4th Grade MATH JOURNALS 4th Grade Math Journals contains 60 math journal tasks

aligned with the Common Core State Standards. All tasks are

based on a problem solving approach and provide valuable

opportunities for students to organize, clarify and reflect on

their thinking while developing key mathematical skills and

understandings.

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What Are Math Journals? A math journal is a book in which students record their math work and thinking. Math journals are used to:

• Record the solutions to math problems: When solving problems in a math journal, students are expected to record their strategy and thought processes, as well as solutions.

Math journals may also be used to:

• Write about learning: For example, students may be asked to write about "what you already know about ......" at the beginning of a unit or "what you did today, what your learned, and any questions you have", or "your most and least favorite activity in this unit and why."

By dating entries a math journal provides a chronological record of the development of a student’s mathematical thinking throughout the year. Why Use Math Journals? While students learn how to "do" math, they must also learn how to articulate what they are learning. It is important to provide many opportunities for students to organize and record their work without the structure of a worksheet. Math journals support students' learning because, in order to get their ideas on paper, children must organize, clarify, and reflect on their thinking. Initially many students will need support and encouragement in order to communicate their ideas and thinking clearly on paper but, as with any skill, the more they practice the easier it will become. Math Journals also serve as invaluable assessment resources that can inform classroom instruction. Requiring students to communicate their reasoning processes provides a useful insight into what a child understands, how s/he approaches ideas and what misconceptions s/he has. What Are The Characteristics of a Good Math Journal Question? A Good Math Journal Question ….

allows for multiple entry points and recording techniques, thereby allowing all students to work at their individual level of thinking,

provides the opportunity for students to learn by answering the question, and the teacher to learn about each student from the attempt,

may have more than one solution,

requires more than just remembering a fact or reproducing a skill,

provides the opportunity for students to communicate their different ways of thinking,

has clear, concise directions,

provides opportunities for group work and discussion.

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The most important thing to consider when developing a math journal question is whether the question involves significant mathematics. Closed questions, such as ‘There are two bowls of apples. Each bowl has eight apples. How many apples in all?’ do little to develop a child's mathematical thinking if the child can answer the question before even getting back to his or her seat. The child may spend 15 minutes drawing and coloring apples but the math thinking is limited. Changing the question from a closed to an open format such as, “There are 16 apples to put into bowls. Each bowl must have the same number of apples. Show as many different solutions as you can.” creates greater potential to stimulate mathematical thinking and reasoning. How Are Math Journal Sessions Structured? Math journal sessions typically consist of three main components: before, during and after. These components are sometimes referred to as the Mini-lesson, Student Activity, and the Share. By devoting time to each component a full period can be devoted to one math journal task.

During the before phase, or mini-lesson, the role of the teacher is to mentally prepare students for the task, ensure that students understand the task and establish expectations. In order to prepare students for the task some teachers like to model the task in a large class math journal while others prefer to pose the task right away and then have students brainstorm a list of possible solution strategies. If the journal task is based on a math read aloud this would be read during the mini-lesson. To ensure that students understand a task the teacher may discuss certain vocabulary involved in the task or have students explain what the problem is asking in their own words. It is important to establish expectations from the outset for math journal sessions. Asking students to record their thinking on paper using pictures, numbers, or words places an emphasis on process, indicating to students that their thinking is as important as the answers.

In the during, or Student Activity stage, it is important to encourage students to use their own ideas and not simply copy what the teacher did during the mini-lesson. This is a time for the teacher to listen and find out how students are approaching a problem. The teacher may confer with individuals or small groups of students and record anecdotal notes.

The after phase, or Share component, is a crucial component of the lesson. The teacher's role is to make sure that all students listen, participate and understand what is being said. Several students may be selected to share their solutions and explain their process. Selecting students who have used different strategies or recording styles will provide a model for other students of different ways to approach problems.

Can Math Journal Tasks Be Revisited During The Year? Definitely! Repeating, or revisiting tasks, allows students to engage with tasks at a deeper level. On the first occasion the student may be focused on ‘how to do’ the task. Subsequent visits provide an opportunity for students to communicate their reasoning more clearly. Making slight variations to an open ended task or changing the materials used to complete a task helps to maintain interest while providing time for students to further develop skills and concepts. For example, by changing the number and the setting in question 4, from ‘there are 40 cupcakes to be put onto plates…. to ‘there are 48 pencils to be packed into boxes’, or ‘there are 120 seeds to be planted in pots’ this task can be revisited multiple times and allow for different strategies and products to emerge. Similarly, question 28, ‘Which is larger, 2/3 or 3/4?’ can be revisited many times during the course of the year by simply changing the fractions.

