Grade Level: 4th Skill: Problem Solving Topic: Explain Your Answer in Many Ways Goal: Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work. Skill Description: Show the process of how the mathematical problem was solved using words and mathematical solutions clearly and accurately.

## Building Blocks/Prerequisites

### Sample Problems

 (1) Find the product. Explain the algorithm used to get your answer. (Allow child to choose options to find the product—various algorithms in Learning Tips #1) 2,402 x 55 What steps did you take to find the product: ____________________ (132,110—steps will vary) (2) Find equivalent measurements 4 m = ____ cm (40 cm) (3) Order linear measurements from least to greatest: 4 dm; 130 cm; 12 dm; 2 m (4 dm; 12 dm;130 cm; 2 m) (4) Find the elapsed time: The Kindergarten class arrived at the zoo at 9:30 am and left at 1:25 pm. How long did they stay at the zoo? Explain how you solved your answer. _________________ (3 hrs. 55 minutes—Imagine the hours on a clock and count forward) (5) Find the value of the variable. List the fact family for the equation. 18 ÷ n = 6 Fact family: __________________ (n =3; 18÷3 = 6/ 6 x 3 =18/ 3 x 6 = 18)

### Learning Tips

 (1) Multiplication Algorithms Lattice Math Algorithm Break Apart Multiplication Break down parts of the multiplication problem (easier multiplication, using accurate place value): 22 x 19 = 20 x 10 = 200 (multiply 1 x 2, then add two zeros) 20 x 9 = 180 2 x 9 = 18 2 x 10 = 20 Then add the products: 200 +180 380 + 18 398 + 20 418 Standard algorithm rule: 13 x 21 Multiply the ones column (multiply the one by each number at the top): 13 x 21 13 Add a zero under the 3 because you are moving to the tens column: 13 x 21 13 0 Multiply the 2 by each number at the top: 13 x 21 13 260 Add the products: 13 x 21 13 + 260 390 Use place value and expanded form* to find the product: 864 x 3 = 800 x 3= 2,400 60 x 3= 180 4 x 3= 12 2,400 + 180 2,580 + 12 2,592 *Review expanded form: 3,492 = 3,000 + 400 + 90 + 2 (2) Equivalent Linear Measurements 1 decimeter = 10 centimeters 1 meter = 100 centimeters 1 meter = 10 decimeters 1 kilometer = 1,000 meters When you change larger units to smaller units, you multiply. For example, change 300 dm to ___cm 300 x 10 = 3,000 cm When you change smaller units, to larger units, you divide. For example, change 300 dm to ___m 300 ÷ 10 = 30 m (3) Have your child measure various items, using different metric units and have them compare the measurements and convert the measurements (dm, cm, m, km) of the various items. (4) Elapsed Time The time that passes from the start to the end of an activity. Units of time 60 seconds = 1 minute 60 minutes = 1 hour 24 hours = 1 day When adding or subtracting time, remember to convert 60 minute increments into hours. Use a clock- practice using a clock, counting minutes and hours. Use a number line to find elapsed time. Locate your start time and count to the ending time. ‹--׀----------------------------------------׀--------------------------------------׀---› 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 Midnight AM noon PM (5) Fact Family Arrays- an arrangement of objects in rows and columns that is used as a manipulative to help with solving problems related to computation. Fact family- set of related multiplication and division equations using the same numbers (i.e. 4 x 3 = 12 3 x 4 = 12 12÷3 = 4 12÷4 = 3) Inverse operations- opposite operations that relate to each other (i.e. 4 x 3 = 12 and 12 ÷ 3= 4) Variable- a letter or symbol that stands for a number. Practice making fact families with your child. It can be played in the form of a Go Fish game. Make cards with fact families and deal them out. Each player chooses 5 cards and tries to find fact families (sets of 4). Ask player for fact family for ____.

