Math Journals

and Other Math Ideas for Primary GradeTeachers

***Scroll down to the *** to read an article of mine on this topic that was published in Chicago Math's Newsletter. There's a few additional insights and more sample questions. TO PURCHASE MY NEW RESOURCE MAKING MATH MARVELOUS PLEASE VISIT THE HOME PAGE AND CLICK ON THE PAYPAL BUTTON.***

"Students should be writing and talking about math topics every day. Putting thoughts into words helps to clarify and solidify thinking. By sharing their mathematical understandings in written and oral form with their classmates, teachers, and parents, students develop confidence in themselves as mathematical learners; this practice also enables teachers to better monitor student progress."

"Standard 4.5: All students will use mathematical processes of problem solving, communication, connections, reasoning, representations, and technology to solve problems and communicate mathematical ideas."

New Jersey Department of Education Core Standards on Math

"Language, whether used to express ideas or to receive them, is a very powerful tool and should be used to foster the learning of mathematics. Communicating about mathematical ideas is a way for students to articulate, clarify, organize, and consolidate their thinking. Students, like adults, exchange thoughts and ideas in many ways—orally; with gestures; and with pictures, objects, and symbols. By listening carefully to others, students can become aware of alternative perspectives and strategies. By writing and talking with others, they learn to use more-precise mathematical language and, gradually, conventional symbols to express their mathematical ideas. Communication makes mathematical thinking observable and therefore facilitates further development of that thought. It encourages students to reflect on their own knowledge and their own ways of solving problems. Throughout the early years, students should have daily opportunities to talk and write about mathematics."

-From Principles and Standards for School Mathematics

The Use of Daily Math Journals

Children's math journals can be a notebook or paper stapled together. The question can be part of the morning message, oral or in a big book format you create and laminate.

At the Kindergarten and first grade level the activities should be quick and developed for students to have a high degree of success. In fact right and wrong is not the emphasis. The focus should be on reasoning and communication. The child may have the wrong answer but if they reasoned it logically and can explain their reasoning to you they should receive a lot of praise. This prepares them for the multi-step problems they have to solve on standardized testing. On tests at the grades three and four level students will receive some credit for their work if it is reasoned and explained well even if the answer is wrong.

A benefit of math journals is the ability for the teacher to highlight, review or spot check a concept briefly. Journals cut down on the number of worksheets needed to be copied and are a good portfolio component. The students can keep journals at their table reducing the time it takes to pass out and collect worksheets. Math journals allow students to write and/or draw their answers increasing their problem solving ability. Math journals encourage the process of discovery as students can learn to create their own math problems.

Minute Math activities like those in Chicago Math lend themselves very easily to math journal questions to get you started but you can create questions that are tailored to the specific needs of your class. As time goes on you can laminate the questions and create a lasting resource.

When giving the students at this early level a word problem it may be best to use the students' own names and experiences. They will feel more comfortable with the problem and have an easier time listening for the important information.

With math journal problems and oral word problems you first have to teach them the process of how to solve word problems. You will want to review with them that there are different types of problems. Once you learn to recognize a certain type it is easier and faster to solve. Some types of problems are those with extra information, not enough information and two-step solutions. The students need to learn to recognize what type of word problem it is.

Initially every time you give the students a problem you should first go over what type it is. Chart it out. Make columns that detail important information and extra information. Draw the two step process. Visual learners will benefit from seeing oral word problems explained in this way; and it prepares them for standardized tests in which they have to show how they got the answer and explain it.

One idea for math journals that you may want to use for a month or so is to give all the students a quick addition or subtraction problem to solve. You may want to post on a record keeping chart each time a child gets a correct answer to a daily problem. Every time a child gets 5 or 10 correct they can get a prize from the prize box, sticker or hand stamp.

Math Journal Problems

Some Examples Based on Literature

1. One day Harry the dirty dog had a cat friend visit. They sat down to enjoy some afternoon sunshine by a window. How many legs did they have total? Draw your answer.

