Mathematically Connected Communities

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Creating Mathematically Connected Communities

Answers to the Sample Assessment Questions

Standards Based Resources

Connecting Our Communities

Kindergarten(K)
1st Grade (1)
2nd Grade (2)
3rd Grade (3)
4th Grade (4)
5th Grade (5)
6th Grade (6)
7th Grade (7)
8th Grade (8)

Math (K)     Science
Math (1)      Science
Math (2)      Science
Math (3)     Science
Math (4)      Science
Math (5)      Science
Math (6)      Science
Math (7)      Science
Math (8)      Science

Kindergarten

Kindergarten Math Sample Assessment:
Collect 5 lids of different sizes from your kitchen. Ask your child to put them in order from smallest to biggest.

NOTE: Ordering objects by size is one big idea example in Kindergarten mathematics addressing the NM Standards and Benchmark for the strands Number and Operation and Algebra.

Additional Math Activities:

Use beans to do counting, addition and subtraction. (Number and Operation example)
Sort things around the house by color (clothes, crayons, etc.), shapes (books, blocks, etc.), and size (books, containers, shoes, etc.) (Algebra example)
Look for different shapes and have your child describe them to you (squares, circles, triangles, rectangles etc.) (Geometry example)
Measure the rooms in your house with a favorite toy. (Measurement example)
Computer related activity: Use the software tool, Attributes Blocks, (a java applet tool), to sort and classify objects. (Algebra example)

Kindergarten Science Sample Assessment:
Select some items in your kitchen. Ask your child to sort the items (examples: sweet vs. sour, hot vs. cold, hard vs. soft, liquid vs. solid.)

There will be numerous answers for the questions provided. The most important thing is to encourage your child to explain what they are doing and why. Having them tell you about what they are doing will encourage their reasoning and communication skills. Take a look at the math and science standards and try to make up similar activities for your child. At this age they are full of questions and encouraging this curiosity will help them enjoy math and science for years to come.

Additional Science Activities:

Have your child observe a specific tree in the yard throughout the year and draw what it looks like in the fall, winter, spring and summer. Keep the pictures displayed in his/her room.
Have your child pick three things from the yard (a rock, a leaf, a feather) and have them describe the object to you.
Have your child come up with a list of questions about the sun, moon and stars. Check out a book at the library that helps to answer these questions.
When your child gets sick, talk to them about germs and how important it is to wash hands.

The most important thing is to make these activities conversations so that you and your child are asking questions about things and figuring out the answers together. Whenever you do these problems, always ask your child questions to make sure they can explain their thinking. Some sample questions are listed below.

How did you get your answer?
Why do you think it happened that way?
Can you describe what you are doing?

First Grade

First Grade Math Sample Assessment:
Have your child draw and describe three characteristics of a rectangle, a square, a triangle, and a circle. Ask you child to find these shapes in their environment.

NOTE: Describing characteristics of shapes is one big idea example in First Grade mathematics addressing the NM Standards and Benchmark for the strand Geometry.

Math Answers:

Although answers may vary, some of the characteristics of these objects are provided below. Remember your child is only in the first grade and may not use the proper mathematical vocabulary, but as long as they use words that make sense their description is fine.

	Rectangle: A rectangle has four sides and four corners. The sides are straight lines. There are two long sides and two short sides. Some examples of rectangles in the house are a tissue box, a refrigerator, a door, a table etc.
	Square: A square has four sides and four corners. The sides are all the same size. The sides are straight lines. Some examples of squares in the house are TV screens, some windows, some mirrors, side tables etc.
	Triangle: A triangle has three sides and three corners. The sides are straight lines. At least one of the sides is a slanted line. (Depending on the triangle being described, it may have two sides that are equal, three sides that are equal, or three unequal sides.) Some examples of triangles in your child’s world include support beams for swing sets, slices of cheese, half of a bread slice, some road signs etc.
	Circle: A circle is round. A circle does not have sides or angles. Some examples of circles in the house are tables, bottoms of cups, lids for jars, tortillas, etc.

