A Visual Approach to Operations, Word Problems, Fractions ...

1 GregTangMath.com copyright © Gregory Tang

A Visual Approach to Operations, Word Problems, Fractions & Measurement

www.gregtang.com

www.gregtang.com

Greg Tang’s

Cabarrus K-2 Workshop February 27, 2017

Concord, NC

GregTangMath.com [email protected]


Single-digit Addition

What’s the number bond?

1. 8 + 6 =

2. 8 + 6 =

3. 9 + 7 =

4. 9 + 7 =


Multi-digit Addition


5. 36 + 36 =

6. 47 + 47 =

7. 29 + 34 =

8. 68 + 15 =


Single-digit Subtraction


9. 13 – 4 =

10. 13 – 4 =

11. 15 – 8 =

12. 15 – 8 =


Multi-digit Subtraction


13. 53 – 17 =

14. 96 – 38 =

15. 74 – 25 =

16. 82 – 57 =


Mental Math Challenge!

Addition & Subtraction

1.

2 6 5 + 3 7 8

2.

4 8 6 + 2 9 6

3.

8 4 1 – 6 7 3

4.

7 5 4 – 3 8 7


Mental Math Challenge

6 x 8 5 7 8 x 4 5 3

8 4 6 ÷ 9 5, 1 8 4 ÷ 12

5. 6.

7. 8.

copyright © Greg Tang www.GregTangMath.com

Add to (join)

Take from (separate)

Put together/ Take apart

(part-whole)

Compare with more

Result Unknown Change Unknown Start Unknown

Total Unknown Addend Unknown Both Addends Unknown

Difference Unknown Bigger Unknown Smaller Unknown

*101. Tammy has two apples. Greg has five apples. How many more apples does Greg have than Tammy?

131. Tammy has two apples. Greg has five apples. How many fewer apples does Tammy have than Greg?

81. Five apples are on the table. Three are red and the rest are green How many apples are green?

111. Greg has three more apples than Tammy. Tammy has two apples. How many apples does Greg have?

*142. Tammy has three fewer apples than Greg. Tammy has two apples. How many apples does Greg have?

1K. Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now?

4K. Five apples were on the table. I ate two apples. How many apples are on the table now?

21. Two bunnies were siFng on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two?

51. Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?

32. Some bunnies were siAng on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before?

62. Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before.

*122. Greg has three more apples than Tammy. Greg has five apples. How many apples does Tammy have?

151. Tammy has three fewer apples than Greg. Greg has five apples. How many apples does Tammy have?

K-2 Word Problems

Compare with fewer

From CCSS, p. 88, which is based on Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity, National Research Council, 2009, pp. 32–33.

7K. Three red apples and two green apples are on the table. How many apples are on the table?

9K. Grandma has five flowers. How many can she put in her red vase and how many in her blue vase?


1. Read the entire problem.

2. Rewrite the question as a statement.

3. Who or what is the problem about?

4. Draw your model.

5. Solve your equation(s).

6. Check your answer.

6-Step Framework C. Forsten & G. Tang

10 copyright © Creative Smarts Inc. GregTangMath.com

Result Unknown (add to, take from) 1. There were 5 baboons in a troop. 3 more baboons joined

them. How many baboons are now in the troop? 2. There were 7 bees in a hive. 4 bees flew away. How many

bees are still in the hive?


Total & Both Addends Unknown 3. There are 2 goldfish and 5 catfish. How many fish are

there all together? 4. Lucy has 9 cats. How many could be males and how many

could be females?


*Comparison: Difference Unknown 5. 5 wolves are grey and 4 wolves are red. How many more

grey wolves are there than red wolves? 6. There are 4 butterflies and 2 moths. How many fewer

moths are there than butterflies?

grey

red

butterflies

moths


Change Unknown 7. 12 birds were in a tree. Some more birds flew over and

landed. Now there are 18 birds all together. How many birds flew over and landed in the tree?

8. Jack bought one dozen donuts. He ate some of them.

Now he has 4 donuts left. How many donuts did Jack eat?


Comparison: More 9. Emily scored 11 goals and Kara scored 7 goals. How many

more goals did Emily score than Kara? 10. In April, it rained 13 days. That’s 8 more days than it

rained in July. How many days did it rain in July?


Comparison: Fewer 11. Erin found 9 fewer shells than Katie. If Erin found 6 shells,

how many shells did Katie find? 12. Cesar is training 4 fewer dogs this week than last week. If

he trained 17 dogs last week, how many dogs is he training this week?


