Grade 4 - Amazon Web Services



Grade 4

CAP

Grade 4- Mathematics Common Core Calendar

[pic]

July 2012

Charles Angeli – Cap Coordinator

Denise Kerr

Carol Neher

Table of Contents

Abstract ......................................................................... 3

Rationale ......................................................................... 4

8 Common Core Practices ........................................... 5

Additional Practice Problems…………………………………… 10

Common Core Standards ….......................................... Addendum 1

Grade 4 Pacing Calendar .............................................. Addendum 2

Abstract

Grade 4

Fourth Grade Common Core Math Calendar

July 2012

This CAP was developed to provide greater focus on mathematical experiences in the classroom. Emphasis is on the Common Core Standards for Mathematical Content and Fluency in Grade 4. The Common Core fosters a greater in-depth understanding of mathematical concepts and their connections to everyday life. The curriculum, instruction and assessment should reflect the focus and emphasis of the standards. The major content (70%) emphasis in each standard is integrated with additional (20%) and supporting (10%) emphasis tying it all together to achieve fluency and cohesive understanding. The major focus in third grade is multiplication, division and fractions with greater emphasis placed on the depth of ideas, time required to master and importance to future mathematics readiness. The focus is in building skills within, and across grades developing speed and fluency to know it, do it, and use it in real world situations.

Additionally, this CAP includes a teacher friendly pacing calendar with some recommendations for bringing the Mathematics Common Core Learning Standards to life in mathematics instruction through sense-making, reasoning, arguing and critiquing, and modeling, etc.

Finally, there is direct advice for teaching the mathematical practices in ways that foster greater focus and coherence for real world applications.

RATIONALE

Grade 4

Fourth Grade Common Core Math Calendar

July 2012

The Mathematics Common Core Learning Standards focus on major content emphasis with fewer, key topics, while building skills across the grades to develop fluency and cohesive understanding. The Common Core practices were developed to help students apply math in real world situations, knowing which math to use for each real-world situation. Students will be prepared to use core math facts faster and be able to apply math in the real world.

Our purpose is to provide a concise curriculum calendar identifying the major, and additional, and supporting clusters as a guide to inform instructional decisions regarding time and other resources with varying degrees of emphasis by cluster. This will allow the focus on the major math work for the grade to open up the Standards for Mathematical Practice in the mathematical instruction.

Mathematics: Standards for Mathematical Practice

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

1. Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

2. Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

3. Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of

others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

4. Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

5. Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

6. Attend to precision.

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

7. Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

8. Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

CC.4.OA.2

CC.4.OA.3

Together, Tom and Max have 72 football cards. Tom has 2 more than 4 times as many cards as Max has. How many football cards does Tom have?

CC.4.OA.2

CC.4.OA.3

Naomi has 50 red beads and white beads. The number of red beads is 1 more than 6 times the number of white beads. How many red beads does Naomi have?

CC.4.OA.2

CC.4.OA.3

Javier rode his bike for a total of 41 minutes. Before lunch he rode for 1 minute less than 5 times the number of minutes he rode after lunch. How many minutes did Javier ride before lunch?

CC.4.OA.2

CC.4.OA.3

Marnie practiced her basketball dribbling. After two tries, she had bounced the ball 88 times. On the second try, she had 2 fewer bounces than 8 times the number of bounces she had on the first try. How many bounces did she have on the second try?

CC.4.OA.2

CC.4.OA.3

A group of science students went on a field trip. They took 7 vans and 8 buses. There were 7 people in each van and 25 people in each bus. How many people went on the field trip?

Show your work.

CC.4.NBT.2

How many eights would you write down if you wrote all of the whole numbers from 1 to 100? How could you find this answer without having to write all of the numbers and count them? If you counted another digit, would you have the same amount?

Explain your thinking.

CC.4.NBT.4

CC.4.OA.3

CC.4.OA.2

Five curious cats went exploring in a freshly painted room. Four got paint on their front paws and one got paint on its back paws. How many paws didn’t have paint on them?

Show your work:

CC.4.OA.1

CC.4.OA.2

CC.4.OA.3

A rose garden has 8 rows of 26 rose bushes each. In each of the first 5 rows, 7 bushes have pink roses. In each of the first 3 rows, 12 bushes have yellow roses. The rest of the bushes have red roses. How many bushes have red roses?

CC.4.NF.7

CC.4.OA.2

CC.4.OA.3

Gina has a choice of whether to get paid in pennies, nickels, dimes or quarters. For each type of coin she will get the following amounts: 1,000 pennies, 200 nickels, 450 dimes, or 41 quarters. Which type of coin should she choose if she wants to get paid the greatest amount of money?

Show your work and order the amounts from least to greatest.

CC.4.OA.3

CC.4.NBT.4

Jay wants to buy a jump rope that costs $9, a board game that costs $20, and a playground ball that costs $10. He has saved $8 from his allowance, and his uncle gave him $5 dollars. How much more money does Jay need to buy the jump rope, the game, and the ball?