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Some teachers like to provide opportunities for students to revisit tasks by introducing math journal tasks to the whole class and then placing tasks in centers for children to revisit at other times throughout the year. Other teachers choose one journal task and repeat it several times throughout the year, with slight variations, as a record of the development of math skills and understandings for student portfolios. How Often Should I Use Math Journals in My Class? This is entirely up to the teacher. Some teachers use them several times a week. Other teachers who have more restrictions on their math sessions due to using a mandated curriculum set aside one session per week for math journals and then select a journal task that correlates with the current unit of study. The important thing is to ensure that students are being given regular opportunities throughout the year to record their mathematical thinking in a way which makes sense to them. What Type Of Book Should My Students Use As A Math Journal? At the K - 5 level many teachers like to use a blank notebook as the math journal so that students are not restricted by lines and have the space to choose whether to use pictures, numbers, words or a combination of these to record their thinking.

About This File: This file contains 60 math journal tasks suitable for use in 4th grade classrooms. Content for all tasks is based on the Common Core State Standards and includes:

• use the four operations with whole numbers to solve problems, • gain familiarity with factors and multiples, • generate and analyze patterns, • generalize place value understanding for multi-digit whole numbers, • use place value understanding and properties of operations to perform multi-digit

arithmetic, • extend understanding of fraction equivalence and ordering, • build fractions from unit fractions by applying and extending previous

understandings of operations on whole numbers, • understand decimal notation for fractions, and compare decimal fractions, • solve problems involving measurement and conversion of measurements from a

larger unit to a smaller unit, • represent and interpret data, • understand concepts of angles and measure angles, and • draw and indentify lines and angles, and classify shapes by properties of their

lines and angles.

Math Rubrics A rubric can be a powerful tool for both teaching and assessment. Use of a rubric can improve student performance, as well as monitor it, by making teachers' expectations clear and by showing students how to meet these expectations. The result is often marked improvements in the quality of student work and in learning. A sample 4th Grade Math Rubric, suitable for use with the journal tasks in this e-book, is included in the resources section. Resources: Resources have been included for use with the following journal tasks:

• Hundred Chart (Tasks 8 and 9) • Fraction Circles (Task 29) • Polygons Sheet (Task 55) • Geoboard Paper (Task 58)

Printing the Tasks The math journal tasks are formatted so that you can either print and cut out the labels or, alternatively, print the tasks on mailing labels (Avery Standard, 5160) to save time cutting and pasting. Just print, peel and pass out for students to stick at the top of their math journal page. If using labels we suggest that you begin by printing just one page to check that the labels sheet is correctly positioned in your printer.

Copyright 2010 k-5mathteachingresources.com Permission is granted to original purchasers to reproduce material for their own classroom use. No other part of this work may be redistributed, reproduced or transferred in any form or by any electronic or mechanical means, including photocopying, information storage or retrieval systems, without the prior written permission of the publisher.

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4th Grade Math Journal Tasks

Operations and Algebraic Thinking 4.OA Use the four operations with whole numbers to solve problems 1. Multiplicative Comparison 2. More Multiplicative Comparison 3. Equal Products 4. Equal Groups 5. Interpreting Remainders Gain familiarity with factors and multiples 6. Find the Factor 7. Find the Factor 2 8. Multiples on a Hundred Chart 9. Common Multiples 10. What might the two prime numbers be? Generate and analyze patterns 11. Identifying and Analyzing Patterns 12. Sam’s Reading Pattern 13. Patterns with Square Numbers 14. How Many Cookies? 15. Increase by Six 16. Decrease by Three Number and Operations in Base Ten 4.NBT Generalize place value understanding for multi-digit whole numbers 17. Rounding to the Nearest Ten 18. Rounding to the Nearest Hundred Use place value understanding and properties of operations to perform multi-digit arithmetic 19. Addition and Subtraction Number Stories 20. People in the Concert Hall 21. 127 Oranges 22. Missing Factors 23. Multiplication Number Story 24. A Difference of 39 25. Finding Differences Mentally 26. Finding Sums Mentally 27. Complete the Equation Number and Operations - Fractions 4.NF Extend understanding of fraction equivalence and ordering 28. Comparing Fractions 29. Equivalent Fractions for ½ 30. Mr. Jones’ Birthday Cake

