Let's start with our standards. Below are links to the unpacking documents of the NC math standards for each elementary grade level.

Kindergarten:

First grade:

Second grade:

Third grade: Operations and Algebraic Thinking and Measurement and Data

Fourth grade: Operations and Algebraic Thinking, Numbers and Operations -- Fractions, Measurement and Data

Fifth grade: Numbers and Operations -- Fractions, Measurement and Data, Geometry

K.OA.1 Examples

K.MD.1 Examples

3.0A.1 Examples:

Jim purchased 5 packages of muffins. Each package contained 3 muffins. How many muffins did Jim purchase? 5 groups of 3, 5 x 3 = 15. Describe another situation where there would be 5 groups of 3 or 5 x 3.

Sonya earns $7 a week pulling weeds. After 5 weeks of work, how much has Sonya worked? Write an equation and find the answer. Describe another situation that would match 7x5.

3.0A.3 Examples:

There are 24 desks in the classroom. If the teacher puts 6 desks in each row, how many rows are there? This task can be solved by drawing an array by putting 6 desks in each row. This is an array model. This task can also be solved by drawing pictures of equal groups.

There are some students at recess. The teacher divides the class into 4 lines with 6 students in each line. Write a division equation for this story and determine how many students are in the class ( ÷ 4 = 6. There are 24 students in the class).

Max the monkey loves bananas. Molly, his trainer, has 24 bananas. If she gives Max 4 bananas each day, how many days will the bananas last?

3.0A.4 Example

Solve the equations below: 24 = ? x 6 72 ÷ = 9 Rachel has 3 bags. There are 4 marbles in each bag. How many marbles does Rachel have altogether? 3 x 4 = m

3.0A.6 Example

Sarah did not know the answer to 63 divided by 7. Are each of the following was an appropriate way for Sarah to think about the problem? Explain why or why not with a picture or words for each one. • “I know that 7 x 9 = 63, so 63 divided by 7 must be 9.” • “I know that 7x10 = 70. If I take away a group of 7, that means that I have 7x9 = 63. So 63 divided by 7 is 9.” • “I know that 7x5 is 35. 63 minus 35 is 28. I know that 7x4 = 28. So if I add 7x5 and 7x4 I get 63. That means that 7x9 is 63, or 63 divided by 7 is 9.”

3.0A.8 Example

Mike runs 2 miles a day. His goal is to run 25 miles. After 5 days, how many miles does Mike have left to run in order to meet his goal? Write an equation and find the solution (2 x 5 + m = 25).

On a vacation, your family travels 267 miles on the first day, 194 miles on the second day and 34 miles on the third day. How many total miles did they travel?

3.MD.2 Example

Students identify 5 things that weigh about one gram. They record their findings with words and pictures. (Students can repeat this for 5 grams and 10 grams.) This activity helps develop gram benchmarks. One large paperclip weighs about one gram. Example: A paper clip weighs about a) a gram, b) 10 grams, c) 100 grams? Explain why.

3.MD.3 Example

Draw a bar graph in which each square in the bar graph might represent 5 pets

Analyze and answer questions about a bar graph and interpret the data

3.MD.4 Example

Measure objects in your desk to the nearest ½ or ¼ of an inch, display data collected on a line plot. How many objects measured ¼? ½? etc…

3.MD.5 Example

Students determine which rectangle covers the most area.

3.MD.6 Example

Students tile a region and count the number of square units in metric, customary, or non-standard square units. Using different sized graph paper, students can explore the areas measured in square centimeters and square inches.

3.MD.7 Example

Students can decompose a rectilinear figure into different rectangles. They find the area of the figure by adding the areas of each of the rectangles together. For example, find the area of an oddly shaped storage shed by decomposing into separate parts and adding the total areas.

3.MD.8 Example

Given a perimeter and a length or width, students use objects or pictures to find the missing length or width. They justify and communicate their solutions using words, diagrams, pictures, numbers, and an interactive whiteboard. Students use geoboards, tiles, graph paper, or technology to find all the possible rectangles with a given area (e.g. find the rectangles that have an area of 12 square units.) They record all the possibilities using dot or graph paper, compile the possibilities into an organized list or a table, and determine whether they have all the possible rectangles. Students then investigate the perimeter of the rectangles with an area of 12.

Enter your
**Fourth grade**

4.OA.2 Example

Unknown Product: A blue scarf costs $3. A red scarf costs 6 times as much. How much does the red scarf cost? (3 x 6 = p). Group Size Unknown: A book costs $18. That is 3 times more than a DVD. How much does a DVD cost? (18 ÷ p = 3 or 3 x p = 18). Number of Groups Unknown: A red scarf costs $18. A blue scarf costs $6. How many times as much does the red scarf cost compared to the blue scarf? (18 ÷ 6 = p or 6 x p = 18).

