Scope and Sequence Unit 1
Unit 2
2
Adding and Subtracting up to 6 Digits
Unit 3 8
Lesson 1
Adding and Subtracting 2 and 3 Digits
10
Lesson 2
Adding and Subtracting 3 to 4 Digits
12
Lesson 3
Adding and Subtracting 4 to 6 Digits
13
Lesson 4
Problem Solving
14
Lesson 5
Adding 3 or More Numbers (3 to 6 Digits)
15
Lesson 6
Addition and Subtraction Practice
16
Lesson 7
Estimating Sums and Differences
18
Lesson 8
Problem Solving
21
Multiplying up to 4 Digits by 3 Digits
24
Lesson 1
Multiplying 1, 2, and 3 Digits by 1 Digit
26
Lesson 2
Multiplying 2 and 3 Digits by 2 Digits
29
Lesson 3
Problem Solving
31
Lesson 4
Multiplying 4 Digits by 1 and 2 Digits
33
Lesson 5
Multiplying 3 and 4 Digits by 3 Digits
36
Lesson 6
Multiplication Practice
39
Lesson 7
Estimating Products
42
Unit 4
Dividing up to 5 Digits by 2 Digits
48
Lesson 1
Dividing 1 and 2 Digits by 1 Digit
50
Lesson 2
Dividing 2 and 3 Digits by 1 Digit
53
Lesson 3
Dividing 3 and 4 Digits by 1 Digit
56
Lesson 4
Estimating Quotients
58
Lesson 5
Dividing 2 Digits by 2 Digits
61
Lesson 6
Dividing 3 Digits by 2 Digits
64
Lesson 7
Dividing 4 Digits by 2 Digits
66
Lesson 8
Dividing 5 Digits by 2 Digits
68
Lesson 9
Division Practice
70
Lesson 10 Problem Solving
71
Understanding Fractions
74
Lesson 1
Numerator and Denominator
76
Lesson 2
Prime and Composite Numbers
79
Lesson 3
Reducing Fractions to Their Simplest Form
82
Lesson 4
Finding the Greatest Common Factor
85
Lesson 5
Changing Improper Fractions to Mixed Numerals 88
Lesson 6
Working With Mixed Numerals
91
3
Unit 5
Unit 6
Adding Fractions
96
Lesson 1
Adding Fractions With Like Denominators
Multiplying Fractions
142
98
Lesson 1
Multiplying Fractions
144
Lesson 2
Adding Mixed Numerals With Like Denominators 101
Lesson 2
Multiplying Fractions and Whole Numbers
147
Lesson 3
Problem Solving
104
Lesson 3
Multiplying Mixed Numerals and Whole Numbers 150
Lesson 4
Finding Equivalent Fractions
105
Lesson 4
Multiplying Mixed Numerals
153
Lesson 5
Adding Fractions With Unlike Denominators
109
Lesson 5
Multiplication Practice
156
Lesson 6
Adding Mixed Numerals With Unlike Denominators 113
Lesson 6
Problem Solving
159
Lesson 7
Problem Solving
115
Unit 7
Unit 8
Dividing Fractions
162
Lesson 1
Reciprocals
164
Subtracting Fractions
118
Lesson 2
Dividing Whole Numbers and Fractions
Lesson 1
Subtracting Fractions With Like Denominators
120
167
Lesson 3
Dividing Fractions by Fractions
Lesson 2 Lesson 3
Subtracting Fractions From Whole Numbers
123
170
Lesson 4
Dividing Mixed Numerals
Subtracting Mixed Numerals With Like Denominators
173
126
Lesson 5
Problem Solving
179
Lesson 4
Problem Solving
129
Lesson 5 Lesson 6
Customary Measurement
182
Subtracting Fractions With Unlike Denominators 130
Lesson 1
Units of Length (Inches, Feet, Yards, and Miles)
184
Subtracting Mixed Numerals With Unlike Denominators
133
Lesson 2
Liquid Volume (Cups, Pints, Quarts, and Gallons) 187
Lesson 7
Subtraction Practice
136
Lesson 3
Weight (Ounces, Pounds, and Tons)
190
Lesson 8
Problem Solving
139
Lesson 4
Temperature
193
Lesson 5
Elapsed Time
196
Lesson 6
Problem Solving
199
Lesson 7
Measuring Perimeter
200
Lesson 8
Measuring Area
203
Lesson 9
Measuring Volume
206
Unit 9
Lesson 10 Problem Solving 4
209 5
Unit 10 Metric Measurement
212
Units of Length (Millimeters, Centimeters, Meters, and Kilometers)
214