2. In the story The Pet Show two pets won prizes for being the smallest pet and the largest pet. Draw a picture to show what you think they looked like.

3. In The Three Billy Goats Gruff there were three goats. How many legs did they have all together? Draw your answer.

4. Before they got to the other side of the bridge to eat the sweet green grass the billy goats were forced to eat garbage. The largest goat ate 4 tin cans. The smallest goat ate three cans and the medium sized goat ate two cans. How many cans did they eat all together? Draw your answer. (It is helpful to teach your students to break down the problem when they draw it. You can teach them to draw the three goats first and then the cans they each ate underneath. They will actually be breaking down the problem in a very similar way to word problems they will be doing in grades three and four.)

5. One day the old woman who swallowed a fly decided to eat only desserts. She really was not a very healthy eater. First, she ate a cake. Then she ate a candybar. Lastly, she ate an ice cream cone. Draw the desserts she ate in the correct sequence.

6. The gingerbread man met a cow and a fox. Which one of these animals is faster? Draw your answer.

7. The gingerbread man tried to get across the river on the fox's back. That was not a very good idea! Can you think of another way the gingerbread man could have gotten across the river? Draw your answer.

8. The old woman baked the gingerbread man at 350 degrees. What do you think would have happened if she baked him at 500 degrees? Draw your idea of what might happen.

9. One day Peter went out to play in the snow. He made a snowball and left it in his snowball in his pocket and it slowly melted. Draw a picture to show another way that Peter could get his snowball to melt faster.

10. One day the little red hen baked a cake for her 8 chicks. She sliced the cake into 8 pieces. Her chicks each got a piece. Draw what this looked like.

11. One day the little red hen baked a loaf of bread for herself and 3 chicks. She sliced the bread into 3 pieces. Her chicks each got a piece but the little red hen didn't get any! How could she slice the bread so that everyone would get a piece? Draw what the bread would look like.

12. Cinderella washed all the floors at 10:00 in the morning. Draw a clock to show the time of day.

13. Cinderella did all the laundry at 2:00 in the afternoon. One hour later she did the sewing. Draw a clock or write the digital time to show when she did the sewing.

14. How many mittens did the three little kittens have total? Show me with a picture of the three pairs. Then write the number to show how many mittens there are.

15. Oh no! The three little kittens are having trouble with their mittens again! They went outside and one of the kittens got his mittens all muddy. Draw a picture to show how many clean mittens were left.

16. The spider frightened Miss Muffet and she dropped her bowl of curds. She had only eaten half the bowl. Draw a picture to show how much she had left.

17. The golden goose laid five eggs one day and two more the next day. Draw how many total she laid.

18. Jack is ten years old. Jill is eight years old. Which one is younger? Draw your answer.

19. The first little pig built his house to be five feet tall. The second little pig built his house ten feet tall. The third little pig built his house 20 feet tall. Draw a picture of what their houses looked like and label with a number one, two and three.

20. Snow White's hair is five inches long. Rapunzel's hair is 50 feet long. Draw a picture of what they look like. Who has longer hair? Label your drawing with their names. (Write the names on the board for the chidren to copy.)

21. Draw a picture of the big bad wolf. Use only shapes. Use a circle for the head. Use triangles for the ears and teeth. Use a rectangle for a snout.

22. The five little monkeys were getting ready for bed. Two of them already had their pajamas on. How many monkeys still needed to get their pajamas on? Draw your answer.

23. Hansel ate nine gumdrops. Gretel ate two less than Hansel. How many gumdrops did Gretel eat? Draw your answer. (You can teach children to figure this out by having them draw all nine gumdrops that Hansel ate. Then have them put an x through two of them to show how many Gretel ate. Showing their work in this way is helpful to learn for standardized tests.)

