. 11 miles total c. 12 P.M. to 1 P.M. d. About 2 miles per hour e. 12 miles
366
Six-Group Activity
Multiplication (Multiply tens and ones by ones)
Materials:10 index cards (5” x 7”)1 black marker1 pencil1 envelope (9” x 6 ½”)
Prepare the following index cards using the black marker to write the problems on the front ofthe cards. Use the pencil to write the answers on the back of the cards.
26
7×47
8×75
6×56
4×88
3×
37
3×49
2×21
4×38
2×52
9×
Answers:
426
7
182
×
547
8
376
×
375
6
450
×
224
256
4×
264
288
3×
237
3
111
×
98
149
2×
84
21
4×
76
138
2×
468
152
9×
Copy this study board on multiplying tens and ones by ones.
Multiplying tens and ones by ones
Say: Multiply 3 by the factor above of it in the ones place.
25
3
A×
3 × 5 = 15
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Say: Step 2: After multiplying 3 × 5 = 15. The number 15 cannot fit into the ones place. Only 0- 9 single digits can fit into the ones place. Rename as 1 ten + 5 ones.
5
125
3× Tip: multiply from right to left.
Step 3: Multiply 3 times 2. This gives you the answer.(6) You are not finished because you haveone that was renamed over to the tens place. Add the number 1 to the answer of 2× 3 = 6.
6 + 1 = 7, place the 7 in the tens place.
25
3
1
×
75
Give the students this sample problem, 45
3
× , and ask these them write the response:
1. What are the two factors being multiplied? (45, 3)2. Which way do you start multiplying? (right to left)3. What is the first number you use to start multiplying the other numbers by? (3)4. Name the first two numbers being multiplied. (3 × 5)5. What is the answer? (15)6. Can 15 fit in the ones place? (no)7. What must we do? (put 5 under the ones place and carry 1 over the 4)8. What is the next number 3 is multiplying? (4)9. What is 3× 4? (12)10. Can we put 12 in the tens column? (no)11. Why not? (because we have to add 1 to it)12. So, is 3 × 4 + 1 = 13? (yes)13. Are we finished? (yes)
Tell the students that you want them to try some problems that you are going to show them andthat there is a time limit on each card. (Allow about 1 minute per problem.) When you lay thecard down, tell the students to begin. When the time is up, turn the card over to reveal theanswer and say: The answer is…… Complete the rest of the cards in the same way. Use the 9½” by 6 ½” envelope to store the activity in.
368
STRUCTURED CURRICULUM LESSON PLAN
Day: 058 Subject: Mathematics Grade Level: 4
Correlations (SG,CAS,CFS): 6C2
ITBS/TAP:Perform arithmetic operations
ISAT:
Unit Focus/Foci
Multi-digit Multiplication
Instructional Focus/Foci
Assessing multiplication by 2-digit numbers
Materials
Educational Strategies/Instructional Procedures
Formal Assessment (See attached.)
369
Test
Multiply.
1) 68 2) 40 3) 285 4) 431 5) 30 x 75 x 16 x 24 x 15 x 31
6) 55 7) 346 8) 800 9) 49 10) 29 x 35 x 412 x 80 x 46 x 92
11) 869 12) 74 13) 248 14) 309 15) 84 x 36 x 28 x 39 x 63 x 84
Solve these problems.
16. Claudia can put 10 photos on each page of her album. How many photos can she put on 49pages?
17. How many minutes are there in 27 hours?
18. There are 15 seats in each row of the auditorium. There are 253 rows. How many seats arethere altogether?
19. A roll of film costs $3.27. How much will 38 rolls of film cost?
20. Ken had 40 jars. He put 500 pennies in each jar. How many pennies does he have?
370
Ten Statements
Review the ten statements and have the students write yes if they heard it in today’s lesson andno if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.
No Ten Statements today.
Free-Choice Lesson
Have the students choose a lesson from the Free Choice Activity sheet (one box per day).
Six-Group Activity
No Six-Group Activity today.
Math Workshop
Have the students work in the Math Workshop after completing their Free Choice Lesson.
Integration with Core Subject(s)
LA: Understanding explicit, factual informationUnderstanding the meaning of words in context
SC: Apply scientific method to solve problemsAnalyze and interpret data
SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose
Connection(s)
Enrichment:
Fine Arts:
Home:
Remediation: No Six-Group Activity today
371
Technology:
Assessment
Formal
Homework
Teacher Notes
Answer key for test:
1. 5,100 2. 640 3. 6,840 4. 6,465 5. 930
6. 1,925 7. 142,552 8. 64,000 9. 2,254 10. 2,668
11. 31,284 12. 2,072 13. 9,672 14. 19,467 15. 7,056
16. 490 17. 1,620 18. 3,795 19. $124.26 20. 20,000