4th Grade - Apply Strategies To Complex Problems

 Grade Level: 4th Skill: Reasoning Topic: Apply Strategies to Complex Problems Goal: Apply strategies and results from simpler problems to more complex problems. Skill Description: Use strategies for simple problems in order to solve difficult problems.

Building Blocks/Prerequisites

Sample Problems

 (1) Mental Math: Use a basic fact and pattern to write the product for the large number. 2 x 8,000 = (16,000) (2) Represent problems using base-ten blocks to find the product. (The child will be required to drag and model the multiplication problem with base-ten blocks) 105 x 5 (525) (3) Mental Math: Use basic division facts and patterns to write the quotient for the large number. 2,700 ÷ 9 = (300) (4) Use the break apart strategy to multiply the product. 297 x 4 7 x 4 = ___ 90 x 4 = ____ 200 x 4 = _____ Add the products: _____ + _____ + _____ = ________ (28 + 360 + 800 = 1,188) (5) Find the area of the complex polygon: Area 1 : ___________________ Area 2: ________________ Total Area: _____________ (Area = 3 x 9 + 8 x 4 = 59 ft2)

Learning Tips

(1)

Break Apart Strategy

Helps the child compute mentally without using pencil and paper.

Multiplication (Solve simpler problems)- find the product for 372 x 4

1. Multiply by the ones 4 x 2 = 8

2. Multiply by the tens 70 x 4 = 280

3. Multiply by the hundreds 300 x 4 = 1,200

4. Add the products 8 + 28 + 1,200 = 1,236

(2)

Break apart complex polygons

Divide figure to find area:

Example

 4 4 7 3 3 7

Divide the polygon into two rectangles. The larger rectangle measures as (4) length and (7) at the width. Use the formula for finding the rectangle (A = l x w) A = 4 x 7 = 28. Next, find the area of the smaller square which is (3) length and (3) width. A= 3 x 3 = 9. Finally, add the two areas together 28 + 9 = 37 sq. units.

(3)

Multiplication with zeros

Multiply the basic facts, then add the remaining zeros to the product (answer to the multiplication problem).

For example,

8,000 x 30

1. Multiply basic facts 8 x 3 = 24

2. Add the remaining zeros to the product 24 (add 4 zeros) 240000

3. Product = 240,000

Division Patterns:

Find the quotient (answer to division problem) to the simple division problem, and then add the zeros left in the dividend to the quotient.

For example,

8,100 ÷ 9

1. Divide the basic facts 81 ÷ 9 = 9

2. Add the remaining zeros to the quotient (add 2 zeros) 900

3. Quotient = 900

(4)

Lattice Math Algorithm

(5)

Base ten blocks –Website you can use to get base ten block cut-outs for ones, tens, and hundreds) http://mason.gmu.edu/~mmankus/Handson/b10blocks.htm

 This is the 1-block or unit block the smallest of all the blocks. This is the 10-block corresponding to 10 units.  It is also referred to as a rod or long. This is the 100-block and corresponds to 100 units. It is also called a flat.

Use base-ten blocks to model a multiplication problem in order to find the product.

You can make a model to find 142 x 3:

1. Model 3 groups of 142 (using (1) hundred block (4) ten- blocks (2) one-blocks)

2. Combine the groups

-(6) one-blocks

-(12) ten-blocks

-(3) hundred-blocks

3. Combine the ten-blocks to make one hundred-block (with two ten-blocks remaining)

4. Count the total number of blocks to find the product (4-hundred-blocks; 2- ten-blocks; and 6-one-blocks) = 426

5. Therefore, 142 x 3 = 426

Extra Help Problems

 (1) Mental Math: Use a basic fact and pattern to write the product or factors for the large number. 7 x __ = 42,000 (6,000) (2) Mental Math: Use a basic fact and pattern to write the product or factors for the large number. 8 x 60,000 = _________ (480,000) (3) Mental Math: Use a basic fact and pattern to write the product or factors for the large number. 7 x ______ = 35,000 (5,000) (4) Mental Math: Use a basic fact and pattern to write the product or factors for the large number. 13 x 3,000 = _________ (39,000) (5) Mental Math: Use a basic fact and pattern to write the product or factors for the large number. There are 50 coins in each roll of dimes. How many coins are in 20 rolls? (50 x 20 = 1,000 dimes) (6) Use base-ten blocks to multiply. 154 x 5 (770) (7) Use base-ten blocks to multiply. 116 x 4 (464) (8) Use base-ten blocks to multiply. 206 x 3 (618) (9) Use base-ten blocks to multiply. 145 x 2 (290) (10) Use base-ten blocks to multiply. 309 x 7 (2,163) (11) Use the break apart strategy to multiply the product. 142 x 61 2 x 1 = ___ 40 x 1 = ____ 100 x 1 = _____ 2 x 60 = _____ 40 x 60 = _____ 100 x 60= ______ Add the products: ________ (2 + 40 + 100 + 120 + 2,400 + 6,000 = 8,662) (12) Use the break apart strategy to multiply the product. 321 x 34 1 x 4 = ___ 20 x 4 = ____ 300 x 4 = _____ 1x 30 = _____ 20 x 30 = _____ 300 x 30= ______ Add the products: ________ (4 + 80 + 1,200 + 30 + 600 + 9,000 = (10,914) (13) Use the break apart strategy to multiply the product. 184 x 73 2 x 1 = ___ 40 x 1 = ____ 100 x 1 = _____ 2 x 60 = _____ 40 x 60 = _____ 100 x 60= ______ Add the products: ________________ (2 + 40 + 100 + 120 = 2,400 + 6,000 =8,554) (14) Use the break apart strategy to multiply the product. 732 x 23 2 x 3 = ___ 30 x 3 = ____ 700 x 3 = _____ 2 x 20 = _____ 30 x 20 = _____ 700 x 20= ______ Add the products: _____________ (6 + 90 + 2,100 + 40 + 600 + 1,400 = 4,236) (15) Use the break apart strategy to multiply the product. 417 x 16 7 x 6 = ___ 6 x 10 = ____ 400 x 6 = _____ 7 x 10 = _____ 10 x 10 = _____ 400 x 10= ______ Add the products: _____________ (42 + 60 + 2,400 + 70 + 100 + 4,000 = 6,672) (16) Mental Math: Use basic division facts and patterns to write the quotient for the large number. 40,000 ÷ 5 = (8,000) (17) Mental Math: Use basic division facts and patterns to write the quotient for the large number. 3,200 ÷ 8 (400) (18) Mental Math: Use basic division facts and patterns to write the quotient for the large number. 15,000 ÷ 5 (3,000) (19) Mental Math: Use basic division facts and patterns to write the quotient for the large number. 20,000 ÷ 2 (10,000) (20) Mental Math: Use basic division facts and patterns to write the quotient for the large number. 3,000 ÷ 6 (2,000) (21) Solve for the area: Area 1: ___________ Area 2: ___________ Total Area: _____________ (2 x 4 + 2 x 10 = 28 cm2) (22) Solve for the area: Area 1: ___________ Area 2: ___________ Total Area: _____________ (2 x 7 + 3 x 4 = 26m2) (23) Solve for the area: Area 1: ___________ Area 2: ___________ Total Area: _____________ (2 x 4 + 2 x 10 = 28 cm2) (24) Solve for the area: Area 1: ___________ Area 2: ___________ Total Area: _____________ (4 x 3 + 5 x 3 = 27 in2) (25) Solve for the area: Area 1: ___________ Area 2: ___________ Total Area: __________ (6 x 2 + 2 x 4 =20 yd2)