Additional Math Activities:

Choose a number from 1 to 10. Have your child use rocks, cheerios, buttons, etc. to explore all the number combinations that make that chosen number. For example: if you chose 10, some combinations of numbers that equal 10 would be 7+3, 6+4, 5+5, 9+1, etc. (Number and Operation example)
Get a paper cup and 10 or 12 small items (e.g. cheerios or beans). Hide some of the items in the cup and have your child guess the amount of hidden items. For example, if you have 10 items and you hide 4 items in the cup, you will see 6 items. (Algebra example)
Have your child practice measuring items with their feet by counting how many of her/his steps (toe to heel) it takes to measure an item (e.g. length of a table, couch, etc) (Measurement example).
Computer related activity: Use the virtual manipulative, Color Patterns, by Utah State University to explore color patterns. (Number and Operation example)

First Grade Science Sample Assessment:
Find pictures of various living and nonliving objects and ask your child to sort the nonliving things from the living things.

Additional Science Activities: Coming Soon

How did you get your answer?
Why do you think it happened that way?
Can you describe what you are doing?

Second Grade

Second Grade Math Sample Assessment:
You were watching the wheels in a parade of bicycles and tricycles, and you counted 12 wheels all together. What combination(s) of bicycles or tricycles might have been in the parade? Explain your reasoning.

NOTE: Describing characteristics of shapes is one big idea example in Second Grade mathematics addressing the NM Standards and Benchmark for the strands Number and Operation and Algebra strands.

Math Answers:

The only correct answer is 3 bicycles and 2 tricycles because the question said that there were both bicycles and tricycles in the parade. The other two possibilities would be 4 tricycles and no bicycles or 6 bicycles and no tricycles. If your child gives these answers have them read the question again and point out that there are both kinds of bikes in the parade.

One way of doing this problem is to make a table like the one below. In second grade, your child will most likely draw pictures of bicycles and tricycles and count them to figure out the answer. Give them plenty of time to play with the question before giving them any help or answers. If they are really stuck you might want to ask the following questions:

Have you tried drawing a picture?
Do you think there are any other combinations?

When your child explains their answer to you, make sure that their reasoning makes sense. If they seem to have a hard time organizing their ideas, help them develop the skills to find their answers using some kind of a system. For example, trying one bicycle, then two, then three, etc.

Bicycles (2 wheels)	Tricycles (3 wheels)	Total Wheels
0 bicycles = 0 wheels	4 tricycles = 12 wheels	0 +12 = 12
1 bicycle = 2 wheels	3 tricycles = 9 wheels	2 + 9 = 11 (doesn’t work)
2 bicycles = 4 wheels	2 tricycles = 6 wheels	4 + 6 = 10 (doesn’t work)
3 bicycles = 6 wheels	2 tricycles = 6 wheels	6 + 6 = 12
4 bicycles = 8 wheels	1 tricycle = 3 wheels	8 + 3 = 11 (doesn’t work)
5 bicycles = 10 wheels	1 tricycle = 3 wheels	10 + 3 = 13 (doesn’t work)
6 bicycles = 12 wheels	0 tricycles = 0 wheels	12 + 0 = 12

The great thing about this problem is that it can be rewritten to make lots of other problems for you and your child to work on. Use the sample below to create other problems for your child. Once they work on a few, they will learn how to figure out these problems using their own system.

You are watching a pet parade with four legged animals. There are 24 legs in the parade. What combinations of humans and pets are possible?

Additional Math Activities:

When driving, give simple mental addition and subtraction problems for your child to solve. (Number and Operation example)
Solve simple number sentences with missing numbers (e.g. 8 + __ = 13, 7 + 7 = __). (Algebra example)
Practice identifying geometric shapes (e.g. circle, triangle, square, rectangle) in your child's world (e.g. windows, clocks, books, toys, etc.). (Geometry example)
Buy an analog clock or watch to practice telling time by identifying hour and quarter hour. (Measurement example)
Buy stickers to symbolize and organize information in a bar graph. For example, have your child collect information (e.g. How many pets do you have? What shoe size do you where? or about any family interests or events, etc.) from friends and relatives to organize in bar graph form. (Data Analysis and Probability example)
Computer related activity: Visit Polygon Playground by Wendi Petti to explore geometric shapes by creating designs, etc. Discuss shapes and symmetry with your child as they create their designs.(Note: Compatible only with Internet Explorer) (Geometry example)

Parent Resource:

Second Grade Parent Guide by the Department of Defense Education, (math on pages 8-12)

Second Grade Science Sample Assessment:
Go outside each night for a month and draw a picture of the shape of the moon each night. Describe the phases of the moon using your pictures.

