Homework help for third grade Investigations units

Homework help for third grade Investigations units

*Note: These suggestions are written for the homework designed by the authors of each unit (usually a Student Sheet).

If teachers choose to send home other work, they may choose to send home additional suggestions for helping your child.

Click here for explanations of the math content in all of the third grade units.

Skip to Landmarks in the Hundreds

Skip to Combining and Comparing

Skip to Turtle Paths

Skip to Fair Shares

Skip to Up and Down the Number Line

Skip to Exploring Solids and Boxes

Mathematical Thinking at Grade 3 Download the two-page parent reference sheet and letter for this unit

Things That Come in Groups Download the two-page parent reference sheet and letter for this unit

Investigation 1

Session 1

Complete SS 1 as directed.

Session 2

Complete SS 2 as directed.

*Parents: See the example on SS 2 for clarification of the directions on the sheet.

Session 3

Complete SS 3 as directed. Choose numbers that are as high as you wish, and try not to draw or count by ones.

*Parents: See the example on SS 3 for clarification of the directions on the sheet.

Session 4

No homework is assigned by the authors in this session. Teachers may choose to assign other tasks.

Investigation 2

Session 1

1) Finish highlighting the hundred charts (SS 4) that you began in class. You need one chart that highlights the multiples of 2, one for the multiples of 3, etc., up to the multiples of 8. You may want to do your work in pencil first, then double check, then use a highlighter or other marker to finish.

2) At the bottom of each chart, fill in the circles by skip counting by the number highlighted on the chart (for example, on the chart with the multiples of 2 highlighted, you would write 2, 4, 6, 8, 10, etc.).

3) Write the patterns you see in each chart on the back of that page.

*Parents: If possible, you may want to check studentsπ work as they are working (see if they have highlighted the correct numbers), so that they hopefully do not make mistakes that affect the rest of the answers on given charts.

Session 2

1) Finish highlighting the hundred charts (SS 4) that you began in class. You need one chart that highlights the multiples of 9, one for the multiples of 10, one for 11, and one for 12. You may want to do your work in pencil first, then double check, then use a highlighter or other marker to finish.

3) Write the patterns you see in each chart on the back of that page.

*Parents: If possible, you may want to check this work as your child is working (see if he/she has highlighted the correct numbers), so that he/she hopefully does not make mistakes that affect the rest of the answers on given charts.

Sessions 3 and 4

(Session 3)

Complete SS 6 as directed. Try not to count by ones.

(Session 4)

If you have not already completed SS 5 in class, finish it at home. You will need your book of hundred charts.

*Parents: For SS 6, see the directions on the sheet for clarification. For SS 5, help students to think carefully and to use detail in their answers – look as deeply into the questions as possible.

Sessions 5 and 6

Play Cover 50 with someone. You will need the Cover 50 gameboard, the directions for the game, and the set of number cards from 2-50 that you made in class. Remember, each player gets 10 cards, face up. On each turn, one player says a number, and then all players (including the one who said the number) find multiples of that number in their sets of cards that have been dealt. Then all players place these cards on the gameboard. For example, if one player says 5, all players find the multiples of 5 in their sets of cards and put them on the gameboard. You do not have to have the number that you say in your set of cards (that is, you donπt have to have 5 to say 5).

*Parents: For the game Cover 50, see the clarification above along with the sheet of directions.

Investigation 3

Sessions 1 and 2

Finish cutting out the array cards that you began cutting out in class. Be sure you have a plastic baggie and a copy of the sheet How to Make Array Cards that will remind you how to label the cards. If your teacher has told you to bring them back to class, do so, and if you are to keep them at home, put them in a safe place.

*Parents: Help students to use the sheet of directions to be sure they are labeling the array cards correctly.

Sessions 3 and 4

1) Play Multiplication Pairs with someone. You will need your array cards, paper and pencil, and the sheet How to Play Multiplication Pairs. Each time you guess the answer for a card, if you are right, record this multiplication fact under Pairs that I know, and if you are wrong, record this multiplication fact under Pairs I donπt know yet.

