Administer the Grade 4 G/T Mathematics Assessment Part 1 as a pretest the first week of school.

Problem Solving Strategies

Instructional Objective(s)
The students will be able to:

1. Select and then apply appropriate strategies to solve a problem from visual (draw a picture or diagram, create list, table or graph, act it out, use manipulatives, use spatial reasoning); numerical (guess and check; look for a pattern); symbolic (write an equation or number sentence, working backwards) perspectives.

1. Use the Processes of Mathematics.

1. Sample Problem (Look for a Pattern): When Mae joined the chorus she knew four songs. At the end of the first week, she knew five songs. After the second week, she knew seven songs, and at the end of third week she knew ten songs. If she continues to learn at this pace, howmany songs will she know after 12 weeks? Find the pattern. (82 songs)

Pattern: Add the next consecutive number to the previous week's songs to get the next week's number of songs.

1. Problem Solver - 5/6

1. Lenchner CPS

1. Puddle Questions - 5/6
   
   

Number Relationships and Computation (Number Theory and Place Value)

Instructional Objective(s)
The students will be able to:

1. Read and write whole numbers to millions and decimals through thousandths in standard and expanded form.

1. Use whole numbers 0 to 1,000,000. (4)
   
   
1. Use no more than 3 decimal places (5)

1. Standard: 34,706

Expanded: 30,000 + 4,000 + 700 + 6

1. Standard: 41,005.805

Expanded: (4 x 10,000) + (1 x 1,000) + (5 x 1) + (8 x .1) + (5 x .001)

1. G1 (97)
   
   
1. G1 Transitions (5, 6, 9)

0. G2 Transitions (13)
   
   
1. M+6 (6-7)
   
   
1. Number Sense 6-8 (142)
   

1. Travel in the Solar System
   

2. Round whole numbers and decimals to any stated place value.

2. 2,127 rounded to hundreds is 2,100.

2. G1 (12-14, 109)
   
   
2. G1 Transitions (11)
   
   
2. M+6 (H2)
   

3. State the value of each digit in a whole number through milions and a given decimal numberal through thousandths.

3. Use whole numbers 0 to 1,000,000 (4)

3. What is the value of the underlined digit?
   243,987—> 40,000 (4 x 10,000)
   97.325 —> .005 (5 x .001)

3. G1 (95)
   
   
3. G2 Transitions (13)
   
   
3. M+6 (8)
   
   
3. Number Sense 5-6
   
   
3. Nimble with Numbers 6-7
   

4. Explore patterns found in ancient number systems including Roman and Egyptian.

4. Roman and Egyptian are non-place value systems of picture math.

4. M+6 (2-5)
   
   
4. Math on Call (552, 554)

5. Compare, order, and describe decimals with or without using relationship symbols (<, >, =, ≠) and by placing decimals on a number line.

5. Use no more than 4 whole numbers with or without using the symbols (<, >, =) and whole numbers (0 - 1,000,000). (4)

5. .007 < .07 < 0.7
   
   
5. Place 1.67 on the number line.
   

5. What fraction is represented by M on the number line?
   
   
    

5. G1 (105-108)

6. Examine relationships among metric units of length (mm, cm, m)

6. 12 mm = 1.2 cm
   
   
6. 37 cm = 0.37 m

6. G1 (102, 164, 202, 292)
   
   
6. G1 Transitions (29-36)
   
   
6. M+6 (H20, 274, 278, 286)
   

6. Puddle Questions - 6 (10-19)
   
   
6. Number Sense 6-8 (45-48)
   
   
6. Investigations 5 Measurement
   
   
6. Groundworks 6 (17-22)
   
   

7. Estimate and measure length, using metric units. Select and use appropriate tools and units.

7. Use the nearest millimeter and centimeter with a ruler. (4)

7. A paperclip should be measured in cm. rather than m.

7. G1 (102, 164, 202, 292)
   
   
7. G1 Transitions (29-36)
   
   
7. M+6 (H20, 274, 278, 286)
   
   
7. Puddle Questions - 6 (10-19)
   
   
7. Number Sense 6-8 (45-48)
   
   
7. Investigations 5 Measurement
   
   
7. Groundworks 6 (17-22)
   
   

8. Identify and describe the characteristics of numbers divisible by 2, 3, 4, 5, 6, 9, and 10.

8. Use rules for 2,3,5,9, or 10 and whole numbers 0 to 10,000. (5)

8. Divisibility rule for 4: A number divisible by 4 must have the number formed by the last 2 digits be divisible by 4 or both digits be zeros.
   Divisibility rule for 6: A number that is divisible by 6 must be divisible by 2 and 3.
   Divisibility rule for 9: The sum of the digits is divisible by 9.