Science Answer:
This is a fun project for you and your child. Using the pictures, make sure to use correct terminology to describe the phases of the moon. The new moon, the crescent moon, the half moon, the gibbous moon and the full moon.

This project can be enhanced by creating a moon book. Your child is the illustrator and the author. As they describe the moon they can add a storyline.

There are also some questions you can ask your child throughout this project.

How many days do you think it will take before we see a full moon again?
How many days does the moon stay in each phase?
Does the crescent moon always look the same?
Why do you think the moon is so bright and the stars are so small?
Can you see more stars when the moon is full or when it is a new moon? Why?

Even if you don’t know all of the answers, it will spark your child’s curiosity and you can find the answers together. That is what science is all about!

Additional Science Activities:

Take a picture of a tree in the yard the first day of every month and explore how it changes throughout the year.
Explore websites online about the moon and the solar system. Some examples are:
- Interactive representation of the phases of the moon by Harcourt School Publishers
- An animation explaining the phases of the moon from the Science Alberta Foundation:
- Interactive exploration of the phases of the moon by the Center for Earth and Space Science Education at TERC, Inc., Cambridge , Massachusetts. Funded in part by a grant from the National Science Foundation.
Buy a telescope to explore the night sky.
Check out the astronomical society in your area for workshops.
Go to the library and find a good book.

How did you get your answer?
Why do you think it happened that way?
Can you describe what you are doing?

Third Grade

Third Grade Math Sample Assessment:
Juan and Jack saw some ducks and goats at the petting zoo. Jack said, “There are 18 ducks and goats.” Juan said, “Altogether they have 52 legs!” How many ducks and how many goats did they see? Explain how you solve this problem and give your answer.

NOTE: This type of problem solving activity is very important for students to develop strategies to solve problems in all strands of the NM Standards and Benchmarks. This particular problem addresses Number and Operations and Algebra strands .

Math Answers:

There are a lot of ways your child can do this problem. Some might feel most comfortable drawing pictures or creating a table. In the end, they are going to make some guesses, check their answer and try again until they find the right combination. As a parent, the most important thing is to encourage them to use a method that is organized. This will help them develop good problem solving strategies in the future.

For example if they start with one goat that has 4 legs, then there would be 48 legs left, or 24 ducks. Well, that is too many animals! If they assume there are 2 goats (8 legs), then there would be 22 ducks…still too many animals. However, if they keep going, they will eventually get the correct answer of 8 goats and 10 ducks.

Additional Math Activities:

When you go to a restaurant, have your child estimate how much the meal will cost. This can be a good way for them to develop the skills necessary to judge when an answer is reasonable or not. (Number and Operation example)
Create a problem similar to the one in the brochure but use cars and bicycles (or even tricycles to make it more challenging). (Algebra example)
Look for different shapes and have your child describe them to you (squares, circles, triangles, rectangles etc.) (Geometry example)
Measure the rooms in your house with a ruler or a yard stick and then have your child convert this to inches. (Measurement example)
Have your child create a bar graph representing how many pairs of shoes each member of the family has in his/her closet. (Data Analysis and Probability example)
Computer related activity: Have your friends and family answer this survey and then graph your results using this graphing tool by the National Center for Education Statistics (NCES). (Data Analysis and Probability example)

Third Grade Science Sample Assessment:
Compare and contrast the characteristics of the sun and the moon.

There are a lot of things your child could say about the sun and the moon. Once again this question can be a teaching tool for helping your child organize his/her thoughts. Have your child develop a chart like the one below to answer the question.

There are a lot of great websites about the solar system that are appropriate for this age level. If your child does not know enough about the sun or the moon to answer this question, visit Kids Astronomy website for a great resource.

Additional science activities:

As a family do the following experiment:

Predict how many jumping jacks you can do in one minute
Have each member of the family do jumping jacks for 1 minute
Record the results
Create a chart to show the results

Buy a magnet and have your child make predictions about what it will stick to and then try it out to see what works.
When your child gets sick, talk to them about germs and how important it is to wash hands and eat well
Have your child watch the weather channel so that they can see how weather affects the environment and how the environment affects the weather.