24. In the treasure cave Aladdin found some beautiful jewels. He found a ruby that was shaped like a circle, a sapphire shaped like a square and an emerald that was shaped like an oval. Draw these treasures of Aladdin.

25. Aladdin lined up his jewels to make an ABC pattern of ruby, emerald, sapphire, ruby, emerald, __________.What jewel does he need next to complete his pattern? Draw it.

26. The little mermaid had a party with some ocean friends. There was one octopus at the party and three fish. How many were at the party? Draw them.

Oral Story Problems

The sooner you start having students solve word problems the better. If students learn early on in a fun way to listen for the important details of a word problem they'll gain the confidence they need to solve this type of math problem.

Before we start our oral word problems I ask the children to get their fingers ready. We do a quick finger stretch, shake out our fingers and do a finger play. The children know that they are listening for the numbers in the story and ignoring information that isn't important. They use their fingers to keep track of the information that is important.

It is easy to create word problems like these once you get used to it. The problems can be modified to make them easier or harder. For more general word problems there are already many good sources out there. I rely on my Minute Math ( Everyday Math) put out by Chicago Math.

Some Examples Based on Literature

1.Tikki Tikki Tembo and his brother Chang didn't listen to their mother telling them to stay away from the well. One day they were flying kites and Tikki Tikki Tembo fell in the well. He was in the well for 15 minutes. On another day they were eating rice cakes sitting on the edge of the well when Chang fell in. He was in there for 10 minutes. Who stayed in the well the shortest time?

2. One day the two brothers were arguing over rice cakes. Chang said he could eat more rice cakes than his brother. Chang ate three rice cakes. Tikki Tikki Tembo ate two and then two more. Which of the brothers ate more rice cakes?

3. One day Harry the dirty dog had a couple of cat friends visit. They sat down to enjoy some afternoon sunshine on the window ledge. How many tails did they have all together?

4. Harry loved to bury things in the backyard. In one hole he buried the wash brush 6 inches. In another hole he buried his bone 10 inches. Which was buried deeper the brush or the bone?

5. In the story The Pet Show there were three cats entered in the contest. There were also four dogs and one rabbit in the contest. How many animals were there all together?

6. Before they got to the other side of the bridge to eat the sweet green grass the billy goats were forced to eat garbage. The largest goat ate 4 tin cans. The smallest goat ate 3 cans and the medium sized goat ate 2 cans. Which goat ate the least?

7. Imagine that Peter decided to have a snowball fight the next day with his friend from across the hall. They each made five snowballs. How many snowballs did they have all together?

8. Peter threw one snowball very fast. Then he threw two more. How many snowballs did he have left?

9. One day the little red hen baked a cake for her 8 chicks. She sliced the cake into 8 pieces. How many pieces did each chick get? How many slices did the little red hen get?

10. Cinderella made breakfast at 7:00. One hour later she washed the breakfast dishes. What time was it when she washed the dishes?

11. Cinderella swept the floor 4 times. But her step sisters were so messy she had to sweep the floor 3 more times. How many times did she have to sweep the floor?

12. Jack and Jill went to fetch a pail of water at 8:00. They came back home at 9:00. How long did it take them?

13. On another day Jack and Jill went out to fetch some water and they found the water was frozen. It was only 20 degrees outside. They heard on the radio that tomorrow the temperature would be 50 degrees. Will the weather the next day be warmer or colder?

14. Jack is ten years old. Jill is eight years old. Whose birthday comes next?

15. Oh no! The three little kittens are having trouble with their mittens again! They went outside and two of the kittens got their mittens all muddy. How many kittens had clean mittens left?

16. Their mommy gave the kittens an apple pie that was cut into 4 pieces. The three little kittens each ate a piece. How much pie was left?

17. One of the kittens lost her mittens again! Mommy gave her a nickel and told her to buy new mittens at the store. At the store new mittens had a price tag that said one quarter per pair. How many mittens was the kitten able to buy?