8. G1 (178)
   
   
8. M+6 (96)
   
   
8. Navigations 3: Algebra
   
   
8. Lenchner CPS (91, 94, 104)
   
   
8. Number Sense 6-8
   
   
8. Nimble with Numbers 6-7
   
   
8. Math On Call (69)
   
   

9. Identify prime and composite numbers through 100.

9. Use whole numbers (0-100). (5)

9. Prime numbers have exactly 2 factors, 1 and the number itself.
   Composite numbers have more than 2 factors.
   
   Alert: The number "1" is neither prime nor composite since it only has one factor, the number itself.

9. G1 (181)
   
   
9. Nimble with Numbers 5-6 (30)
   
   
9. Math On Call (58-60)
   
   

10. Identify factors and prime factors using factor trees.

10. The prime factorization of 18 = 2 x 3 x 3.
    
    
10. Factor tree:

10. The Factor Game
    

10. G1 (182)
    
    
10. Nimble with Numbers 6-7 (41-46)

11. Identify multiples

11. Use the first 5 multiples of any single digit whole number. (4)

11. Lenchner CPS (90)

12. Identify and define perfect squares and their square roots

12. Use no more than 3 exponents for integers (-10 to 20) or square roots of perfect square whole numbers (0-100). (No Calculators). (7)

12. M+7 (344-348)
    
    
12. Super Source 5 Pattern Blocks (78)
    
    
12. Math On Call (77)
    
    
12. SuperSource Base Ten Blocks 5-6 (82-84)

13. Write exponent to express powers of numbers and convert powers of numbers to standard form.

13. Use no more than 3 exponents for integers (-10 to 20) or square roots of perfect square whole numbers (0-100). (No Calculators). (7)

13. 4 x 4 x 4 = 4³
    4³     = 64       

13. G1 (28, 40)
    
    
13. M+6 (20-21)
    
    
13. SuperSource 5 Color Tiles (22, 62)
    
    
13. Exponents and Patterns
    
    
13. Math First H (33-34)

14. Explore writing numerals in expanded form using exponential notation.

14. Use the whole numbers (0-1,000,000). (4)
14. Use exponential form with powers of 10 (0-10,000). (6)
14. Use exponential notation with bases no more than 12 and exponents no more than 3, or in standard form (0-1000). (7)

14. 2,456 =
    (2 x 10³) + (4 x 10²) + (5 x 10¹) + (6  x 10⁰)

14. M+6 (Enrich 1.8)

15. Explain and apply the order of operations to evaluate numerical expressions using whole numbers.

15. Use no more than 4 operations (+, -, x, ÷ with no remainders) and 1 set of parentheses or a division bar (0-100). (No Calculators) (6)

15. Order of operations is a set of rules that tell you the order in which to compute.
    - Compute inside the parentheses.
    - Do powers or roots.
    Alert:
    - Multiply or divide in order from left to right.
    - Add or subtract in order from left to right.
    (Mnemonic device:
    Please Excuse My Dear Aunt Sally!)
    6 + 4 x 5 ÷ 6
    4 x 3 = 12, 12 ÷ 6 = 2, 6 + 2 = 8
    
    3,710 + (12 -  2)
    3,710 + 10 = 3,721
    
    12 ÷ 4 x (3 + 2)²
    3 + 2 = 5 and 5² = 25
    12 ÷ 4 x 25 and 3 x 25 = 75

15. G1 (16)
    
    
15. M+6 (18-19)
    
    
15. Nimble with Numbers 5-6 (14, 17-19, 22-23)
    
    
15. Number Sense 4 (131-135)
    
    
15. Math First H (33-34)

Number Relationships and Computation (Whole Numbers and Decimals)

Instructional Objective(s)
The students will be able to:

1. Estimate and calculate sums and differences of whole numbers and decimals using appropriate method of computation (mental mathematics, use of a calculator, use and discovery of alternate algorithms).