The most important thing when looking at both the math and science questions is to encourage your child to justify their answers. Having them tell you about what they are thinking will encourage their reasoning and communication skills. Take a look at the math and science standards in the brochure and try to make up similar activities for your child to work on at home. At this age they are able to look online and in books to answer questions about things that interest them. Encouraging this curiosity will help them enjoy math and science for years to come.

How did you get your answer?
Why do you think it happened that way?
Can you describe what you are doing?

Fourth Grade

Fourth Grade Math Sample Assessment:

What are all of the numbers you can use to skip count and land on 100?
What are all of the factors of 100?

NOTE: Recognizing classes of numbers (odd, even, factors, multiples, etc.) and understanding and using numbers up to 100,000 are some examples in Fourth Grade mathematics activities which address the NM Standards and Benchmark. This particular problem addresses the Number and Operation strand .

Math Answers:

Skip count: Skip counting is the same thing as ‘counting by two’s or three’s or twenty’s for that matter’ and can be done using the table provided. This is an essential skill for mastering multiplication, division and factoring. Through skip counting, children are better able to see that multiplication is repeated addition and division is repeated subtraction.

What are all of the numbers you can use to skip count and land on 100?
Answers: 1, 2, 4, 5, 10, 20, 25, 50, 100

What are all of the factors of 100? Find all the factors of a number by asking yourself what are all the numbers that divide evenly into 100.
Answers: 1, 2, 4, 5, 10, 20, 25, 50, 100

Additional Math Activities:

Have your child bake with you in the kitchen. Use a standard recipe and cut it in half or double it. This will give your child practice with fractions. (Number and Operation and Measurement examples)
Have your child create 5 equations for you to solve and have them check your answers. Good luck! (Algebra example)
Have your child locate your house, and other local landmarks on the map in the phone book. Each map uses a grid system and this is a practical use of a coordinate system. (Geometry example)
Have your child find the area of a room in your house and the area of your dining room table. (Measurement example)
Have your child keep track of their spelling test scores each week. At the end of a grading period have them calculate the mean, median, mode, maximum, minimum and range of their data. (This activity can be done with any list of numbers) (Data Analysis and Probability example)
Computer related activity: Go to Webmath.com, to get help in finding factors of a number. Or play the Factor Game, at the National Council of Teachers of Mathematics’ Illumination website. (Numbers and Operation example)

Fourth Grade Science Sample Assessment:
Describe how severe weather can affect the food web of an ecosystem. Think of an example from where you live.

Science Answer:

An example might be the drought that the state has suffered in recent years. Because New Mexico has many ecosystems, your child could describe many different scenarios, such as the impact on the Elephant Butte Lake ecosystem and food web, the impact on the ecosystem and food web of the Kiowa National Grasslands, or the impact on their family farm.

A lack of rain could mean several things for the plants in an ecosystem, for example:

The plants could be smaller
The plants could grow more sparsely in an area
The plants’ chemical composition could be changed
The plants could have a shorter life cycle
The plants may die before they have a chance to reproduce
The plants may die before they get to a reasonable size for consumption

Any one of these things, or these things in combination, will affect the consumers higher up in the food chain. For example, if plants are sparser and have a different chemical composition, this will alter the insect populations that feed on them. All the predacious insects, birds, and small mammals that eat the primary insects will have to widen their feeding area or feed somewhere else. Animals that eat the plants, such as deer and antelope, will also be affected. The grazers will also have to widen their feeding area. This may be difficult, depending on where the nearest water source may be, and some animals may produce fewer offspring, may not reproduce at all and, in the most extreme cases, will die from the impact on the food web. The same results will happen to the predators in the food web. Finally, the humans at the top of the food web will be affected as our harvests decrease, our livestock need more supplemental food, and the native plants and animals in our food web suffer.

An example your child may give should first include how the ecosystem and the lowest producer in their food web would be affected by the severe weather. They should then sequentially describe all the other producers and consumers that would be affected and the impacts on them.

Additional Science Activities: Coming Soon

How did you get your answer?
Why do you think it happened that way?
Can you describe what you are doing?

