Monday, April 30, 2012

Basic Division

Day One – Introduction

        Pasta division is something a teacher can use to help students understand the idea of dividing among individuals. The teacher puts 30 pieces of pasta on a plate. One student comes and counts the pasta to ensure there are 30. The teacher then calls up five or six students and tells the first to give each student an equal number of pasta pieces. The student will give out one pasta piece at a time until they are all in the hands of the five or six other students. The teacher can then tell the other students to count the pieces. They should have either six if there are five students or five if there are six students. Tell the children that this is division. The pasta was divided by five or six students, which means 30 divided by the five or six equals six or five pieces of pasta each. This gives a hands-on understanding of the concept.

        * While you are walking them through this introduction, be sure to show the students on the board what this division problem looks like.  Use both signs for division – the students will be exposed to both in this unit.


            Pasta division shows students that division just means splitting up into equal groups.  We do this all the time in real life!  Ask the students if they can think of a situation in their lives where they have had to divide?  Share a couple as time allows.  Tell the students that you have gathered some situations where people have to split into equal groups or DIVIDE.  Alone or with a partner they will read the situations on the worksheets and complete it by drawing equal groups.  Gather the worksheet as data to drive instruction.
* As an extension for fast students, have them go back to each problem and write a number sentence to represent the division problem they did.
Day Two – Guided Learning
Story Division
        Teachers can incorporate both math skills and writing skills into a single lesson by giving students a project to write a three-paragraph story. The teacher gives a theme, such as two friends go to an amusement park and are given 53 tickets for bowling. The teacher then tells the students to write a short story telling how the two friends decide to divide up the tickets. This teaches students the division skills, allows them creativity, and creates a situation where the students work on problem-solving skills, since there is a remainder. Teachers can change up the story situation so students end up with even numbers, remainders or must incorporate a specific element of creativity, such as telling a funny story or telling a sad story. The teacher can allow students to share the stories as time allows.

        Do one story together and then ask students to write their own story. 

*Fast finisher- students can complete the rocket ship division coloring page.

Day Three – Division Memory Match Game

            Briefly review division (splitting into equal groups).  If students brought back their story from Tuesday allow them to share (if a lot brought them back, divide into 3-4 smaller groups to maximize sharing time).  As students read their stories, pass out the dry erase paddles and have students write the division problem from their story to practice properly forming a division problem (model on the boards as well).

After reviewing division we are going to play a game called Memory Match Division.  Students will split into pairs to play a memory game where they try to match the division problem with its matching quotient. 
* For an extra challenging game, students can play the version where one of the digits is missing and they must work backwards to find the missing number, rather than the answer.

Day Four – Division Tic-Tac-Toe and Division Test

            To prepare students for a division assessment, we will play a review game.  Divide students into pairs and have them play Division Tic-Tac-Toe.  In this game, students will complete division problems to earn a square.  If they complete a division problem correctly they get to take the square with their “x” or “o”.  Players try to get three problems correct in a row to win the tic-tac-toe. 

After they have played a couple of rounds, ask them to move back to the table to complete the division test to assess their understanding of the unit.

BONUS DAY: Give each student a calculator, and teach them how to perform the four basic functions on it.  Give each student a copy of the calculator worksheet, and emphasize that the calculator will help us with the arithmetic, but we still figure out how to solve these problems.

Saturday, April 21, 2012

2D and 3D Shapes: Week Two

Day 1: Perimeter and Area

Draw a rectangular field on the whiteboard with animals in it. (Draw dotted lines in a grid through the field.) Introduce the concepts of area (how much room the horses have in their corral) and perimeter (how much fence the farmer had to build to make the corral.)

Teach students how to calculate the perimeter by adding up all four sides of the rectangle. Pass out geo boards and geo bands and ask them to make a rectangle that is four spaces long and three spaces wide. What is the perimeter of this rectangle? Repeat for other perimeters, and consider giving the students a perimeter and making them figure out the length and width.