2) Play Count and Compare with someone. You will need your array cards, paper and pencil, and the sheet How to Play Multiplication Pairs. Each time you guess the answer for a card, if you are right, record this multiplication fact under Pairs that I know, and if you are wrong, record this multiplication fact under Pairs I donπt know yet. Remember, you are not allowed to count by ones in this game.

3) Continue to work on the Arranging Chairs puzzle. You will need 30 small objects, such as coins, paper clips, blocks, small pieces of paper, etc., and the sheet The Arranging Chairs Puzzle.

*Parents: For the games, see the sheets of directions along with the clarification above. Be sure students are recording the pairs they know and do not know accurately so that they will know which facts they need to work on. For the Arranging Chairs puzzle, see the directions sheet for an example.

Session 5 – Teachers will assign some part of this homework.

3) Continue to work on the Arranging Chairs puzzle. You will need 30 small objects, such as coins, paper clips, blocks, small pieces of paper, etc., and the sheet The Arranging Chairs Puzzle.

Investigation 4

Sessions 1 and 2

(Session 1)

Complete SS 9, being sure to follow each step in the directions at the top.

(Session 2)

Complete SS 11 as directed.

*Parents: For SS 9, a number sentence is just an equation.

Sessions 3 and 4

Take home your class book of multiplication and division problems, and continue to work on solving them. Be sure to show your strategy for solving each problem. Try not to count by ones in these problems. Look for ways to relate the facts – for example, if you know 5 x 4, how can you use it to find 6 x 4?

Investigation 5

Session 1

Complete the last column on SS 12. Remember, you should try to find items that you could buy for the amount of money saved after 30 days (in each row). Fill in at least 8 rows (more if you can).

*Parents: For SS 12, help students to find or think of items that would cost about as much as the amounts in the third column.

Session 2

Complete SS 14. You do not need to spend more than 5 minutes looking for your data, but try to find at least three creatures to record. Do not feel that you have to include every creature you see if you see a great number of them. Leave the third and fourth columns blank.

Session 3

Finish your line plot and story problem display page for homework. Be as creative and challenging as you can with the questions you write.

*Parents: For the line plot and story problem page, students should have created a line plot of their data in class, and now they should be writing questions about it for other students to answer. For example, if the line plot was called Legs around my house, and showed the number of birds, people, and spiders around the house, possible questions might be: How many more birds than people are around my house? How many bird legs are there? How many legs in all? Most questions should require students to use multiplication to solve.

Session 4

No homework is assigned by the authors in this session. Teachers may choose to assign other tasks.

Landmarks in the Hundreds Download the two-page parent reference sheet and letter for this unit

Investigation 1

Session 1

Complete SS 2 (twice) as directed. (You should have chosen or been assigned numbers in class, but if the blanks at the top of either or both sheets have not been filled in, use the numbers 18 and/or 30.) When it says to skip count by the number of cubes, actually write the numbers that you say.

*Parents: For SS 2, students should be focusing on the groups and the number in each group since this will help them to develop a deep understanding of multiplication and division.

Sessions 2 and 3

Complete SS 4 and/or 5 at home if you did not finish them in class. You will need 3 copies of each sheet. Remember that on each sheet, you will fill in numbers that you believe are factors of the larger number (36 or 48), then fill in how many you need to make that larger number, and finally fill in the number sentence that matches what you have done. You should try to find all of the factors of 36 and 48.

*Parents: For SS 4 and 5, see the note above. It is important for students to see that 36 and 48 are made up of groups of smaller numbers (factors), and that the number of these groups is important (also a factor).

Sessions 4 and 5

Complete the activity on SS 8 as directed. Remember that you should use equal-sized groups so that it easy to tell that there are 100 items in your display.

*Parents: SS 8 is designed to help students to get a true sense of what 100 is. Many students at this age do not have a good grasp on how many items make up 100. They should also be thinking about how to easily group the items, not counting by ones.