18. One day the mommy cat just didn't have time to bake a pie so she gave one of the kittens three nickels and one penny to go buy a pie at the store. The store pie cost 15 cents. Did the kitten have enough money to buy the pie? How much money did he have left?

19. Jack decided to plant some more beans. Jack's beanstalk grew five feet the first night and two feet the next day. How tall was the beanstalk?

20. One of Jack's beanstalks was 7 feet tall. Another was 8 feet tall. Which beanstalk was taller?

21. The golden goose laid 27 eggs. Chicken Little laid 35 eggs. Who laid more eggs? The goose or the chicken?

22. While he was sitting on the wall Humpty Dumpty was humming a little tune. It went like this "Boop boop biddy boop, boop boop biddy boop, boop_______. What comes next in the song?

23. Humpty Dumpty, Mother Goose, Jack Be Nimble, and Miss Muffet were having a feast. They had roast beef, green beans, pasta, cake and pie. One of them didn't eat the green beans. Who didn't eat the green beans?

24. Cinderella, Snow White, Miss Muffet and Mother Goose were all at the beauty parlor getting their nails painted. Cinderella likes pink. Snow White likes pink. Miss Muffet likes red and Mother Goose likes pink. They all got their nails painted pink except for one of them. Which of them got her nails painted red?

25. Cinderella's hair was 10 inches long. She had a hair cut and got two inches cut off. How long was her hair then?

26. Little Red Riding Hood is seven years old. How old will she be two years from now?

27. Little Red went to visit her grandma on Saturday. Her grandma came to visit her the next day. What day of the week did her grandma come to visit?

28. Little Red went on a long train trip. She left in the month of October and came back the following month. What month was it when she returned?

29. At first Pinnochio's nose grew four inches long and then it grew another 2 inches. How long did his nose grow?

Use of the Overhead

The overhead projector is one of my favorite teaching tools. I don't usually use it until after winter break and then it adds a great new dimension to our whole class lessons. The students get excited about the machine and it sparks a lot of enthusiasm. I use it for both reading and math. The projector really focuses the children's attention, more so than when I use the board, since the classroom is dark and there are fewer distractions.

For reading you can put up an emergent reader and have the kids use a pointer to read to the rest of the class. The large size of the projector is even better than a big book. Children learn concepts of print faster and you can point out high frequency words easily and even circle them on the transparency. Focusing in on the H brothers (ch,sh,th,wh), tricky y or the -VCE formula are easier than using highlighter tape in a big book. I've made several beginning reader books into overhead stories simply by laying the transparency down and tracing the drawing.

For math there are many commercially made resources for the overhead projector but you can easily make many yourself. I like to use the overhead to reinforce counting, sequencing and identification of larger numbers. Using an overhead 100's chart; the children follow along with their own chart at their seat, we count and look for number patterns such as numbers that end in 0. Students can use the pointer to find the number. I ask them to color 57 blue, color all the numbers that end in five red and count by 10's or 2's. I can immediatly reinforce the correct answer with the overhead. Another idea is to give students a 100's chart and then have them follow your directions (as you color on the overhead) to color a mystery picture ( ex.find #57 and color it blue). Some picture ideas are a house, butterfly, snowman, heart, etc. You can have a picture to go with each theme.

We use the overhead with five and ten frames. Again the students have their own at their seat and/or come up and move the manipulatives on the transparency themselves. With this tool the students can use thinking skills to see the different ways they can arrange the number 15 (as three rows of five, five rows of three, ten plus five, in a straight line, in a circle,etc.

When we are discussing 10's and 1's the overhead helps me to demonstrate effectively. I have strips of ten ( a row of 10 squares with circles colored inside) and then single circles. The students use popsicle sticks with ten beans glued on and single beans or base ten blocks. This helps students understand that 36 is three tens and six ones. They see me build it on the overhead and they build it at their seat.