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Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers 31. Adding Mixed Numbers 32. Subtracting Mixed Numbers 33. Multiplying a Whole Number by a Fraction 34. Fraction Subtraction Understand decimal notation for fractions, and compare decimal fractions 35. Comparing Decimals 36. Sorting Decimals 37. How Many Different Decimal Numbers? 38. Seven in the Hundredths Place Measurement and Data 4.MD Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit 39. Perimeter of a Rectangle 40. Area of a Rectangle 41. Designing a Rabbit Run 42. Same Area, Different Perimeters 43. Same Perimeters, Different Areas 44. Weighing Fruit 45. Elevator Weight 46. Elapsed Time 47. Calculating Costs 48. Measuring a Table in Different Units Represent and interpret data 49. Constructing a Line Plot 50. Letters Line Plot 51. Pet Shop Line Plot Geometric measurement: understand concepts of angle and measure angles 52. Predicting and Measuring Angles 53. Naming and Measuring Angles 54. Angles in a Right Triangle Geometry 4.G Draw and identify lines and angles, and classify shapes by properties of their lines and angles 55. Sorting Polygons 56. Comparing 3D Shapes 57. Lines of Symmetry 58. Perpendicular, Parallel, and Intersecting Lines 59. Parallel Sides 60. Interior Angles

A ladder is 30 feet tall. It is 5 times as tall as Mr. Jones. How tall is Mr. Jones? Explain your thinking.

Jake scored 42 points. Tom scored 6 points. How many times as many points did Jake score as Tom did? Explain your thinking.

The following multiplication problems have the same product: 9 x 24 = ?, 24 x 9 = ? Find two other multiplication problems that have this product. Explain your strategy.

There are 40 cupcakes to be put onto plates. Each plate must have the same number of cupcakes. Show as many different solutions as you can using pictures, numbers, or words.

Sarah solved two word problems correctly. The answer to the first problem was 7 R2. The answer to the second problem was 7 ½. What might the two problems have been?

___ x 3 = ___ What factor can you use in this equation to make a product that is even and between 20 and 50? Show all possible solutions and explain your strategy.

4 x ___ = ___ What factor can you use to make a product that ends in zero and is between 199 and 301? Show all possible solutions. Explain your strategy.

Choose a number less than 10. Record the multiples of this number by counting off numbers on a 100 chart. Describe any patterns that you notice on the chart. Repeat.

Cover the multiples of 4 on a 100 chart with transparent counters of one color. Cover the multiples of 6 with transparent counters of another color. Identify and record the common multiples. Repeat for other pairs of numbers that you select.

I added two prime numbers together and got a sum that is less than 15. What might the two prime numbers be? Show all possible solutions.

Consider the following sequence: 1, 4, 7, 10, 13…. Is 100 a member of this sequence? Explain your reasoning.

Sam read for 5 minutes on Monday, 10 minutes on Tuesday and 20 minutes on Wednesday. If the pattern continued how long would Sam have read for, in total, by the end of the week? Explain your thinking.

Trace around one square tile. Use four, then nine square tiles to make larger squares. Make the next two squares in the pattern. Explain how the pattern is growing.

A man ate 100 cookies in 5 days. Each day he ate 6 more than the day before. How many cookies did he eat on the first day? Explain your thinking.

Record a number sequence of at least 10 numbers where each number is six more than the previous number.

Record a number sequence of at least 10 numbers where each number is four less than the previous number.

A number has been rounded to 60. What might the number be? Explain your thinking.

I rounded two numbers to the nearest hundred and added them for a sum of 500. What might the two numbers have been? Show 5 possible solutions.

Choose two 3-digit numbers less than 500. Write and solve an addition and a related subtraction number story using these numbers.

Some people were seated in a concert hall. 27 more people entered the hall after the concert began making a total of 232 people in the concert hall. How many people were seated before the concert began? Solve this problem in two ways. Show your work and explain your thinking.

A box contained 127 oranges. Some apples were eaten at lunch time, leaving 66 oranges in the box. How many oranges were eaten at lunch time? Solve this problem in two ways. Show your work and explain your thinking.

Two numbers multiply to make 160. One of the numbers ends in zero. What might the two numbers be? Show all possible solutions.

Create a number story that involves multiplying the factors 25 and 16. Explain how you could solve the problem.

The difference between two three-digit numbers is 39. What might the two numbers be? Show 5 possible solutions. Explain your strategy.

Describe how you would find the difference between 118 and 151 in your head. Show two other problems that you could solve using this strategy.

Describe how you would find the sum of 300 and 306 in your head. Show three other problems that you could solve using this strategy.