Sessions 6 and 7

Complete SS 10 as directed.

*Parents: For SS 10, when students write their own problems, they should involve splitting a dollar evenly among some number of people.

Investigation 2

Sessions 1, 2, and 3

(Session 1)

Finish some of the Money Problems (from the class sets) or other similar problems that your teacher assigns. Be sure to write a number sentence for each problem.

*Parents: For the Money Problems, students should use strategies that are as efficient as possible while still making sense to them. Using landmark numbers like groups of 10, 25, and 50 will be very helpful.

(Session 2)

Take home your 300 chart, and find as many numbers as you can that get you exactly to 300 when you skip count by each number (starting from 0).

*Parents: Students are to find all of the factors of 300 that they can. They could also write multiplication equations that relate these factors (ex: 2 x 150 = 300).

(Session 3)

Complete SS 13 as directed. (Your teacher may have decided to change the number 4 on this sheet for you.) Be sure to write an equation that matches this problem (you will need to decide whether multiplication or division is the better choice).

*Parents: For SS 13, students should work as efficiently as possible, using the relationships among numbers like 4, 20, 100, etc. to solve the problem. Skip counting should be used only if students are stuck. The picture should not include ones but symbols that represent larger groups.

Session 4

Finish the Money Problem that you were assigned in class. Be sure to write an equation that relates to your solution.

*Parents: For the Money Problem, students should use strategies that are as efficient as possible while still making sense to them. Using landmark numbers like groups of 10, 25, and 50 will be very helpful. An equation (for the Money Problem) might look like 42 ∏ 3 = 14.

Sessions 5 and 6

1) Complete SS 15 as directed. You could also look for packages of food, since you might have several of the same package at home. Be sure to estimate the total first, as it says toward the top of the sheet. Write down your estimate before finding the total.

2) Complete SS 16 as directed. Be sure to write an equation that relates to each problem you write and solve. An example problem might be, I have 300 peanuts in a bag and 25 kids in my class. How can I split the peanuts so we all get the same number?

*Parents: For SS 15, it suggests that students count by tens so that they can get a sense of how many tens are in larger numbers. They could also count by 20s or 25s. For SS 16, see the note above and the directions on the sheet.

Investigation 3

Session 1

Complete SS 17 as directed. When you are counting items at home, do your best to count them efficiently, perhaps by 10s, 20s, 50s, or even 100s. If you can use multiplication to find the items quickly, you can do this as well.

*Parents: For SS 17, see the note above.

Sessions 2 and 3

There is no homework assigned by the authors in these sessions due to assessments in class. Teachers may choose to assign other tasks.

Combining and Comparing Download the two-page parent reference sheet and letter for this unit

Investigation 1

Sessions 1 and 2

Complete SS 2, following the directions.

*Parents: For SS 2, students should get as much information as they can; if not every blank is filled in, this is OK.

Session 3

No homework was assigned by the authors in this session. Teachers may choose to assign other tasks.

Investigation 2

Session 1

Play Close to 100 with someone. You will need SS 1 (several copies), and a copy of the rules (in your activity booklet), and Numeral Cards.

*Parents: For the game, students should be thinking in terms of combining tens and ones in order to get close to 100 – help them to think about how many tens and ones are in each two-digit number they create. For instance, they might choose to use 35 and 67, so they could think: 30 and 60 is 90; 5 and 7 is 12; 90 and 12 is 102. Or, they could think: 35 and 70 is 105, minus 3 (from the 70) is 102.

Session 2

No homework was assigned by the authors in this session. Teachers may choose to assign other tasks.

Investigation 3

Sessions 1 and 2

(Session 1)

Complete SS 7, following the directions.

(Sessions 2 and 3)

No homework was assigned by the authors in this session. Teachers may choose to assign other tasks.

