3rd Grade - Give Clear Evidence For Your Answer

Problem Solving
Give Clear Evidence for Your Answer
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.
Mathematical Reasoning: mathematical notation, logic, problem solving The ability to show the answer (and how he/she got there) clearly in pictures or words. The ability to properly label answers in writing.

Sample Problems


One way to write an addition problem is this way:

6 + 9 = (15). Can you write it in another format? Line up the numbers carefully!


+ 9



Rewrite this problem as you did above:

21 + 36 = (57)

(When rewriting make sure the 1, 6, and 7 are aligned in a vertical column; then the 2, 3, and 5 align in the tens column)


Draw a picture to illustrate how you will solve this problem and then solve it. Be sure you label your answer.

Six friends play hide and seek. Jack is the seeker. One friend hides behind the big oak tree and two others hide behind the house. Jack is in front of the house and sees the rest of the group trying to run away. How many people does Jack see running away? How many legs does he see running? (2 kids are running; 4 legs…unless he sees his own and counts those, too=6)


Solve this problem. Be sure that your digits are aligned correctly: 45 x 2 (90)


Cole and Jaspar go surfing and each catch four waves all the way to shore. Two of them were caught going to the left and two to the right. Jaspar wiped out on two more and never made it to shore on those. Cole caught three more, but jumped off his board before making it to shore. How many waves did both boys catch all the way to shore? (8)

Learning Tips


For problems that do not involve mental math exclusively, your child needs to become proficient in explaining how he/she reached the conclusion, both in writing and orally. If a more complicated problem is one that your child seems to be able to do mentally, writing down only the answer, it is possible that he/she has devised a pattern that can be used to complete the problem without further computation. Ask your child to explain how he/she reached his answer. Some children are really able to do more complicated problems and you don’t want to discourage this, but because classroom teachers cannot always listen to each child’s oral explanation, make sure your child knows how to express his/her thinking in writing and that you come to some acceptable compromise with the school so that your child is not writing out many solutions he/she can do mentally just to prove that the work is original.


Make sure that your child can write neatly and legibly all of the digits in our number system (0-9), can draw the operations symbols for addition, multiplication, subtraction, and division; these are different depending on whether problems are written horizontally or vertically.


Make sure that your child knows that word problem solutions always include a label and that several “label patterns” not only put the correct label after the numerical solution but also help you be sure that you solved a problem correctly. For example, if you want to add together the number of apples in a basket and the number of oranges, you can do that, but what will the label be? It can’t be “orange” or “apples”. Make sure that your child knows, if that really was the calculation requested (and not a mis-reading of a word problem that came with extraneous information) that the label wording can be changed to “fruit” or “apples and oranges.” If multiplying two lengths, the label will be “square (length word)” and that if adding those lengths, the label is just the name of that length, such as feet, inches, etc. If three groups of toys each contain 6 toys, then the label will be toys; there is no need for part of the label to express “group” as that is implied in multiplication problems.


It is completely acceptable at the third-grade level for a student to show the solution to a word problem in the form of a picture or diagram rater than writing out a long explanation. The idea is to sketch the solution you plan to use as a way of helping the learner reason out what is needed for the solving of the problem and then to help remember (in the case of multi-step problems) exactly where the steps were leading. Students should not be completing some sort of a drawing later when an adult reminds them that one was expected. Teachers and parents cannot discern from that approach whether the student really understands the process and thus cannot help their growth in mathematical reasoning ability.


Help your child learn to complete calculations in a neat fashion, with adequate room allowed on the paper to line up the digits in their place-value columns and complete the solution without running into the next problem on the page. When digits are placed casually on the page, with no regard for their place-value column, eventually your child will, for example, end up adding some numbers from a tens column with numbers in a ones column, resulting in a wrong answer when probably your child knew how to do the problem. Workbook pages and worksheets often do not allow for the amount of space that a child needs to produce legible numbers and work the problem in neat, straight columns; you may need to work with your school about how best to handle it. This caution is an example of an issue that does not greatly affect the young child so it’s easy to overlook it but will come back to haunt the learner when the problems are more complex and require most, if not all, of a page to complete. It’s easier to develop good habits now.

Extra Help Problems


Solve this problem. Be sure that your digits are aligned correctly: 7 x 89 (Write the 89 on top to make alignment easier) (623)


Solve this problem. Be sure that your digits are aligned correctly: 8,675 – 43 (8,632)


Solve this problem. Be sure that your digits are aligned correctly: 7 + 2 + 12 + 10 + 6+ 71 (101)

(Ones digits should be aligned; tens digits, when present, aligned as well. Digits in the answer align also. There is an addition symbol only at the bottom of the column, just above the line that is drawn between the last digits in the problem and the answer.)


Solve this problem. Be sure that your digits are aligned correctly: 23 x 7 (161)


Solve this problem. Be sure that your digits are aligned correctly: Add together 455 and 423. From the sum of these numbers, subtract 87. (791)

(Add the first 2 numbers, aligning the ones, tens, and hundreds columns, and placing an addition sign beside the second number. The 32 may be written below the sum and subtracted, again aligning digits and using the minus sign to show the operation being performed, or a separate problem may be written to the right of the addition problem.