Lesson 2
Liquid Volume (Milliliters, Liters, and Kiloliters)
217
Lesson 3
Weight (Milligrams, Grams, and Kilograms)
220
Lesson 4
Temperature
224
Lesson 5
Measuring Perimeter and Area
227
Lesson 6
Measuring Volume
230
Lesson 7
Problem Solving
232
Lesson 1
Unit 12 Geometry Lesson 1 Lesson 2
Points, Lines, Rays, and Angles Parallel and Perpendicular Lines
262 267
Lesson 3
Measuring Angles
270
Lesson 4
Quadrilaterals
275
Lesson 5
Polygons
278
Lesson 6
Solid Figures
280
Unit 13 Preparing for Algebra Unit 11 Graphs and Probability
6
236
Lesson 1
Reading Bar Graphs
238
Lesson 2
Drawing Bar Graphs
240
Lesson 3
Reading Line Graphs
244
Lesson 4
Drawing Line Graphs
246
Lesson 5
Calculating the Mean
248
Lesson 6
Calculating the Median, Mode, and Range
251
Lesson 7
Problem Solving
253
Lesson 8
Calculating Probability
255
260
284
Lesson 1
Number Patterns
286
Lesson 2
Variable Expressions
288
Lesson 3
Open Sentences
291
Lesson 4
Problem Solving
293
7
My Goals Lesson 1 - Adding and Subtracting 2 and 3 Digits Lesson 2 - Adding and Subtracting 3 to 4 Digits Lesson 3 - Adding and Subtracting 4 to 6 Digits Lesson 4 - Problem Solving Lesson 5 - Adding 3 or More Numbers (3 to 6 Digits)
Adding and Subtracting up to 6 Digits
Unit I
Lesson 6 - Addition and Subtraction Practice
n This Unit
Lesson 7 - Estimating Sums and Differences
Your child will learn to add and subtract up to four numbers. The numbers will vary from two to six digits. They will build up their skills gradually by adding and subtracting with and without regrouping. Add the ones. Addend
33 +67
regroup I0 as I ten and 0 ones.
33 +67 I0
I
33 +67 0
Add the tens. I
33 +67 I00
Your child will learn to round and estimate to get an approximate answer for addition and subtraction problems.
Lesson 8 - Problem Solving
Ways to Help Help reinforce addition and subtraction by writing different problems on index cards and writing their answers on other cards. Have your child match each problem to its solution.
At Home Activities Make two cubes out of paper and write a two to six digit number on each side. Have your child roll both cubes five times and add the two numbers that show up. Have your child roll the cubes another five times and subtract the smaller number from the larger number that appears.
8
Unit I Adding and Subtracting up to 6 Digits
Essential Question: How do you add and subtract?
9
I-I
Adding and Subtracting 2 and 3 Digits
Add or subtract.
In addition, you add two addends to get a sum. When you have two or more digits, add from right to left.
Add the ones.
Addend
regroup I0 as I ten and 0 ones.
33 +67
I
33 +67 I0
33 +67 0
Add the tens. I
I22 + 34
53 +22
73 +I8
642 + 76
260 + 46
82 +36
52 +32
770 + 77
36 +7 3
4I2 + 33
940 + 89
85 +25
63 +73
364 + 33
63 - 24
252 - 39
60 -36
8I - 26
I 52 - 67
5 92 + 67
73 +I 8
I53 - 89
85 - 57
762 - 97
95 -26
I00 - 58
33 +67 I00
In subtraction, you subtract the subtrahend from the minuend to get the difference. When you have two or more digits, subtract from right to left.
Regroup 3 ones as I3 ones and 5 tens as 4 tens. Minuend I 53 Subtrahend
10
- 38
Subtract the ones. 4 I3
I 53 - 38 I5
Subtract the tens and the hundreds. 4 I3
I 53 - 38 II5
11
I-2
I-3
Adding and Subtracting 3 to 4 Digits
Add or subtract.
4I9 +5I9
692 +526
I 05 +8 I 3
12
Adding and Subtracting 4 to 6 Digits
Add or subtract.