*Parents: For SS 7, students should use their knowledge of landmarks (multiples of 10, 25, 50, 100) to solve these problems with efficient and flexible strategies. For instance, they might solve 29 + 72 by adding 30 to 72 and then subtracting 1. Students should not be using the standard algorithm unless they have at least one other efficient strategy (preferably more) because the standard algorithm is not always the most efficient strategy.

Session 3

Solve two or three more problems on SS 9 that you did not solve in class. Be sure to follow the directions on the sheet.

*Parents: For all of these tasks, students should use their knowledge of landmarks (multiples of 10, 25, 50, 100) to solve these problems with efficient and flexible strategies. For instance, they might solve 64 + 55 by adding 60 to 50, then adding 4 + 5 (9) to this answer. Students should not be using the standard algorithm unless they have at least one other efficient strategy (preferably more) because the standard algorithm is not always the most efficient strategy.

Investigation 4

Session 1

Complete SS 10, following the directions. You might use paper clips, coins, cereal pieces, etc.

*Parents: For SS 10, students should use their knowledge of landmarks (multiples of 10, 25, 50, 100) to solve these problems with efficient and flexible strategies. For instance, they might solve 89 + 27 by adding 80 and 20, then adding 9, then adding 7. Students should not be using the standard algorithm unless they have at least one other efficient strategy (preferably more) because the standard algorithm is not always the most efficient strategy.

Session 2

Complete SS 13, following the directions. Be sure you have filled in the class information and your data before you leave class.

*Parents: Students should use their knowledge of landmarks (multiples of 10, 25, 50, 100) to solve these problems with efficient and flexible strategies. For instance, they might solve 89 + 27 by adding 90 and 30 and then taking away 1 and 3. Students should not be using the standard algorithm unless they have at least one other efficient strategy (preferably more) because the standard algorithm is not always the most efficient strategy.

Sessions 3 and 4

Choose a Paper Clip problem and a Related Problem Set that you have not solved yet. Glue or tape the problems to SS 14, and show how you solve each one. You will probably want two copies of the 300 chart.

*Parents: Students should use their knowledge of landmarks (multiples of 10, 25, 50, 100) to solve these problems with efficient and flexible strategies. For instance, they might solve 115 + 58 by adding 60 to 115 and then taking 2 off. Students should not be using the standard algorithm unless they have at least one other efficient strategy (preferably more) because the standard algorithm is not always the most efficient strategy.

Investigation 5

Session 1

No homework was assigned by the authors in this session. Teachers may choose to assign other tasks.

Sessions 2 and 3

Complete SS 16, following the directions. Be sure you have the school days chart and a 300 chart (if you need one). Try to solve the problems without the 300 chart.

*Parents: Students should use their knowledge of landmarks (multiples of 10, 25, 50, 100) to solve these problems with efficient and flexible strategies (see above notes for Investigations 2-4 for examples). Students should not be using the standard algorithm unless they have at least one other efficient strategy (preferably more) because the standard algorithm is not always the most efficient strategy.

Turtle Paths Download the two-page parent reference sheet and letter for this unit

Investigation 1

Session 1

Complete SS 3 as directed.

*Parents: This type of spatial activity can be very tricky because students often leave out parts of the directions. Encourage your children to actually walk the paths they are describing and actually say when they are going forward or backward and turning left or right (writing each step down as they do it). Rt 90 and Lt 90 refer to right angle turns.

Investigation 2

Sessions 1 and 2

1) Finish SS 9 at home as directed.

2) Create a plan on SS 10 to help the turtle get to all of the berries.

*Parents: On SS 9, be sure that students estimate the turn (angle) measure before actually measuring with the Turtle Turner. To measure a turn, students place the double line with the arrow at the beginning of the turn, with the vertex (point of rotation) of the turn underneath the Turtle. Then they can read the measure where the turn ends (estimating in between lines if needed). Be sure they check the reasonableness of their answers, as students often tend to read the wrong measurements on angle-measuring tools. Narrow (acute) angles should be less than 90 degrees; wide (obtuse) angles should be greater than 90 degrees. For example, turning your head from left to right might be slightly more than a 180-degree turn. On SS 10, the turtle starts at the bottom of the maze, and students are to use the commands forward, backward, left, and right to move the turtle through the maze. They should use the ruler on the page to decide how far forward or backward to go, and they should use the Turtle Turner to decide how far to turn left or right.