Teach students how to calculate an area by multiplying the length of the rectangle by
the width. Ask students to make their 3 by 4 rectangle again. What is the area of this rectangle? 3 x 4 = 12. Is there another way we can make a rectangle with an area of 12 on our geo boards? What if we had bigger boards? What would the perimeter of that rectangle be?

Give students a copy of the Farm Area worksheet and allow them to start working with
any remaining time. Encourage students to find both the area and the perimeter for each question, and to bring it back completed (areas and perimeters) for a treat. (This will definitely require some parent help, which is good!)

Day 2: Tangrams

Make a set of magnetic tangram shapes. As a review, have the students name each of the shapes and tell which shapes have parallel and perpendicular lines. Tell the students a tangram story, using your shapes on a magnetic board to make the animals and objects in the story. 

Print and cut out a tangram for each student on cardstock. Give each student a set of tangram shapes, a piece of paper, and a pencil.  Have students make a picture using their tangram shapes (and trace it onto the page), then write a short story about their picture.  (Encourage students to use all seven tangram shapes to make their picture.)  Tell students that if they take their page home and finish it, they can share their picture and story with the class tomorrow.

Day 3: 3D Shapes

Invite any students who finished their tangram stories and brought them back to share them with the group.

Introduce the following 3D shapes: sphere, cube, cone, cylinder, pyramid, rectangular prism, triangular prism.  Give the students a few Wikki Stix and have them make the best representation of each shape that they can, either alone or in groups.  With each shape, ask students to think of real-life examples of objects that are that 3D shape.  If possible, bring one example of each shape.

If enough time remains, take the students on a quick shape field trip around the school and look for spheres, pyramids, cubes, rectangular prisms, cylinders, cones, etc.

Day 4: Shape Pictionary/Charades

Print a list of all the shape vocabulary we've learned in the last two weeks.  Cut the list into word strips, and play pictionary/charades.  Students take turns coming up, picking a word, and then helping the class guess the word by either drawing a picture on the whiteboard, acting it out (or pointing to an object in the room), or shaping it with Wikki Stix.  Play continues until all of the vocabulary words have been reviewed.

Give students a shape test using all of the new vocabulary words covered in the game.  Instead of writing words to answer the questions, they may draw pictures.

Friday, April 13, 2012

2D and 3D Shapes: Week One

Day 1: Geo Board Challenge

Review basic shapes of circle, square, rectangle, and triangle briefly with students on the white board, but ask more difficult questions. For example, is a square a rectangle? (Yes! It's a special kind of rectangle, but it's still a rectangle.) Introduce parallel, perpendicular, and (if there's time) trapezoid, parallelogram, quadrilateral, pentagon, hexagon, octagon, etc. For the bigger polygons, emphasize that it doesn't have to be a regular polygon (one with all the same length sides and same angles.) Draw some weird pentagons and hexagons and see if the students can still recognize them. (Write terms on the board as you go.)

Pass out geo boards and geo bands. Tell students that you're going to ask some easy questions first, so they need to work quickly! Ask students to make a square on their geo board. (Use your geo board to make a square with all diagonal lines, and ask students if it's still a square.)
Next, ask students to make a rectangle. Again, have students check each other. Show your diagonal square again. Is this a rectangle? (If you covered these vocabulary words earlier, is it a parallelogram? A quadrilateral?) Continue through triangle, perpendicular, parallel, and any other terms you covered.

Now for the challenge questions. Divide students into two teams if desired, and see which team can get all its members to have the correct shape on their geo boards. (Helping is allowed, but emphasize that there's more than one correct way to make all of these shapes.)

Can you make a square from two triangles? A rectangle from two triangles? A rectangle from two squares? A square from two rectangles? A big triangle from two smaller triangles? A pentagon from a square and a triangle? etc.

Day 2: Symmetry

Attention grabber: Tell students that you have a riddle, and whoever solves it will get a
treat. Draw an eight on the board. Ask the students, "What is half of eight?" (Hopefully they will answer four!) Here's the riddle: "I think half of eight is 0. Or 3. How could that be possible?" Show students the lines of symmetry in the number eight that answer this riddle.