4.OA.3 Example

On a vacation, your family travels 267 miles on the first day, 194 miles on the second day and 34 miles on the third day. How many miles did they travel total?

Your class is collecting bottled water for a service project. The goal is to collect 300 bottles of water. On the first day, Max brings in 3 packs with 6 bottles in each container. Sarah wheels in 6 packs with 6 bottles in each container. About how many bottles of water still need to be collected?

There are 1,128 students going on a field trip. If each bus held 30 students, how many buses are needed?

4.OA.4 Example

Students should understand the process of finding factor pairs so they can do this for any number 1 - 100, Example: Factor pairs for 96: 1 and 96, 2 and 48, 3 and 32, 4 and 24, 6 and 16, 8 and 12.

4.OA.5 Example

There are 4 beans in the jar. Each day 3 beans are added. How many beans are in the jar for each of the first 5 days?

4NF.1 Example

Explain and model equivalent fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.

4NF.2 Examples

Use patterns blocks. 1. If a red trapezoid is one whole, which block shows 3 1 ? 2. If the blue rhombus is 3 1 , which block shows one whole? 3. If the red trapezoid is one whole, which block shows 3 2 ?

Mary used a 12 x 12 grid to represent 1 and Janet used a 10 x 10 grid to represent 1. Each girl shaded grid squares to show 4 1 . How many grid squares did Mary shade? How many grid squares did Janet shade? Why did they need to shade different numbers of grid squares?

4.NF.3 Examples

There are two cakes on the counter that are the same size. The first cake has ½ of it left. The second cake has 5/12 left. Which cake has more left?

Susan and Maria need 8 3/8 feet of ribbon to package gift baskets. Susan has 3 1/8 feet of ribbon and Maria has 5 3/8 feet of ribbon. How much ribbon do they have altogether? Will it be enough to complete the project? Explain why or why not.

A cake recipe calls for you to use ¾ cup of milk, ¼ cup of oil, and 2/4 cup of water. How much liquid was needed to make the cake?

4.NF.5 Examples

In a relay race, each runner runs ½ of a lap. If there are 4 team members how long is the race?

If each person at a party eats 3/8 of a pound of roast beef, and there are 5 people at the party, how many pounds of roast beef are needed? Between what two whole numbers does your answer lie?

4.NF.7 Example

Draw a model to show that 0.3 < 0.5. (Students would sketch two models of approximately the same size to show the area that represents three-tenths is smaller than the area that represents five-tenths.

4.MD.2 Examples

Charlie and 10 friends are planning for a pizza party. They purchased 3 quarts of milk. If each glass holds 8oz will everyone get at least one glass of milk?

How many liters of juice does the class need to have at least 35 cups if each cup takes 225 ml?

Tonya wakes up at 6:45 a.m. It takes her 5 minutes to shower, 15 minutes to get dressed, and 15 minutes to eat breakfast. What time will she be ready for school?

4.MD.3 Examples

A rectangular garden has as an area of 80 square feet. It is 5 feet wide. How long is the garden? Here, specifying the area and the width creates an unknown factor problem. Similarly, students could solve perimeter problems that give the perimeter and the length of one side and ask the length of the adjacent side.

A plan for a house includes rectangular room with an area of 60 square meters and a perimeter of 32 meters. What are the length and the width of the room?

4.MD.4 Examples

Students measured objects in their desk to the nearest ½, ¼, or 1/8 inch. They displayed their data collected on a line plot. How many object measured ¼ inch? ½ inch? If you put all the objects together end to end what would be the total length of all the objects.

4.MD.5 Examples

A water sprinkler rotates one-degree at each interval. If the sprinkler rotates a total of 100º, how many one-degree turns has the sprinkler made?

4.MD.7 Examples

A lawn water sprinkler rotates 65 degress and then pauses. It then rotates an additional 25 degrees. What is the 4th Grade Mathematics ● Unpacked Content page 55 total degree of the water sprinkler rotation? To cover a full 360 degrees how many times will the water sprinkler need to be moved? If the water sprinkler rotates a total of 25 degrees then pauses. How many 25 degree cycles will it go through for the rotation to reach at least 90 degrees?

here...Present students with the problem 1/3 + 1/6. Encourage students to use the clock face as a model for solving the problem. Have students share their approaches with the class and demonstrate their thinking using the clock model.

Jerry was making two different types of cookies. One recipe needed 3/4 cup of sugar and the other needed 2/3 cup of sugar. How much sugar did he need to make both recipes?

Sonia had 2 1/3 candy bars. She promised her brother that she would give him ½ of a candy bar. How much will she have left after she gives her brother the amount she promised?