Assessment: Single-step Word Problems 13. Marie had some beads on a string. She added 8 more to

the string. Now there are 13 beads all together. How many beads were first on the string?

14. Some cans were on a supermarket shelf. A customer

bought 6 cans and now there are 9 cans left. How many cans were originally on the shelf?

15. In Mr. Bock’s class, there are 5 fewer girls than boys.

If there are 7 girls, how many boys are there?


Multi-Step Problems

16. In the 2nd grade classroom, there are 4 rows with 4 desks in each row. In the 3rd grade classroom, there are 3 rows with 5 desks in each row. How many desks are there altogether?

17. Louise read 99 pages during the 3-day weekend. If she

read 35 pages on Friday and 31 pages on Saturday, how many pages did Louise read on Sunday?


Multi-Step Problems

18. Mario drove 30 minutes before stopping for lunch. After lunch, he drove 27 miles on Interstate 90 and 24 miles on Route 13. If Mario drove 75 miles all together, how many miles did he drive before lunch?

19. For Halloween, Emily and Katie combined all of their

candy into one big bowl. Together, they collected 60 pieces of candy. If Emily collected 24 pieces of candy, how many more pieces did Katie collect?


Multi-Step Problems

20. Natalie and Lauren put 95 songs in a playlist. Natalie picked 50 songs. How many fewer songs did Lauren pick?

21. Three second grade classes are going to the museum.

The largest class has 3 more students than the next largest class. There are 24 students in the largest class and 63 students altogether. How many students are in the smallest class?


Multi-Step Problems

22. One side of a rectangle measures 56 inches. Another side is 17 inches shorter. What is the perimeter or total length of all 4 sides?

23. The sum of two numbers is 14. The larger number is 4

more than the smaller number. What are the two numbers?


Algebraic Thinking

24. The sum of two numbers is 17. The smaller number is 5 less than the larger number. What are the two numbers?

25. Emily found 6 more shells than Katie. Together, the sisters

found 16 shells. How many shells did Katie find?


Shift focus away from the answer! 1. Jill caught 8 fish. Jack caught 6 fish. 2. Dustin ate some cookies. Kelsey ate fewer cookies

than Dustin.


Edit the story so it makes sense.

How many ways can you do it?

1. There were 11 fish in the tank. Jacques added 7 more fish. Now there are 15 fish altogether.

2. 9 pigs were in the pen. Oscar removed 3 pigs.

Now there are 12 pigs altogether. 3. Taylor has 7 apples and Tamara has 12 apples.

Taylor has 5 more apples than Tamara. 4. Oliver has 4 fewer trophies than Odell. Oliver has 9

trophies and Odell has 6 trophies.


Write your own!

1.  Add to, change unknown. 2.  Take from, start unknown. 3.  Take apart, addends unknown. 4.  Compare with more, smaller unknown. 5. Compare with fewer, larger unknown.


State Performance Tasks: Grade K K.CC.6 Give the student a set of 7 green cubes and a set of 9 red cubes. Say: There are some green cubes in this set and some red cubes in this set. How many green cubes are there? How many red cubes are there? Which set has less or is there an equal amount of cubes in each set? K.CC.7 Show the 7 card. Ask: What is this number? Show the 9 card. Ask: What is this number? Pointing to both cards, ask: Which number is greater? Repeat with cards: 5 & 6 K.OA.3 There were 10 children at the park. Some were boys and some were girls. How many girls and boys are at the park? Show as many ways as you can. Show your thinking with objects, pictures or numbers. Prompt if needed: Can you show one more way? K.NBT.1 Present student with 14 counters and the ten frame. Say: I have some counters. How many do you think there might be? Do you think they will fit on the ten frame? Use the ten frame to find out how many counters there are. Then, ask the student to write the total amount. Repeat with 16 counters .


State Performance Tasks: Grade 1 1.OA.6. Kate has 4 markers. Jill has 9 markers. How many fewer markers does Kate have than Jill? Write a number sentence that matches this story. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and show your thinking with pictures, numbers, or words. Santiago has 5 seashells. How many can he put in his blue bucket and how many in his green bucket? Find as many different combinations as you can. Solve the problem and show your thinking with pictures, numbers, or words. Write a number sentence for each combination. 1.OA.7. Provide the student with the materials. Say: Read each number sentence. Decide if it is a true number sentence or false number sentence. Check ‘true’ if you think the number sentence is correct. Check ‘false’ if you think the number sentence is incorrect (wrong). Then, explain your reasoning with pictures, numbers, or words. If it is false, also change the number sentence to make it true. 5 + 6 = 6 + 5 ________true ________false 7 = 9 - 1 ________true ________false 9 = 8 ________true ________false 1.NBT.1. Susan is counting students as they enter the gym for the play. She has just counted the 109th student. What numbers will Susan say for the next 5 students? 109, __, ___, ___, ___, ___. Provide materials to the student. Read the directions to the student: Solve each problem. Show your thinking with pictures, numbers, or words. 31 + 7 = ☐ ☐ = 55 + 7 ☐= 32 + 50 74 + 9 = ☐ the total amount. Repeat with 16 counters .