Introduce the concept of symmetry (when both sides of an object are the same size and
shape). Demonstrate symmetry of shapes from Day 1 (while reviewing their names) as well as complex 3D shapes (like people, chairs, etc.) Show some examples of shapes that don't have a line of symmetry, like the letter G. Play a quick game of Symmetrical or Not Symmetrical by naming objects and having students show you thumbs up if the object is symmetrical and thumbs down if the object is not symmetrical (or asymmetrical.)

Give students a copy of the symmetry worksheet and ask them to draw the line(s) of symmetry on each shape, then check their answers with a neighbor when they are finished.

Give each student a small piece of paper and ask them to fold it in half. Is this a line of symmetry? Give students scissors and ask them to cut a small shape along the fold. Have students draw what they think their shape will look like when the paper is unfolded on the back of their worksheet, then unfold the paper and see if they were correct. Repeat this activity with more elaborate shapes.

Day 3: Pentominoes and Transformation

Introduce the transformation terms flip (mirror image), slide (translation; moving up,
down, over, etc.), and turn (rotation). Draw a familiar shape, such as a heart or smiley face, on the board. Draw the shape again and ask students whether you did a flip, slide, or turn.
Give each student a copy of the Flip, Slide, Turn worksheet, facedown. Give each student a pentomino. Have them trace their pentomino on the back of their worksheet, then ask them to show you a flip, slide and turn from the traced shape. When the concepts are mastered, have students turn their paper over and complete the worksheet.

If extra time remains, divide the students into small groups or pairs and give each group or pair a full set of 12 pentominoes. Ask them to fit all their pentominoes together to make a rectangle. (This is very difficult!)  Tell students that we'll find a solution to this problem tomorrow.

Day 4: Pentomino Puzzles

Divide students into pairs and give each pair a set of pentominoes.  If desired, teach the students the letter names of the pentominoes.  Give students several challenges, such as those found here.
(For letter names and one large rectangle solution, see this site.)  As a final challenge, ask the students to make one large rectangle using all of their pentominoes.

Monday, April 9, 2012

Adding and Subtracting 1, 10, and 100

Prep: Print a copy of the egg hunt questions and put each question into a plastic Easter egg. Hide the eggs around the room.

Introduce the topic by writing a 3-digit number (such as 462) on the board. Ask the students what number is more than your number, and write the answer above in another color. What number is one less than 462? Ask the same questions for 10 more/less and 100 more/less, explaining that we look in the tens column when adding or subtracting 10 and then hundreds column when adding or subtracting 100.

Repeat the instruction with more numbers as necessary. When the class seems comfortable with the concepts, give each student a copy of the egg hunt number list. Tell the students that there are eggs hidden around the room. Their job is to find as many of the eggs as they can and answer the questions inside. When they are finished with an egg, they must put the question back inside and hide the egg right where they found it. Demonstrate finding an egg, figuring out the answer ot the question, crossing off the answer on their number list, and re-hiding the egg. Students may work alone or in pairs. Challenge the students to find as many of the answers/eggs as possible.