If Mary ran 3 1/6 miles every week for 4 weeks, she would reach her goal for the month. The first day of the first week she ran 1 ¾ miles. How many miles does she still need to run the first week?

Elli drank 3/5 quart of milk and Javier drank 1/10 of a quart less than Ellie. How much milk did they drink all together?

Ludmilla and Lazarus each have a lemon. They need a cup of lemon juice to make hummus for a party. Ludmilla squeezes 1/2 a cup from hers and Lazarus squeezes 2/5 of a cup from his. How much lemon juice do they have? Is it enough?

5.NF.3 Examples

If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get?

Ten team members are sharing 3 boxes of cookies. How much of a box will each student get?

Two afterschool clubs are having pizza parties. For the Math Club, the teacher will order 3 pizzas for every 5 students. For the student council, the teacher will order 5 pizzas for every 8 students. Since you are in both groups, you need to decide which party to attend. How much pizza would you get at each party? If you want to have the most pizza, which party should you attend?

The six fifth grade classrooms have a total of 27 boxes of pencils. How many boxes will each classroom receive?

Your teacher gives 7 packs of paper to your group of 4 students. If you share the paper equally, how much paper does each student get?

5.NF.4 Examples

Three-fourths of the class is boys. Two-thirds of the boys are wearing tennis shoes. What fraction of the class are boys with tennis shoes?

The home builder needs to cover a small storage room floor with carpet. The storage room is 4 meters long and half of a meter wide. How much carpet do you need to cover the floor of the storage room? Use a grid to show your work and explain your answer.

5.NF.5 Examples

Mrs. Bennett is planting two flower beds. The first flower bed is 5 meters long and 6/5 meters wide. The second flower bed is 5 meters long and 5/6 meters wide. How do the areas of these two flower beds compare? Is the value of the area larger or smaller than 5 square meters? Draw pictures to prove your answer.

5.NF.6 Examples

There are 2 ½ bus loads of students standing in the parking lot. The students are getting ready to go on a field trip. 2/5 of the students on each bus are girls. How many busses would it take to carry only the girls?

Mary and Joe determined that the dimensions of their school flag needed to be ft. by 2 ft. What will be the area of the school flag?

5.NF.7 Examples

Four students sitting at a table were given 1/3 of a pan of brownies to share. How much of a pan will each student get if they share the pan of brownies equally?

You have 1/8 of a bag of pens and you need to share them among 3 people. How much of the bag does each person get?

Create a story context for 5 ÷ 1/6. Find your answer and then draw a picture to prove your answer and use multiplication to reason about whether your answer makes sense. How many 1/6 are there in 5?

Angelo has 4 lbs of peanuts. He wants to give each of his friends 1/5 lb. How many friends can receive 1/5 lb of peanuts? A diagram for 4 ÷ 1/5 is shown below. Students explain that since there are five fifths in one whole, there must be 20 fifths in 4 lbs.

5.MD.2 Examples

Students measured objects in their desk to the nearest ½, ¼, or 1/8 of an inch then displayed data collected on a line plot. How many object measured ¼? ½? If you put all the objects together end to end what would be the total length of all the objects?

5.MD.5 Examples

When given 24 cubes, students make as many rectangular prisms as possible with a volume of 24 cubic units. Students build the prisms and record possible dimensions.

Students determine the volume of concrete needed to build the steps in the diagram.

5.G.1 Examples

Plot these points on a coordinate grid. Point A: (2,6) Point B: (4,6) Point C: (6,3) Point D: (2,3) Connect the points in order. Make sure to connect Point D back to Point A. 1. What geometric figure is formed? What attributes did you use to identify it? 2. What line segments in this figure are parallel? 3. What line segments in this figure are perpendicular?

Emanuel draws a line segment from (1, 3) to (8, 10). He then draws a line segment from (0, 2) to (7, 9). If he wants to draw another line segment that is parallel to those two segments what points will he use?

5.G.2 Examples

Sara has saved $20. She earns $8 for each hour she works. If Sara saves all of her money, how much will she have after working 3 hours? 5 hours? 10 hours? Create a graph that shows the relationship between the hours Sara worked and the amount of money she has saved. What other information do you know from analyzing the graph?

5.G.3 Examples

Examine whether all quadrilaterals have right angles. Give examples and non-examples.

A parallelogram has 4 sides with both sets of opposite sides parallel. What types of quadrilaterals are parallelograms?

Regular polygons have all of their sides and angles congruent. Name or draw some regular polygons.

All rectangles have 4 right angles. Squares have 4 right angles so they are also rectangles. True or False?

A trapezoid has 2 sides parallel so it must be a parallelogram. True or False?