When I am showing them how to use a calculator a transparency of the calculator helps them to locate the buttons I am asking them to press. The overhead is also useful when reviewing addition and subtraction. The children can see you move the manipulatives and they do the same at their seat with their counters.

General Math Ideas For Ongoing Activities

Use straws to keep track of ones and tens as you count up to the 100th day.
Use rows of velcro to keep track of days with coins. Every 5th day change your five pennies to a nickel,etc. Make a set of coins that have velcro on the back. You can count the days of the month this way or continue counting up to the 100th day.
Keep track of days with tally marks. Couny by 5's as you get into higher numbers.
Keep track of daily weather with tally marks.
Help your students understand tally marks with a xylophone. Count individual marks tapping the xylophone and slide across the xylophone when you get to the 5th/hash mark.
Use thematic erasers as counters to keep interest high throughout the year. Store a set of 20 counters per child in baggies. These are small enough to keep at tables and pull out quickly.
Draw a simple scene on a piece of paper with a line drawing. Include some mountains in the distance, a tree, lake and bridge. Laminate these and use all year for math problems instead of worksheets. Example, two bears were in the water, three were climbing a tree and one was on the bridge. How many bears were out today? Make a transparency and you can model for the children the solutions.
Keep two clear plastic estimation jars. Use one as a reference that always contains ten or twenty of an item. Some types of objects that work well are counters, erasers, little toy cars for a unit on transportation, dolls, little plastic farm or zoo animals, acorns for fall, marbles, little pinecones, conversation hearts for February, candy bars for Halloween, etc.

************************************

***Using Math Journals in Kindergarten***
by Terry Tunkel, Kindergarten Teacher, North Plainfield, NJ

“ I like them because you can do a lot of imagining.”
“ I think it’s great to write a math story and we can read them whenever we want.”
“ They make me have to think more.”
“ I think they’re great because you get to color your math.”

--A sampling of quotes from my kindergarten students who
have created math journals in my class.

The mission of the Everyday Mathematics program is “to enable children to learn more mathematical content and become lifelong mathematical thinkers”. Math journals support this goal throughout grades 1-6 of the program, and provide students with the skill practice and strategies they will need to succeed in today’s standardized tests. I felt the math journal format might also benefit my kindergarten students. Therefore, I created similar math journals with my kindergarten students as part of their math class. I have found their journals help them prepare for the standardized testing to come in later grades.

Two years ago my son was beginning third grade and the NJASK was a brand new standardized assessment to be given to third and fourth grade students in New Jersey. No one was exactly sure what to expect from the test. It was supposed to be similar to but harder than the previous fourth grade state tests. I attended a workshop for parents given by the teachers at my son’s school and I was surprised at the very high expectations that the new NJASK would be requiring of students. In particular, the mathematics portion of the test required students to complete several steps to answer just one question, and the questions sometimes had several parts. Often students had to make a drawing, label their picture and provide written explanations for their thinking process. I realized it would be impossible to prepare students for these tests in just one year, and thought it would help to have students begin to prepare for this approach to problem solving early as Kindergarten.

I was intrigued by the possibility of having my kindergarten students keep journals to get them writing and talking about math each day. The New Jersey Department of Education’s core standards promote using language as a tool to help clarify and solidify students’ thinking about math. Students are to express their ideas in oral and written form. I thought journals might be a way to reinforce my state’s core standards in my kindergarten classroom. Creating math journals with my kindergarten students could help familiarize them with this process of answering math questions by drawing pictures, labels, and providing written explanations.

To create our kindergarten journals I gave each student a little blank notebook which they kept right at their desks. I first demonstrated the process of drawing and diagramming work when solving a problem. Then I read a problem aloud to the class and asked the students to create a journal entry of the answer in his or her journal by drawing and diagramming the problem. Minute Math activities make great journal topics, as does the Everyday Mathematics core activity of “Number Stories through out the Year.”