Wednesday, March 21, 2012

Multiplication: Week Two

Day 1: Multiplication Storybook Problems
Seat the students on the floor with a marker, tissue, and dry erase paddle. Read Humbug Rabbit by Lorna Balian (or another seasonably appropriate book) and stop to ask students multiplication problems throughout. (Example: Mother and Father Rabbit have five rabbit children. How many feet do five rabbits have?) Students should write the multiplication problem (either 4 x 5 = 20 or 5 x 4 = 20 would be correct) on their dry erase paddle and show it to the class. Continue reading the story and stopping for multiplication problems until you reach the end of the story.
Day 2: Review and Commutative Property
Briefly review the multiplication facts we've learned so far. (0, 1, 2, 3, 4, 5, 10.) Remind students that they can find the answers to threes and fours by skip counting. Play an Around the World multiplication game. Set chairs in two rows facing each other with one extra chair at the head of the rows. (You'll need an ODD number of people for this to work, so play yourself if necessary.)
________X (head chair)
Students sit in the chairs and are given a multiplication flash card. When the person in the head chair says "go", one line asks their multiplication question and the other line answers. (Tell students that they're going to be the expert on their card, so they need to help their partner figure it out any time their partner has trouble.) Then the other line asks their question and the first line answers.
When both sides have asked and answered, players advance one seat clockwise. They are now in front of a new partner with a new question (and a new person is saying "go"), so rows take turns asking and answering again. Continue playing until students have gone all the way around the circle. Give each of the students a new card and play the game again.
If there's time for a third round, have students think of their own problem (anything 0-5 or 10 is fair game.) You can also introduce the commutative property by having them ask the reverse of the question printed on their card (e.g. 7 times 2 rather than 2 times 7.) Save the flash cards to use on day 3.
Day 3: Nines and Review
Teach the students their nine times tables by learning the nines trick. (Show the video to the students if possible.)
Review multiplication facts by putting students in groups of two or three and having them play the Multiplication Board Game. (You can use any multiplication flash cards for the game cards; just make sure all the cards in play are facts the students have learned.)
Day 4: The Big Test!
Give the students their final multiplication test. Students who finish early can work on a multiplication math maze or multiplication coloring page.
Give the students their multiplier's licenses and teach them how to use the multiplication table on the back. Congratulate the students on working so hard and learning so much.

Saturday, March 17, 2012

Multiplication: Week One

Day 1: Zeros and Ones

Show the students your driver's license and ask them the following questions:

What is this? [A driver's license]
What does it mean? [You're allowed to drive and you know what you're doing.]
How did I get it? [By learning how to drive, learning all the rules, and then passing a test.]

You can't get your driver's license until you're sixteen, but there's another kind of license that you can get earlier. Most kids don't get it until they're in third grade, but you have learned so much math and worked so hard that we're going to see if you can get yours in FIRST GRADE!
We're going to work on multiplication for the next two weeks, and learn all the rules to follow. If you pass a test at the end, I will give you your very own multiplier's license. (Take a picture of each student at some point during the unit to put on their multiplier's license.)

Introduce the "×" symbol. What does this mean? Why do some people call multiplication
"times"? (Because you're adding that number together a certain number of times.) We are going to learn two whole sets of times tables today, and I promise you can all learn them.
Write some zero multiplication problems on the board. Teach the students the proper
words for reading these number sentences. (e.g. "x times y equals z.")
Teach the students that no matter what they multiply by zero, the answer is always zero. You can make this fun/funny by using word variables. (e.g. "What's zero times banana?" "Zero!")

Teach multiplication by one in the same manner. No matter what I multiply by one, it stays the same. Tell them that these two are both very easy, but they're also easy to mix up! Have the students sit in a circle for a short game. (What about zero times one? Does it follow both rules?)

Tell them that this is the lightning round, and they have to answer their questions as quickly as possible. Walk around the outside of the circle and ask students 0's and 1's
multiplication questions in turn. If they get it right, they get a small treat (like a chocolate chip or
Skittle.) The faster they go, the more chance they'll have for treats. (But try to emphasize accuracy too!)

Day 2: Twos and Review

Review doubles addition facts using the "lightning round" game from Day 1. Did you know that if you can add doubles, you can do 2's multiplication? Draw examples on the whiteboard to illustrate that multiplying by two is doubling (which we already know how to do!) Say multiplication problems aloud and have students use unifix cubes to model them. (Can you show me two groups of five? What number sentences can I write on the board that show this? (5 + 5
= 10, and 2 × 5 = 10.)

When the students seem comfortable with this concept, briefly review 0's and 1's (and model with unifix cubes if there's time), then tell them that they're doing so well that they're ready for their first test.

Day 3: Threes and Fours

Give each student a handful of unifix cubes (~24) and ask them to line them up in groups of three. If they have one or two left over that don't fit into a group of three, they can put them back in the box. If we want to quickly see how many cubes you have, a good way to do that is multiplication or skip counting! Since every group has three in it, we'll find the answer if we skip-count by threes. (You may want to model this with one student's blocks or on the white board.) (If students are unsure about counting by threes, write the numbers on the whiteboard for reference.) Ask the students to skip-count their blocks by threes, then go around the circle and tell how many you had. (All numbers should be multiples of three.)