1. Use up to 3 addends with no more than 4 digits in each addend and whole numbers (0-10,000). (No Calculators) (4)
1. Use a minuend and subtrahend with no more than 4 digits in each and whole numbers (0-9999). (No Calculators) (4)
1. Use no more than 3 addends with no more than 3 decimal places in each addend or the difference of a minuend and subtrahend with no more than 3 decimals places and numbers 0-1000. (5)

1. Add decimals in vertical and horizontal formats using various place values.
   
   
1. 2,127 —> 2,000
   + 997 —> 1,000
                   ≈ 3,000
   
   
1.  16.175 —> 16.2
   -11.613 —> 11.6
                     ≈   4.6
   
   
1. When you add .2344 + .838, will the sum be more or less than one whole? Explain how you know.

1. G1 (549-552)
   
   
1. G1 (118-120)
   
   
1. G1 (564-565)
   
   
1. Math On Call (102-103, 116, 119-125, 128-131)

2. Apply addition and subtraction of whole numbers and decimals to money.
   

2. Use 2 sets of mixed currency and money ($0 -$100). (4)
2. Use no more than 4 addends and no more than 3 decimal places in each addend and numbers (0-1000). (No Calculators) (5)
2. Use a minuend and subtrahend with no more than 3 decimal places and numbers (0-1000). (No Calculators ) (5)

2. If you have $5 and spend $1.15 for ice cream, how much money do you have?
2. At the supermarket, you buy milk for $2.19, cookies for $1.79, and gum for $0.59. What was your total cost for those items?
   
   

2. G1 Transitions
   
   
2. Mental Math in Junior High (59-62)

3. Multiply multiples of 10 by a one or two-digit factor using mental computation.

3. 26 x 20 = 26 x 10 = 260 x 2 = 520
   
   or
   
     (20 x 20) = 400
   + (20 x 6) =  120
                       520

3. G1 (553-554)
   
   
   
   

4. Estimate and calculate products of whole numbers using appropriate method of computation (mental mathematics, use of a calculator, use and discovery of alternate algorithms).
   

4. Calculate: Use a 3-digit factor by another factor with no more than 2-digits and whole numbers (0-10,000). (No Calculator) (5)
4. Estimation: Use a 1-digit factor with the otherfactor having no more than 3 digits or a dividend having no more than 3 digits and a 1-digit divisor and whole numbers (0-5000). (5)
4. Determine the product of a decimal in monetary notation by a single digit whole number (0-100). (5)

4. G1 (553-554)
   
   
4. G1 (138)
   
   
4. Lenchner CPS (156)
   
   
4. Nimble with Numbers 5-6
   
   
   

5. Estimate and calculate quotients of multiples of 10 by multiples of 10 using mental computation.
   
   
   

5. 23,450 ÷ 10 = 2,345
5. 640 ÷ 20 = 32
   
        
   
   

5. G1 (553-554)

6. Estimate and divide whole numbers with 1 and 2-digit divisor using appropriate method of computation (mental mathematics, use of a calculator, use and discovery of alternate algorithms).
   

6. Use a dividend with no more than a 4-digit divisor and whole numbers (0-9,999). (No Calculator) (5)
   
6. Use a 1-digit factor with the other factor having no more than 3 digits or a dividend having no more than 3 digits and a 1-digit divisor and whole numbers (0-5,000). (5)

6. How many digits are in the quotient of 384 ÷ 4?
   
   Possible answer: I know 4 x 90 = 360 so there are 2 digits in the quotient.
   
   Alert: Zeros may need to be added to quotient to show there is nothing in a place in your quotient.
   
   1316 ÷ 12 = 109 r8

6. G1 (555-556)
   
   
6. Math On Call (181)
   
   
   

7. Identify and apply identity, zero, commutative, associative, and distributive properties.

7. Use the distributive property to simplify numeric expressions and whole numbers (0-1000). (6)
7. Use the commutative property of addition or multiplication, associative property of addition or multiplication, additive inverse property, the distributive property, or the identity property for one or zero with whole numbers (0-100). (7)

7. Identity: a + 0 = a   a x 1 = a
   Zero: a x 0 = 0
   Commutative: a + b = b + a
                          a x b = b x a
   Associative: (a + b) + c = a + (b + c)
   Distributive: a(b + c) = ab + bc
   

7. G1 (137)
   
   
7. M+6 (68)
   
   
7. Math On Call (211)

8. Interpret the meaning of a remainder in a problem-solving situation and justify in writing.
    

8. Use dividend with no more than 3-digit by a 1 or 2 digit divisor and whole numbers (0-999). (5)
    

8. Add the remainder: Each picnic table seats 8 people. There are 52 people. How many picnic tables do you need?
   Drop the remainder: Movie tickets cost $7.00. How many cna be purchased with $25? (3)

8. M+6 (97)
   
   
8. Nimble with Numbers 5-6 (53-70)
   
   
8. Math On Call (182)
   

9. Select operations and appropriate symbols to solve multi-step problems, including problems involving perimeter and area

9. A room measures 12 feet by 10 feet. How much carpet will be needed to replace the old wall-to-wall carpet that is in the room? How much wallpaper border will be needed for the entire room? (44 ft)

9. Puddle Questions 6
   
   
9. G1 (147, 566)
   
   
9. Investigations 8 (68-75)