500 +453
2,660 + 226
584 +558
637 +763
50 I +567
873 +457
957 -278
572 -238
5I 3 -435
2,6 I 9 - 594
5,536 - 655
4,376 - 824
9I0 +2I0
7,300 + I 94
654 -429
6 I2 -348
662 + I 42
9I2 +685
642 -589
3I9 - I 78
6,342 + I 52
950 +609
4,825 +3,26 I
6,357 +4,239
7,292 +4,577
32,506 +37,432
82,I 56 +46,837
6,662 -3,36 I
8,352 -3,220
9,067 -6,239
38,556 -26,424
95 ,I 8 I - 66,827
28,845 +22,385
69,6 I 3 +73,532
96,072 +28,379
25,736 +29,945
474,925 - I 9,347
48,952 -26,028
39,82 I -2 I ,964
58,342 -26,797
296,378 - 37,492
739,76I - 43,785
536,3 I 5 + 28,446
827,7I 6 + 6I,465
436,489 + 74,5 I 5
359,779 + I 06,038
82 I ,4 I 9 + I 36,038
947,7 I 4 - 86,348
637,762 -207,686
474,I 03 -308,306
69 I,532 -246,955
745,090 - I 23,347
3 I6 - I 26
9I2 -297
13
I-4
I-5
Problem Solving
Solve each problem. Write add or subtract. I. Nina has 43 toy cars and 56 toy airplanes. How many toys does Nina have in all? Nina has _______ toys in all.
Show your work!
Adding 3 or More Numbers (3 to 6 Digits)
Add.
457 I3 5 +778
524 6I 3 +729
473 597 735 +304
3,784 3,420 5I7 + 245
663 225 887 I 38 +567
605 287 3 I5 450 562 +7, I 24
640 945 +9 I 3
5I 2 834 +260
6,002 246 + 3 00
I2,633 5,067 2,45I + 263
9,627 497 20,362 + 8,63 I
240,329 I 7,633 46,395 + 24,77I
327 792 574 382 +280
4,395 727 2,I 45 89 I + I I2
33,746 4 I ,727 7,824 2,430 + 602
360,432 57,203 33,397 I ,484 + 3,904
5,480 2,064 7,722 493 260 + 284
55,9 I 3 3,762 8,373 I ,6 I 0 I4I + I32
3 I ,964 25, I 73 46,490 8,I 55 2,893 + 4,764
325,692 I I 9,740 363,993 27,440 3 I,2 I 8 +77,348
Would you add or subtract? _________
2. Karen drove I,526 miles and flew 952 miles. How many more miles did Karen drive than fly? Karen drove _______ more miles than she flew. Would you add or subtract? _________
3. Mrs. Liza washes 852 loads of laundry a year. Her sister Mrs. Isabelle washes I,205 loads of laundry a year. How many more loads of laundry does Mrs. Isabelle wash than her sister Mrs. Liza? Mrs. Isabelle washes _______ loads of laundry more than her sister Mrs. Liza. Would you add or subtract? _________
14
15
I-6
Addition and Subtraction Practice
Subtract.
Add.
16
90 +92
49 +68
705 +477
3I2 +734
6,622 + 749
3,398 +6,047
7,045 +2,555
32,I 99 + 7,440
26,748 +38,853
346,299 +465,0I 7
7I5 205 +528
5,764 3,944 +2,376
I 5,79 I 5,626 + 9,473
8,6 I 4 64,968 +46,248
29,625 833,570 + 58,2 I 7
86,265 24,370 +I 5,324
I42,633 347,924 +3 I 6,597
783 676 928 +4 I 6
6,482 9,623 738 +7,9 I 3
88,473 4,7 I 0 + I 8,046
56 -I 7
I02 - 57
94 - 29
83 - 58
400 - 86
3I0 - 68
8 I7 - 98
9I2 - 386
5,625 - 437
8,436 - 4,086
4,620 - I,837
5,660 - 3,435
6,3 I 2 - 3,8 I 7
82,3I 2 - 2,839
36,036 - 6,458
76,362 - 26,324
83,653 - 57,342
I64,362 - 83 ,I 98
260,000 - 94,667
902,3I 2 - 347,028
17
I-7
Estimating Sums and Differences
Estimate the numbers to the nearest place value of each column. thousands
Round the numbers, then add from right to left.