That's all we have to do to multiply by threes! Teach students that skip counting is another way of doing multiplication. If we want to know what three times six is, we can skip count by threes until we get to the sixth number (3, 6, 9, 12, 15, 18!)

Repeat the exercise for fours- line up unifix cubes in groups of four (discard any remainders), practice skip-counting your groups, and tell how many you had. (Answers should be multiples of
four this time.)

Give students the skip-counting worksheet. Show them (either on the worksheet or on the board) that when they have the skip counting lines done, they can just count over to do their
multiplication like we did earlier!

Day 4: Fives and Tens (Multiplication with Coins and Clocks)

Review 10 times tables. ("Just add a zero!") Review skip-counting by fives and how to find the answer to 5's multiplication problems using this method.

Give each student a handful of dimes and nickels and an index card. Tell them that you're going to pull items out of the bag and tell them the price. (Or have students take turns pulling an item out of the bag and announcing the price.) Students will then need to put the correct number of dimes and nickels on their card to represent the price. Have students check their neighbors to make sure that everyone is figuring things out. On the smaller-priced items, ask students to show the price using just dimes, then the same one using just nickels.

If you have extra time, review telling time (to five minute increments). Tell students that if they learn their five times tables, telling time will be even easier! Then instead of counting all the way around the clock, they can do the multiplication problem in their head to find the number of minutes. Practice this with the small clocks.

Encourage students to practice over the weekend. We're going to have a practice test on Monday so we can get our multiplier's licenses!

Monday, March 12, 2012

Multiples of 10

Day One – Multiples of 10 – What are they?
Using cubes/counters represent a given number. Can you split that number of cubes into piles of 10 with none left over? If so, that number is a multiple of 10. Practice with several numbers – multiples and not (write them on the white board so students can see the numbers to decide about the pattern). Do you see a pattern/something similar about each number that is a multiple of 10? Describe the rule/pattern. (Numbers that end in 0 are multiples of 10)
Teach the students that to know what numbers are multiples of a number, just count by that number. (For example, to know what numbers are multiples of ten, just count by tens.)
Play slapjack with cards. Each player gets a “deck” of index cards with numbers on them.
Partner up. Players take turns flipping over 1 card into the middle. If the card
is a multiple of 10, the first player to slap it wins the stack. The goal is to capture all your opponent’s cards.

Day Two – Practice Adding 10 to a number
Briefly review yesterday’s lesson. Today we will practice adding 10 to a number. Each pair gets their own game board of chutes and ladders. Players alternate spinning the spinner and advancing as normal and rolling a die and advancing by that multiple of ten. (Example: if you rolled a four, you'd move up 40 spaces.)
* Final challenge round (if time)– figure out the answer to this math problem – The zoo had 650 tigers and 1,000 leopards. They sold 230 tigers and 100 leopards. Then they got 60 more leopards and 70 more tigers. How many were there in all?

Day Three – Add 10 to the target number
Today we’ll be having a race like Family Feud. Split into 2 teams – sit together in circles on the floor. Distribute a dry-erase paddle, marker, and tissue for erasing to each member of the team. We’ll be taking turns answering a number about multiples of 10. Everyone should write the answer on his or her dry erase paddle. When it is your turn, you’ll be showing your paddle to the teacher to determine whether or not your team will receive a point.
**I’ll tie in pennies and dimes today while doing this review activity.
*Final Challenge Round (if time) – As a team – add multiples of 10 to these numbers then order them greatest to least. (30, 70, 140, 330, 320, 590)

Day Four – Adding Multiples of 10
Pass our hundreds boxes and paper with addition problems. Use color chips/cubes to represent the number then add multiples of 10 to show the new number. Do a total of 10
problems front/back.
*Final Challenge Round (for fast-finishers)– revisit the day’s activity using subtraction.