Fifth Grade

Fifth Grade Math Sample Assessment:
In Ms. Guzman’s class there are 15 kids who have brown eyes, 6 kids who have green eyes, 5 kids have blue eyes, and 4 kids have hazel eyes.

What fraction of the kids have brown eyes?
Answer: 15/30 or ½ of the kids have brown eyes.
What fraction of the kids have blue eyes?
Answer: 5/30 or 1/6 of the kids have blue eyes.
What percentage of kids have brown eyes?
Answer: 6/30 = 1/5 = 0.2 = 20% of the kids
What percentage of kids have hazel eyes?
Answer: 4/30 = 2/15 = 0.1333 ≈ Approximately 13% of the kids have hazel eyes.

Explain how you can use the fractions to determine the percentages. Collect the data on the students in your class or in your family. Organize the data in a graph or table and answer the questions above using your data.

The answers to this part of the problem will vary depending on the data collected by your child.

This problem is designed to help students make the transition from fractions to decimals to percentages. This is a key concept in 5^th and 6^th grade and it is very important that your child understands that all of these numbers, even though they look different, are the same thing. A fraction is changed into a decimal by dividing the top number by the bottom number and the decimal is turned into a percentage by multiplying the decimal by 100 or (moving the decimal point over two places to the right).

NOTE: This type of problem solving activity is very important for students to develop strategies to solve problems in all strands of the NM Standards and Benchmarks. This particular problem addresses Number and Operations strand .

Additional math activities:

Have your child bring home three graded tests from his/her class. Have them calculate their grade. For example if there are 20 problem on the test and they miss 2, then they got 18/20 correct. Well 18/20 = 0.9 = 90%. By doing this with their own work, they will have a better understanding of where their ‘grades’ come from. (Number and Operation example)
Give your child a series of numbers that follow a pattern and have your child discover the pattern. (For example: 2, 5, 11, 23, 47…..) To get the next number, you multiply the previous number by 2 and then add 1. (Algebra example)
Have your child identify symmetry in different objects or places. (Geometry example)
When you are taking a long trip, have your child estimate your time of arrival depending on the distance and your rate of speed. (Measurement example)
Get a set of two dice from a board game and play simple probability games with your child. Ask them questions like: “What is the probability of rolling a ___?” and help them figure it out. Good Luck! (Data Analysis & Probability example)
Computer related activity: Explore perimeters using the Perimeter Explorer , (a java applet tool), by Shodor Interactive. (Measurement example)

Fifth Grade Science Sample Assessment: Coming Soon

How did you get your answer?
Why do you think it happened that way?
Can you describe what you are doing?

Sixth Grade

Sixth Grade Math Sample Assessment:

Name	Ann	Bart	Lucy	Luis	Pam	Lupe	Juan
School days absent last year	3	11	2	3	2	19	2

Figure out the mean, median, and mode of the data in the table.
What measure is the best way to describe the data in the table? Why?
If you add the number of days you were absent from school last year, how does this impact the mean, median, and mode?

NOTE: Learning the concepts of mean, median, and mode is one example in Sixth Grade mathematics addressing the NM Standards and Benchmark for the Data Analysis and Probability strand.

Answers:

1. Figure out the mean, median, and mode of the data in the table.

Mean: Mean is just another word for average. To find the mean, add all of the numbers in the table (3+11+2+3+2+19+2) and divide by 7. 42/7 = 6. The mean of the data is 6.

Median: Median is the ‘middle’ number. To find the median, put the numbers in order from smallest to largest and identify the middle number. If there is an even number of data points, to find the median you take the average of the two middle numbers. 2, 2, 2, 3, 3, 11, 19 The median of the data is 3.

Mode: Mode is the number that appears the ‘most’. To find the mode, find the number in the data that appears the most. The mode of the data is 2 because it appears in the list three times.

2. What measure is the best way to describe the data in the table? Why?

The answers to this question might vary and depending on how your child justifies his/her answer. If the reason for a particular selection seems reasonable, it is probably ok. However, it is important to discuss why mean, median and mode are all important.

3. If you add the number of days you were absent from school last year, how does this impact the mean, median, and mode?

The answers to this question will vary depending on how many days your child was absent. Just make sure that they are able to figure out the mean, median, and mode correctly. The other part of this question is also important because the measures will either stay the same, increase or decrease. Help them to use proper mathematical language to describe the impact.