Complete the following equation in as many different ways as you can: 2 x 12 = ___ x ___ Explain your strategy.

Which is larger, 2/3 or ¾? Explain your reasoning.

Using the fraction circles how many different ways can you show equivalent fractions for ½? Order your fractions. What would the next 5 fractions in the sequence be?

Mr. Jones blew out ¾ of the candles on his birthday cake. How many candles might there have been on the cake and how many did Mr. Jones blow out? How old might Mr. Jones be? Explain your reasoning.

When added together two mixed numbers equal 7. What might the two mixed numbers be?

The difference between two mixed numbers is 5 ¼. What might the two mixed numbers be?

Write a word problem using the following equation: 3 x 2/5 Solve the problem in two different ways. Explain your work.

What two fractions might I subtract to get an answer of ¾? Which is larger 0.9 or 0.13?

Explain your reasoning.

Classify the following decimals as: Near to 0, About ½, or Close to 1. 0.4, .15, .8, 0.33, 0.94 Explain your reasoning. Name 3 other decimals that belong to each group.

How many different decimal numbers can you write using the digits 7, 0, and 8? Order your numbers from smallest to largest. What is the difference between the smallest and largest decimal numbers?

a) How many numbers less than 3 have a 7 in the hundredths place? Record.b) Show three of the numbers you recorded on a number line.

The perimeter of a rectangle is 24cm. What are some possible lengths and widths? Record.

The area of a rectangle is 36in². What might the width and length be? Which possibility gives the smallest perimeter?

Tara is designing a run for her pet rabbit. The run must be rectangular with whole number dimensions. If Tara wants to enclose 48 square feet, how many options does she have?

Draw three different shapes with the same area. Compare their perimeters.

Draw and label three different rectangles with a perimeter of 12cm. Compare their areas.

Dad bought 1 kg of fruit. What might he have bought and how much did each piece of fruit weigh?

An elevator can hold 1200lbs. About how many children of your age would be able to take the elevator at one time? Explain your reasoning.

A plane left the airport after 9.00a.m and arrived at its destination before noon. If the total flight time was 170 min. what time might the plane have left and what time might it have arrived at its destination?

You went to a supermarket with $20.00. You bought three items and got $1.89 change. What might you have bought and how much did each item cost?

What is the length of your table in: millimeters, centimeters, decimeters, meters? If you find one measurement, how can you find the others without measuring?

Use the following data to make a line plot. Choose a possible title and label the axis: Monday: 5 ½ Tuesday: 3 ¼ Wednesday: 4 ½ Thursday: 5 ¼ Friday: 5 ½ Saturday: 5 ½

Collect data on the number of letters in the first name of 10 students in your class. Use your data to create a line plot. Record three facts about your data.

A pet shop had 27 animals. Draw a line plot to show what the animals might be.

Use a ruler to draw 10 different angles that are less than 180°. Predict the measure of each angle. Measure each angle. Record the difference between your prediction and the actual measure of each angle.

Using a protractor draw two right, two acute, and two obtuse angles. Label and measure each angle.

Tom drew a right triangle and marked the right angle. What might the measures of the second and third angles be? Show 5 different possible solutions.

Select 8 different polygons and sort them in two different ways. Describe your criteria for sorting the polygons.

Select 2 three-dimensional shapes and compare their properties using math vocabulary. What is the same/different about the 2 shapes?

Draw and cut out a square, an equilateral triangle, a regular hexagon and a regular pentagon. Investigate lines of symmetry by folding the polygons. Which of these polygons has the most lines of symmetry? Which has the least?

Use a geoboard and rubber bands to find as many different ways as you can to make 2 line segments that touch exactly 7 pegs. Draw the line segments on dot paper and label them as perpendicular, parallel, or intersecting.

I drew a shape with parallel sides. What might my shape have been?

I drew a shape. The total of the interior angles in my shape was 180 degrees. What might my shape have looked like?

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Polygons

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We hope that you enjoy using these math journal tasks with your students. If you have any questions regarding the contents of this file please do not hesitate to contact us at: k5mathteachingresources@gmail.com Our website offers a wide range of free math center task cards and resources suitable for use in 4th Grade classrooms. Please see the pages below as a starting point. http://www.k-5mathteachingresources.com/4th-grade-number-activities.html http://www.k-5mathteachingresources.com/data-and-measurement-activities.html http://www.k-5mathteachingresources.com/geometry-activities-2.html We hope that you find the resources on our website useful and come back to visit often!