Session 3

Complete SS 13 as directed.

*Parents: Students are to determine how many different triangles were used to create this drawing – that is, some triangles may have been repeated throughout the drawing, but we are only counting these once (not as many times as they were used). Students will need to use several different colors to color the sets of triangles that look exactly the same as each other. If two triangles look different, they should not be the same color (but they should be the same color if they look the same).

Session 4

No homework is assigned by the authors in this session. Teachers may choose to assign other tasks.

Sessions 5 and 6

Complete SS 17 as directed.

*Parents: Help students to look at the relationships between the lengths in each task. Students should be thinking about these as real objects – the answers should be logical as if students were going to actually build these objects. Be sure students also create at least one similar task of their own on the back.

Investigation 3

Sessions 1 and 2

Complete SS 21 as directed.

*Parents: Perimeter is the measure of distance around the outside of a shape. Students should be thinking about these as concrete rectangles – the answers should be logical as if students were going to actually construct them. It might help some students to actually cut out a rectangle and fold or double it to get the answers.

Sessions 3, 4, and 5

Work on SS 22 to plan your Face Drawing.

*Parents: Students are to plan a drawing of a face with the parts listed on the sheet. Perimeter is the measure of distance around the outside of a shape. Students are to use the commands forward (fd), backward (bk), left (lt), and right (rt) to move the turtle to create each shape. They can use the ruler on SS 10 to draw the lengths fairly accurately (though this is not necessary for this draft), and they should use the Turtle Turner to decide how far to turn left or right. See the notes for Sessions 1 and 2 in Investigation 2 above for directions on using the Turtle Turner.

Fair Shares Download the two-page parent reference sheet and letter for this unit

Investigation 1

Sessions 1 and 2

Make the fraction cards as directed on How to Make Fraction Cards.

*Parents: See the directions on the sheet. You can try the Ideas at the bottom to see how well your child recognizes various fractions of the whole.

Sessions 3 and 4

Finish SS 4 as directed.

*Parents: In the first part, one whole rectangle represents one whole brownie. Help your child to see how many wholes and what fraction of a whole is shown in each task. In the second part, it may be necessary for your child to draw pictures first and then think about why the numbers are all correct. They should be using the same size rectangle for each whole, and they should divide the rectangles as needed to show each fraction.

Investigation 2

Sessions 1 and 2

Finish SS 6 as directed. Draw a small picture next to each answer to prove it is correct. You may want to trace the blue rhombus, triangle, and trapezoid to think about at home.

*Parents: Students should write at least two ways to make the number in each box. For example, one way to make 1 whole would be 1/3 + 2/3 (and they would draw a small picture which showed 1/3 and 2/3 in the same whole). There are many solutions for each box; encourage your child to think at his/her own level.

Session 3

Since there is an assessment in this session, no homework was assigned by the authors.

Session 4

Play the Fraction Card game as directed on SS 9. You will need the set of fraction cards that you made in Investigation 1 (directions on How to Make Fraction Cards). For steps 3 and 4 in the directions for the game, remember how many of each piece make up 1 whole (you cannot just come close to a whole).

*Parents: For the game, help students to remember how many (for ex.) thirds are in 1 whole. Read step 3 in the rules for more help.

Sessions 5 and 6

Complete SS 11 as directed. Be sure to solve the problem that you write for #3.

*Parents: Students basically need to follow the directions. The total number of people listed in each problem is the number of people among which the brownies are shared.

Session 7

Create another mystery pattern block design with at least some yellow in it. Determine what fraction is yellow, and show how you know. You can use one sheet of triangle paper to try different designs and one for your final design. You may want to trace one of each pattern block one on of the sheets at school so that you know what each looks like.