Solve this problem, following the guidelines you have learned from similar problems:

Add together any 3 numbers of your choice. At least one of those numbers must have a digit in the hundreds place. Multiply your sum by 5. Then subtract any number you wish from your product. The only requirement is that the number you subtract must be smaller than your product. Can you explain to someone else how you chose your numbers and how you solved the problem?


Draw a picture to illustrate how you will solve this problem and then solve it. Be sure you label your answer.

You take the bus to visit your aunt Marge. The first day the bus travels 460 miles. The next day, the bus broke down and you all had to wait for it to be fixed so you only traveled 200 miles. On the third day you look on your itinerary and see that the entire trip will be 830 miles. Can you calculate how many miles you still need to travel to reach your destination? From what you have learned about the patterns of the bus, is it likely that you can reach your destination in one more day of travel? (170 miles left; yes it is likely you will make it in one more day of travel)


Draw a picture to illustrate how you will solve this problem and then solve it. Be sure you label your answer.

A cat walks her 6 kittens across the street. One kitten wanders under a parked car and two more disappear behind a fence. How many kittens does the mother see when she tries to count her litter? (Could be one picture, with 2 circumstances or two separate illustrations.)


A backyard is divided into fourths. In the first section there are two grassy areas. In the second section, there is a children’s play area with four swings and a slide. In the third section there are children’s games, like a slip and slide and mini-golf. In the last section, there are six pet rabbits in their hutch. How many activities can you think of doing in this backyard? Draw a picture to support your answer. (answers will vary)


Draw a picture to illustrate how you will solve this problem and then solve it. Be sure you label your answer.

Your little brother likes to play with toy trucks and drivers. He has 8 dumpster trucks and each of them has 3 accessories that fit just that truck (e.g roof tops, pretend dirt, cargo.) In addition your brother has a collection of drivers that will fit any of his trucks. Five drivers have hats, 3 have belts, 2 have toolboxes and 1 has a jacket. How many different types of drivers does your brother have altogether? (11-- Use the child’s illustration to guide you in evaluating the work.)


You decide to plant a garden. You start off small by planting four sections of plants you can eat. You plant 6 corn, 2 green beans, 3 tomatoes and twice as many strawberry plants as green beans. How many plants are in the garden? (15 plants)


The garden is going well and you decide to expand. You double the number of original strawberry plants and triple the number of green beans. One of the tomato plants died when you watered it too much, though. How many plants are there now? (22 plants)


You are thinking of planting an even bigger garden, but first you need to know how much space you need. You decide to measure the perimeter to see how big it is now and measure the space you would like to occupy and see how much room you really have. The current garden is a 3 -foot by 4-foot rectangle and you have 2 feet on each side that you can expand into. How big is the current garden? How big is the space you can expand into? What is the difference between the two spaces? (current 14 feet; 22 feet expand; 8 feet difference)


Sue has $5.00 to spend at the faire tucked into her pocket when she sets out to walk to the Winter Faire at her school. She walks three blocks south from her house, then 2 blocks west. She turns left and walks 4 more blocks to reach the school. Draw a map of the route that she took from her house to the school. When she arrives at the school, how much money does she have to spend? (Check map for directions; money does not change since the other numbers have nothing to do with spending any.) ($5.00)


Your friends ask you to draw a treasure map. You bury some pretend jewels and trinkets under a tree 10 blocks from your house. The tree is in a park. Write a problem that requires the finder of your map to figure out how many blocks (10) the park is from your house just from looking at your map. Then show one way to solve the problem you wrote. (Student should draw any map that indicates 10 blocks; cross streets, stop signs, or a change in house numbers are possible ways to indicate the blocks. Then the student should indicate how those blocks might be counted, or added, to reach 10.)


Make sure to include the right label when writing your solution.

Tommy had 6 stickers. He bought 12 more, then he gave half of his stickers to his brother. How many did he give to his brother? (9 stickers)


Make sure to include the right label when writing your solution.

In a class there are 20 children. 14 of them walk to school. 5 come by bus. The rest come by car. How many of the children come to school in a car? (1 child comes by car)


Make sure to include the right label when writing your solution.

4 children made some cakes. They made 6 plain cakes and 10 chocolate cakes. They shared them equally. How many cakes did they each have? (4 cakes)


Make sure to include the right label when writing your solution.

Jane had 32 pennies. Mickey gave her 4 more. She lost 6. How many did she have left? (30 pennies)


Make sure to include the right label when writing your solution.

Gary and Larry are going to play miniature golf. It costs $3.00 each. They pay with a $5.00 bill. How much change do they get? ($2.00)


Make sure to include the right label when writing your solution.

Harold’s mother says he can invite 15 people to his party. So far, he has invited 7 boys and 2 girls. How many more children can he invite? (6 children)


A school building has 2 levels. There are 5 classrooms with 20 kids each on each level. Eight children are absent today. How many children could be in the building if all of them were there? (200 children)


In the problem above: How many children are currently in the building. (192 children)


You have four coins in your pocket. The total is 26 cents. One of my coins is a dime. What are the other three coins? (a dime, a nickel and a penny)


I have the same coins as the problem above, but I’ve added one more and have thirty-one cents. What would the fifth coin be? (another nickel)



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