3,589 + 528
hundreds
tens
ones
2,458 3,897
3,600 + 500 4,I00
8,658 6,234 7,589 3,042 I ,345
Round the numbers, then subtract from right to left.
3,589 - 528
3,600 - 500 3,I00
Estimate, and then add.
With each set of numbers, round them to the highest place value they have in common. If the number in the next highest place is greater than 5, round up.
3,625 ________ 256 ________
18
5,236 ________ 4 ,I 25 ________
32 ________ I 25 ________
6 ________ 3,657 ________
29,875 +36,589
I ,548 + I ,436
4,265 +6,325
7,689 + 568
965 + 632
I 2,589 +25,689
2,635 + 365
3,458 + 356
8,564 + 958
19
I-8
Estimate numbers. Add or subtract.
2,3 I 4 +3,296
2,453 +3,257
Problem Solving
Show your work!
Solve each problem. I. The airlines made a profit in 20I4 of I5,226 euros. In 20I3, The airlines made a profit of I3,524 euros. Estimate the amount of euros the airlines made in both years.
8,676 -4,5 I 7
64,730 - I 8,634
I 2,645 +66,773
47,276 + I 6,505
The airlines made about ________ euros in 20I3 and 20I4.
2. A car weighs I,923 pounds. A boat weighs about I,368 pounds. Estimate the difference in weight. The car weighs about _______ pounds more than the boat.
73,464 -52,692
920,634 -375,023 3. Last year there were 568 students in the school. This year there are 436. Estimate the difference in the amount of students this year and last year.
644, I 72 - 285,493
20
86,245 53,792 +20,696
There were about _______ more students last year than there are this year.
21
Check What You Learned Solve each problem. Write add or subtract.
Show your work!
Add or subtract.
63 +36
60 +68
9I 2 +456
237 +372
782 +206
I. What is the sum of 56,894 and I,548? The sum of 56,894 and I,548 is ___________. Would you add or subtract? ______________
80 -4I
72 - 54
543 - 62
453 - 78
732 - 49
404 +528
736 +745
5,0 I 6 + I,247
3,546 +3,475
4,32 I +2,7 I 8
956 - I 68
3,046 - I 36
7,8 I 3 - 285
7,650 - 783
2,I I 0 - I,987
6,356 +8,294
26,550 +32,347
40,367 +22,597
776,344 + 65,987
50,530 +36,29 I
52,3 I 5 - 3,704
65,0 I I - 3,2 I 4
82 , I 35 - 9,487
443,7 I 0 - 2 I ,754
27 I ,562 - 84,536
2. The baker has sold I9,254 loaves of bread this month. Last month, he sold I6,2I4. Estimate the amount of loaves of bread the baker sold in the last two months. The baker has sold about _______ loaves of bread in the past two months. Would you add or subtract? ______________
3. Dan has 28,365 travel points. Tim has 30,245 travel points. How many more travel points does Tim have than Dan? Tim has ________ more travel points than Dan. Would you add or subtract? ______________
32,694 +28,469
22
474,8 I 2 + 278,343
720 424 + 468
7,300 3,6 I 8 + 6, I 74
I 0,365 57,547 + 26,644
23
My Goals Lesson 1 - Multiplying I , 2, and 3 Digits by I Digit Lesson 2 - Multiplying 2 and 3 Digits by 2 Digits Lesson 3 - Problem Solving Lesson 4 - Multiplying 4 Digits by I and 2 Digits Lesson 5 - Multiplying 3 and 4 Digits by 3 Digits Lesson 6 - Multiplication Practice
n This Unit Your child will build up their skills slowly by first multiplying single digit numbers by one-, two-, and three-digit numbers, then they will learn to multiply two and three digits by two-digit numbers, then four digits by one- and two-digit numbers and finally three and four digits by three-digit numbers. 2 3 x
I 2 4 6
+2 3 0 2 7 6
Your child will use their gained skills to read and form equations to solve word problems. Your child will learn to round and estimate to get an approximate answer to different multiplication problems.
At Home Activities Make two cubes out of paper and write a one- to four-digit number on each side. Have your child roll both cubes five times, and multiply the two numbers that show up.
24
Unit 2 Multiplying up to 4 Digits by 3 Digits
Lesson 7 - Estimating Products
Ways to Help Help reinforce multiplication by writing different problems on index cards and writing their answers on other cards. Have your child match each problem to its solution.