State Performance Tasks: Grade 2 2.OA.1, 2.NBT.5, 2.NBT.9 Provide materials to the student. Read the problem to the student: Allen has cats and dogs. He has 16 pets. If he has at least 10 cats, how many cats and dogs could he have? Find as many different ways as you can. Use words, numbers or pictures to explain your reasoning. Write a number sentence for each combination. Prompt if needed: Can you find another combination? Amanda has 14 fewer stuffed animals than Beth. Beth has 40 stuffed animals. How many stuffed animals does Amanda have? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. There are 11 fewer cinnamon candies than chocolate candies. There are 30 cinnamon candies. How many chocolate candies are there? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. Zoe stood on one foot for 55 seconds. Felipe stood on one foot for 38 seconds. How many more seconds did Zoe stand on one foot than Felipe? Write an equation that represents this problem. Use a symbol for the unknown number. Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning. 2.NBT.7-9 Sunshine Elementary has 216 first graders and 278 second graders. All of the first and second graders are on the playground. How many students are on the playground? Explain your reasoning with drawings, words, and/or numbers. Of all the first and second graders on the playground, one hundred of the students were playing on the blacktop. The rest of the students were playing on the field. How many students were playing in the field? Explain your reasoning drawings, words, and/or number and write an equation to match the situation.


1. Unit Fractions: Find the Part Cuisenaire Rods

Whole Fraction Part

red

purple

light green

white

yellow

one half

one half

one half

one half

one half

1.

2.

3.

4.

5.

purple

brown

dark green

red

orange


2. Unit Fractions: Find the Whole Cuisenaire Rods

Whole Fraction Part

red

purple

light green

white

yellow

one half

one half

one half

one half

one half

1.

2.

3.

4.

5.

purple

brown

dark green

red

orange


3. Unit Fractions: Find the Part Cuisenaire Rods

Whole Fraction Part

white

red

red

white

light green

one fourth

one fourth

one third

one third

one third

1.

2.

3.

4.

5.

purple

brown

dark green

light green

blue


4. Unit Fractions: Find the Whole Cuisenaire Rods

Whole Fraction Part

white

red

red

white

light green

one fourth

one fourth

one third

one third

one third

1.

2.

3.

4.

5.

purple

brown

dark green

light green

blue


5. Unit Fractions: Find the Fraction Cuisenaire Rods

Whole Fraction Part

purple

light green

red

yellow

white

one half

one third

one half

one half

one fourth

1.

2.

3.

4.

5.

brown

blue

purple

orange

purple


6. Unit Fractions: Find the Fraction Cuisenaire Rods

Whole Fraction Part

light green

white

red

white

red

one half

one third

one third

one half

one fourth

1.

2.

3.

4.

5.

dark green

light green

dark green

red

brown


1. Measurement K.MD.2. Directly compare 2 objects and describe the difference. 1.MD.2. Express the length of an object as the number of

length units that span it with no gaps or overlaps. 2.MD.2. How does the measured length of an object relate

to the size of the unit chosen?

Unit Length Object

purple

dark green

brown

brown

brown

___ reds

___ reds

___ reds

___ purples

___ whites

1.

2.

3.

4.

5.

red

red

red

purple

white




to the size of the unit chosen? .

Unit Length Object

blue

dark green

dark green

dark green

black

6.

7.

8.

9.

10.

light green

light green

red

white

white

___ lt greens

___ lt greens

___ reds

___ whites

___ whites




to the size of the unit chosen?

Unit Length Object

orange

orange

2 oranges

2 oranges

2 oranges

11.

12.

13.

14.

15.

red

yellow

yellow

purple

red

___ reds

___ yellows

___ yellows

___ purples

___ reds


DigiCross

Grade K


DigiCross

Grade 1

a rectangle has ___ vertices


DigiCross

Grade 2


Greg Tang’s Tangy Tuesday weekly puzzle pack for grades K-5. 5 new puzzles each week. Visit store.gregtangmath.com.

A Visual Approach to Operations, Word Problems, Fractions ...

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