### Extra Help Problems

(1)

1,679

x 64

What steps did you take to find the product: ____________________

(107,456—steps will vary)

(2)

9,213

x 82

What steps did you take to find the product: ____________________

(755,466—steps will vary)

(3)

7,122

x 35

What steps did you take to find the product: ____________________

(249, 270—steps will vary)

(4)

Find the error made in the algorithm:

1,219

x 50

50 x 9 = 450

50 x 10 = 500

50 x 200 =10,000

1,000 x 5 = 5,000

10,000 + 5,000 + 500 + 450 = 15,950

Error: ____________________

(Error = 1,000 x 5; should have been 1,000 x 50 = 50,000)

(5)

Find the error made in the algorithm:

1 5 2

8,283

x 70

0,000

+ 57,981

57,981

Error: ____________________

(The zero used as the place holder for moving to the tens column is missing in order to begin multiplying the 7)

(6)

Find equivalent measurements

35 dm = ____ cm

(35 x 10 = 350 cm)

(7)

Find equivalent measurements

9 m = ____ cm

(9 x 100 = 900 cm)

(8)

Find equivalent measurements

4,000 m = ____ km

(4,000 ÷1,000 = 4 km)

(9)

Find equivalent measurements

___ m = 80 dm

(80 ÷10 = 8 m)

(10)

The desk is 3 m long. The store clerk said it was 3,000 cm long. What error was made? ___________

(The clerk changed the linear units by multiplying 3 x 1,000; and it should have been 3 x 100 = 300 cm)

(11)

Order linear measurements from greatest to least:

8 km; 4 m; 12 cm; 8 dm

(8 km; 4 ; 8 dm; 12 cm)

(12)

Order linear measurements from least to greatest:

5 m; 200 cm; 3 dm; 4 km

(3 dm; 200 cm; 5 m; 4 km)

(13)

Order linear measurements from least to greatest:

8,000 m; 8 dm; 8 km, 800 cm

(8 dm; 800 cm; 8,000 m; 8 km)

(14)

Compare linear units. Write <, >, or = in each O.

14 m O 120 cm

(14 m > 120 cm)

(15)

Compare linear units. Write <, >, or = in each O.

30 dm O 12 m

(30 dm < 12 m)

(16)

Start time: 1:30 pm

End time: 8: 15 pm

(6 hours and 45 minutes, subtract 8:15- 1:30, borrow 60 minutes from 8:15, becomes 7:75-1:30= 6:45 or 6 hours and 45 minutes.)

(17)

Start time: 9:12 pm

End time: 4:04 am

(5 hours 52 minutes; Imagine a clock to count the hours ahead. For the minutes, subtract 60 minutes from 12= 48, and then add 4 minutes = 52 minutes).

(18)

If Janice begins work at 8:30 am, and works for 7 hours and 30 minutes. What time will she end work?

(4:00; add the hours and minutes to 8:30)

(19)

Find the elapsed time. _________

Jane’s swim class begins at 10:40 am and lasts 50 minutes. What time will the class end?

(11:30; add the minutes 10:40 +0:50=10:90, subtract 90 – 60 min, add 1 hour and remaining is 30 minutes = 11:30am)

(20)

Complete the table with the correct times:

 Start Time End Time Elapsed Time 6:15 pm 9:00 pm □ (2 hr 45 min.) 10:04 am □ (2:16 pm) 4 hours 12 min.

(21)

Find the value of the variable. List the fact family for the equation.

56 ÷ n = 8

Fact family: __________________

(n =7; 56 ÷8 = 7; 7 x 8 = 56; 8 x 7 = 56)

(22)

Find the value of the variable. List the fact family for the equation.

8 x n = 72

Fact family: __________________

(n=9; 8 x 9 = 72; 72÷9 = 8; 72÷8 = 9)

(23)

Find the value of the variable. List the fact family for the equation.

36 ÷ 4 = r

Fact family: __________________

(r=9; 36÷9 =4; 9 x 4=36; 4 x 9 = 36)

(24)

List the fact family for the array.

Fact family: __________________

(7 x 3 = 21; 3 x 7 = 21; 21÷7 = 3; 21÷3 = 7)

(25)

List the fact family for the array.

Fact family: __________________

(14 x 4= 56; 4 x 14 = 56; 56÷14= 4; 56÷4= 14)