Have your child view stem-and-leaf plots (visit the Shodor Interactivate web link) of their data and then practice finding means, medians, and modes with other data.

Additional math activities:

When you go out to eat, have your child add up the bill in his/her head. (Number and Operation example)
Give your child a series of numbers that follow a pattern and have your child discover the pattern. (For example: 2, 5, 11, 23, 47…..) To get the next number, you multiply the previous number by 2 and then add 1. (Algebra example)
Have your child use the map (and coordinate system) in the telephone book to describe how to go from one location to another. (Geometry example)
Have your child chart the temperatures for each day in a week. Have them place the information on a graph and have them calculate the mean, median and mode for the data. (Data Analysis example)
When you are taking a long trip, have your child estimate your time of arrival depending on the distance and your rate of speed. (Algebra example)
Get a set of two dice from a board game and play simple probability games with your child. Ask them questions like: “What is the probability of rolling a ___?” and help them figure it out. Good Luck! Have your child represent these probabilities in fractions, decimals and percentages. (Probability example)
Computer related activity: Do map reading activities at the Enchanted Learning website to practice describing locations and relationships. (Geometry example)

Sixth Grade Science Sample Assessment: Coming Soon

How did you get your answer?
Why do you think it happened that way?
Can you describe what you are doing?

Seventh Grade

Seventh Grade Math Sample Assessment:

You and your friends are ordering pepperoni pizza for movie night. The restaurant has 10 inch pizzas for $7 and 20 inch pizzas for $15. What is the better deal: two 10 inch pizzas or one 20 inch pizza? Explain how you know.

NOTE: Exploring relationships between radius, diameter, and area of a circle are examples in Seventh Grade mathematics addressing the NM Standards and Benchmark for Geometry.

Note: Pizzas are round and the size of the pizza is given by the diameter in inches.

Answers: There are quite a few different ways to approach this problem.

One way: If your child is familiar with the formula for area, he/she might choose to use the formula. The formula for the area of a circle is A = лr² where
л =3.14 and r = the radius of the circle.

The area of the small pizza: (3.14)(5²)=78.5 in²
There are two small pizzas, so the total area of two small pizzas is 2 (78.5 in²) or 157 in²

The area of the one large pizza: (3.14)(10 in²) = 314 in²

If you do the problem by figuring out the areas, it is very clear that the large pizza is the best deal.

Another approach:

If your child is more visual, he/she might want to just draw the pizzas like the diagram below and then explain his/her solution.

Additional math activities:

When you go shopping for clothes, try to hit the sales racks. “Take an extra 30% off the sales price.” Have your child try to figure out what the discounted price will be. (Number and Operations example)
Give your child a series of numbers that follow a pattern and have your child discover the pattern. Have your child place these points on a graph and predict what the output would be if the input was 10. For a challenge, have them figure out the equation of the line that passes through these points. (Algebra example)

Input	1	2	3	4
Output	3	5	7	9

Have your child draw and describe three dimensional figures. (Geometry example)
Investigate which cylinder holds more: Take 2 sheets of 8 ½ by 11 inch paper. Roll one into a short cylinder and the other into a tall cylinder. Make visual estimates and use popcorn to help you solve this. For more exploration with this problem go to Figure This website!. (Measurement example)
Have your child chart the temperatures for each day in a week. Have them place the information on a graph and have them calculate the mean, median and mode for the data. Have them predict what the temperature will be the same time next year. (Data Analysis and Probability example)
Computer related activity: Visit A Maths Dictionary for Kids to explore mathematical terms.

Seventh Grade Science Sample Assessment: Coming Soon

How did you get your answer?
Why do you think it happened that way?
Can you describe what you are doing?

Eighth Grade

Eighth Grade Math Sample Assessment:

You have been offered two different jobs represented by line A and line B. Both jobs have similar duties and responsibilities and the pay for both is based on the hours worked per week. Which job would you take? Justify your decision.

Answer:

If I looking for work, I would take Job A. The line for Job A is increasing at a faster rate than the line for Job B. This means that you get paid more per hour for Job A than you do for job B.

Additional math activities: Coming Soon

EighthGrade Science Sample Assessment: Coming Soon

How did you get your answer?
Why do you think it happened that way?
Can you describe what you are doing?