Show your work:

CC.4.NBT.4

A frog fell into a well that was 20 feet deep. Each day he climbed 3 feet up the well’s sides. At night he slid back down 1 foot. How many days did it take him to climb out of the well? Share your solution with your classmates.

Show your work:

CC.4.NBT.4

CC.4.OA.3

Connor saved $38 in September. He saved $22 in October and $43 in November. Then Connor spent $78 on a video game. How much money does Connor have left?

Show your work:

CC.4.NBT.5

Juice boxes come in cases of 24. A school ordered 480 juice boxes. How many cases of juice did the school order?

Show your work:

CC.4.NBT.5A

A bank received a supply of 2,000 quarters. Each roll of quarters has 40 quarters in it. How many rolls of quarters did the bank receive?

Show your thinking.

CC.4.NBT.5

There are 10 tickets in each strip of carnival tickets. A total of 3,850 tickets were sold in one day. How many strips of tickets were sold that day?

Show your work:

CC.4.OA.3

CC.4.NBT.4

A parking garage near Dee’s house is 4 stories tall. There are 24 open parking spots on the first level. There are 6 more open parking spots on the second level than on the first level, and there are 6 more open parking spots on the third level than on the second level. There are 18 open parking spots on the fourth level. How many open parking spots are there in all?

Show your work:

CC.4.NBT.4

CC.4.OA.3

Mandy bought stamps at the post office. Some of the stamps had a snowflake design, some had a truck design, and some had a rose design. Mandy bought 17 snowflake stamps. She bought 9 more truck stamps than snowflake stamps, and 2 fewer rose stamps than truck stamps. How many stamps did Mandy buy in all?

Show your work:

CC.4.MD.2

CC.4.MD.1

Don can spend two hours at the museum. He spends 45 minutes looking at paintings and then 50 minutes looking at pottery. How much time does he have left?

Show your thinking.

CC.4.MD.1

CC.4.MD.2

Luke wrote a note to his mother. It took him 68 seconds to find a pen, 42 seconds to find paper, and 41 seconds to write it. Did it take Luke more than 3 minutes to complete the note?

Show your work:

CC.4.OA.3

CC.4.OA.5

Molly works in the summer for her dad’s lawn service, 5 days a week for 4 weeks. Her dad offers to pay her $125 a week. Instead, Molly wants to be paid $0.01 for the first day, $0.02 for the second day, $0.04 for the third day, $0.08 for the fourth day and so on. If Molly wants to make the most money possible, should she accept her dad’s offer?

Show your work:

CC.4.NF.3d

A chef has 9 cups of milk. He uses ½ of the milk plus ½ a cup to make pancakes. He uses ½ of what is left plus ½ a cup to make french toast. Next he uses ½ of what is left plus ½ a cup to make muffins. How much milk does he use for each of the three recipes? How much milk is left?

Show your work:

CC.4.NBT.5

Pea plants usually produce 5 or 6 peas in each pod. Suppose a pea plant had 5 pods and a total of 26 peas. How many of its pods would have only 5 peas? How many of its pods would have 6 peas? How many peas could a pea plant have if it had 6 pods?

Show your thinking:

CC.4.NBT.5

Imagine that you are a hungry ant trying to get yourself and 99 ant friends to a picnic.

Think about all the different ways 100 ants could march in rows and columns. Organize your information in a table and look for a pattern.

Show your work:

CC.4.NBT.5

CC.4.OA.3

Many people bake cookies for special holidays. If you need 7 1/2 dozen cookies for a holiday celebration, how may cookies do you need?

If you wanted to serve equal amounts of your cookies on serving platters, how could you distribute them so each platter had the same number of cookies?

Show your work.

CC.4.NBT.5

In strength training you use weights and do exercises for different parts of the body. Repeating the same exercise is called “doing reps”. If you do 4 different exercises and 12 reps of each, how many reps are you doing in all? At this rate, if you do 3 sessions of strength training each week, how many reps are you doing each week?

Show your work:

CC.4.NBT.6

Scientists have determined from tracks made by dinosaurs that the fastest speed that they could travel was about 27 miles per hour. At this speed about how long would it take a dinosaur to travel about 60 miles? How long to travel about 300 miles?

Show your work:

CC.4.NF.3d

In many schools, students run laps for exercise on the school track. You have set a personal goal to run 100 miles in one year. If your school track is 1/5 mile, how many laps would you have to run to reach your goal for the year? About how many laps would you run each week?

Show your work:

CC.4.NF.1

CC.4.NF.6

Joe wants to buy a TV that costs $100. If he buys the TV on a Monday he can use a coupon at the store for 15% off the price. Online, Joe can buy the TV and receive 1/5 off the price. If Joe wants the best possible deal, how should he purchase the TV? How much will he pay for the TV?

Show your work:

CC.4.NF.6

Sue and Raj both live near the school. Raj lives 0.75 miles from the school. Sue lives ¾ of a mile from the school. Raj says his house is closer to the school than Sue’s house. Is he correct?

Prove your answer.

-----------------------

1

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download