*Parents: For the pattern block design, students should create their own design using the pattern block shapes and determine what fraction is yellow. To do this, it helps to look at the total number of triangles filled in on the sheet and how many of these are within yellow hexagons.

Investigation 3

Sessions 1 and 2

Complete SS 14 as directed. Be sure to show how you solved each problem, and use dollar signs and/or cent signs in your answers.

*Parents: Help students to read each task carefully and to logically reason about how the money would be divided. Students do not need to use standard algorithms to do this; there are a variety of efficient and logical ways to get the correct answers.

Session 3

Complete SS 15 as directed. Be sure to solve the problem you write for #3.

*Parents: Students do not need to draw pattern blocks or crayons; they can use dots, xπs, or tally marks to represent the items. It is key for students to start to recognize that (for example) dividing by 5, or sharing among 5 people, is equivalent to finding 1/5 of the total.

Up and Down the Number Line Download the two-page parent reference sheet and letter for this unit

Investigation 1

Sessions 1 and 2

On SS 1, add more elevator trips with the net change for each one. If you feel you are able, you can choose floors that are not on the skyscraper.

*Parents: Students will have a version of a skyscraper with floors to use. They are to choose a starting and ending floor for an elevator trip. They record these floors, then find the net change, which is the distance from the starting to the ending floor, either positive (if moving up), or negative (if moving down).

Sessions 3 and 4

Play several rounds of the Game of Many Changes with someone, and record your work on SS 2. You will need two sets of the Change Cards, SS 2, SS 3, one set of Net Change cards, and the skyscraper sheet.

*Parents: The net change is the distance from the starting to the ending point, either positive (if moving up), or negative (if moving down). See SS 3 for the directions.

Session 5

Complete SS 5 as directed. The numbers in the second part should be larger than those in the first part, and none of them should be the same. Remember, you should assume you are starting at 0 each time.

*Parents: Students should use efficient strategies to find the net change (the simplified answer). Do not impel your child to use a procedure that he/she does not understand, but encourage him/her to look for relationships among the numbers in order to simplify the task.

Sessions 6 and 7

Since there is an assessment in these sessions, no homework was assigned by the authors.

Session 8

Play Pick up Chips with someone. You will need SS 8, SS 9, a skyscraper and Changes cards. Record your work on SS 8.

*Parents: See SS 9 for the directions (read carefully).

Investigation 2

Session 1

Look in newspapers, books, and other places for graphs that show something changing as time passes. Examples could be: graphs of temperatures over a year, a height of a child as he grows, or decreasing population. Record what you find on SS 10, and if you can, save the graph to take to class.

*Parents: Be sure students choose a graph that really shows how a quantity changes over time. An example that would not work would be a bar graph that shows how many dogs of each breed are in a town, because this data was collected at one point in time.

Sessions 2 and 3

No homework was assigned by the authors in this session. The teacher may choose to assign tasks.

Session 4

Complete SS 13 as directed.

*Parents: The net change is the distance from the starting to the ending point, either positive (if moving up), or negative (if moving down). Encourage your students to find at least one very efficient way to find the net change on each graph.

Investigation 3

Session 1

Play Save the Siberian Tiger with someone. You will need a copy of the gameboard, the Tiger cards, SS 14, and two sets of Changes cards (from Investigation 1). Record each turn you take on a separate sheet of paper.

*Parents: See SS 14 for the directions. Remember that there are really two things players think about in this game: the changes (or their moves left and right), and the number of tigers they have gained or lost. There is not a relationship between the net change and the total tigers gained or lost.

Sessions 2 and 3

Finish re-writing the instructions for your board game if you did not finish in class.

*Parents: Be sure the instructions your child writes are clear and concise.

Exploring Solids and Boxes Download the two-page parent reference sheet and letter for this unit

Homework help for this unit will be posted later in the year.

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