After students are comfortable creating journal entries that draw and diagram their work on problems, I ask them to provide a written explanation of the answer in their journals as well. Sharing answers is then another requirement I gradually work into our journal time. When we share our work, the process naturally takes more class time. As the students become familiar with the requirements, the process will speed up significantly and journaling can only be a portion of your class math time. If time is limited, we would save the sharing time for the following day when we would simply review the previous days work rather than create a new journal entry. I pick only a small handful of students to share each class period, but make sure everyone gets to share at some point.

The writing of math explanations is not a significant problem for most of my students. From the beginning of September I encourage the students in their developmental writing using phonetic spelling. I follow the approach outlined in Kid Writing by Isabell Cardonick and Eileen Feldgus. However, I have found that the main part of most student’s explanations take place orally as they do their thinking aloud while sharing their answers.

When I first began this journaling activity with my class, I kept a packet of over 150 possible math journal questions. As the year progressed I found that many math journal questions flowed naturally from the math lesson, reading story, or everyday events so my packet grew. Some journal questions help me to highlight, review, or spot check comprehension and fluency. It was simple to make the questions easier or harder depending on what the class was ready for. The journals also support the spiral approach by giving me an opportunity to revisit skills through out the year. Some of our journal questions became excellent topics for class books, so I had the class as a whole work together on some journal entries which we recorded on large sheets of paper. I bound these group entries together into class books as the year progressed. We made addition and subtraction books, triangle books, and many more. The students enjoyed revisiting these throughout the year in our class library. I also used the journals as a quick assessment aid to see if I need to cover a topic further or to determine which students need extra help. The journals have proven to be very flexible.

I started using students’ own names and experiences in journal questions to help the students connect to the material more readily. This helps them feel more comfortable with the problem and have an easier time listening for the important information. I also try to vary the way I word the questions. For example, I may ask either “How many altogether?” or “How many total?” Learning the different ways a question can be phrased is an important strategy they will need in later testing.

I have found that by sharing their journals, the students are learning to be open minded toward math. They learn that there is not only one way to find the answer. During one journal activity, I asked the class the following math question. The golden goose laid 27 eggs. The little red hen laid 35 eggs. Which one laid more eggs? I compared the responses of four students who all got the answer correct. The first student correctly drew and labeled the golden goose and red hen. She proceeded to actually draw 27 eggs next to the goose and 35 next to the hen. Her count was accurate. She finished off with a written explanation, “Because 30 is bigger then 20.”

The second student, one of my ESL students, took the same approach of drawing and labeling the characters. Then he drew a small pile of eggs next to the goose and a big pile next to the hen. He didn’t give a written explanation, but his drawing showed me that he understood the number 35 is more than 27. In my opinion, he supplied a correct answer but his score on a standardized test like NJASK would be even higher if he were able to provide a written explanation. After more journal activities, he will be able to provide that written explanation.

The third student drew and labeled the golden goose and the red hen but no eggs. He captioned his work by writing, “27 < 35.” He did not provide any other written explanation, though again, he was able to demonstrate how he got his answer. The fourth student drew and labeled both goose and hen characters and wrote the numbers 27 and 35 under the appropriate drawing. She further wrote, “The red hen had 35 and goose had 27 but the hen had more.”

All four of these students knew the answer but would have scored differently on the NJ ASK. I asked these four students to share their journals with the class and explain their thinking. I emphasized the need for a written explanation and guided the class to create a written explanation for the responses that were missing one. The class benefited from seeing their classmates different approaches as well as modeling the written explanation. Some students struggled to answer a problem with a drawing, labels, and complete explanation, but clearly my students were beginning to understand the procedure.

Journaling math problems can help teachers differentiate content, process, and product according to a student’s readiness and interests. It takes only a moment to alter a question to a student’s interests. The question about the goose and the hen could have been changed to bubbles blown by two children, or any number of other ideas. Through these journals assessment and instruction are inseparable, the working environment is flexible, and all students participate. All are key elements of differentiation.