Kai inspired us this week with a sensational math book, The Book of Perfectly Perilous Math . We couldn’t get enough of these “death-defying challenges” and decided it was time to write our own book! In partner pairs, we came up with a theme for our story problems. Then we set to work creating four story problems using our four main operations this year: addition, subtraction, multiplication & division. Math is alive and well in our classroom in these last weeks of school and carefully crafted activities hope to keep this energy around math into the summer!
Tiger & Wolves:
This week the 3rd graders were busy working with coupons! In pairs, the Tiger & Wolves chose grocery coupons to fit a particular criteria. For example, students were asked to find coupons for things that "couldn't be eaten" and that add up to $2.75. This week's work focused on estimating the sum of serval addends, using estimation to find an approximate solution, and adding in the context on money.
IXL practice: 3rd grade Money N.1, N.2 & N.3
Bears:
4th graders were busy making sense (cents :) of money on a calculator this week! The Bears used mental estimation and calculators to solve addition problems involving money amounts. They discussed how to input various amounts of money and interpret the results as displayed on the calculators- a hit game was "Beat the Calculator". This week's work focused on inputting different amounts of money on the calculator, interpreting calculator displays as amounts of money and adding money on the calculator.
IXL practice: 4th grade Money M.1, M.2 & M.3
Tigers & Wolves:
This week the Tigers & Wolves brought data in from home and compared it with world record data. They compared the record ages of animals and people with the ages of their own pets and relatives. Later in the week 3rd graders make predictions about what would happen to an orange left in my car for a week. They learned how to use a pan balance and then weighed the orange to prepare to compare this weight with the weight after a week in my car :) This week's work focused on developing strategies for comparing two numbers, using landmark numbers while making comparisons, developing predictions of what will happen to data and learning to weight objects accurately using a pan balance.
IXL: 3rd grade addition C.4 & C.6 and subtraction D.4
Bears:
4th graders were busy this week estimating and finding totals for items purchased at the grocery store. They shared strategies for finding estimates and exact answers. Independently and with partners the Bears were introduced to and begin working on three choice time activities, "Buying Groceries", "What's for Lunch?" and "Pre-K Book Orders". Check-in with your child about their favorite choices! This week's work focused on estimating total amounts for money and adding money.
IXL: 4th grade addition B.5 & B.8 and subtraction C.6
Tigers & Wolves:
This week 3rd graders began a unit on addition and subtraction focused around combining and comparing numbers! Tigers & Wolves started the unit comparing their own date and number of children in their family with the record number of children listed in The Guinness Book of Records. They also got a chance to learn and play a new game “Close to 100” with the 4th graders. In “Close to 100”, students are asked to compose a number that is close to 100 and compare this number with 100. This week’s work focused on developing strategies for comparing two numbers, exploring combinations of numbers that make 100 and using landmark numbers while making comparisons.
IXL practice:Addition C.1 & C.4 and Subtraction D.1 & D.4
Bears:
4th graders started a new unit on addition & subtraction this week that focuses on money, miles and large numbers! The week started off with the 4th graders teaching the 3rd graders a game called, “Close to 100”. Later in the week Bears estimated and found totals for items purchased at the grocery store. They shared their strategies for finding estimating and exact answers. This week’s work focused on estimating totals for amounts of money and adding money.
IXL practice: Addition B.1 and Subtraction C.1
We are strong mathematicians and it is time to show all we have learned about fractions! On Monday Tigers, Wolves and Bears will all take a summative assessment on fractions. Below are the standards the assessment will cover. On Tuesday we begin an investigation on addition and subtraction!
3rd grade:
4th grade:
Tigers & Wolves:
This week 3rd graders used pattern-blocks to make designs that are half yellow. Tiger-Wolves drew, colored and labeled designs. After making a design that was half yellow, students focused on making designs for other fractions of yellow. Later in the week students began to think about how to share different kinds of items, including items that cannot be split into parts (balloons) and items that have a limited number of parts (money). To become familiar with decimal equivalents for common fractions, they found solutions to brownie problems with and without the calculator. This week’s work focused on recognizing designs that are half or another fraction of yellow and relating meanings for division and fractions.
IXL practice: 3rd grade Fractions-S.10 & S.13
Bears:
4th graders worked together this week to make a deck of 60 fraction cards on which they visually represented fractions, including fractions that are greater than 1. Bears then learned to play the game, “Fraction Fish” to practice finding equivalent fractions. Work this week focused on developing visual representations of fractions, understanding numerical representation of fractions greater than 1 and recognizing fractions such as 1/2 and 2/4 both visually and numerically.
IXL practice: 4th grade Fractions-Q.3 & Q.8
Tiger & Wolves:
This week 3rd graders used pattern blocks to solve problems that gave the number of people and the size of each share. They then solved problems that gave only the size of the share. Making lists of the number of people, size of the shares, the Tiger-Wolves looked for patterns. This week’s work focused on putting pieces together to make wholes and looking for number patterns.
Bears:
4th graders worked in pairs this week to create squares with specified fractions of area colored (two-thirds, three-fourths, five-sixths and seven eighths). The fraction of the square’s area that is colored could be kept as one piece or broken up with several non-connected regions that together equal the specified amount. After finishing their own designs, students worked to figure out how much of the other students’ designs are colored. This week’s work focused on using measurement to divide up a square into fractional parts, comparing fractions that have “one missing piece” and working fractions that have a numerator larger than 1.
Tigers & Wolves:
This week our 3rd graders worked on comparing sizes of “brownies” and “cookies” in different sharing situations. After they compared sizes, students were challenged to write a letter to second graders explaining why one and one third is a larger share than one and one-fourth. At the end of week students learned the “Fraction Cookie” game! This game involved identifying fraction parts, exchanging equivalent fractions and adding and subtracting fractions. The game proved to be a big hit!
IXL practice: 3rd grade fractions-S.12 Order fractions with like numerators
Bears:
4th graders sharpened their wits this week learning to use a larger whole to explore size and equivalence relationship among fractions based on one-third. They divided dot-paper rectangles (as opposed to squares) into thirds and sixths. They were very busy discussing which shape (rectangle or square) had larger fractions. Their work focused on exploring the relationship between thirds and sixths, as well as understanding that the same fraction of different-sized wholes will be different in area and being able to justify their division of rectangles into thirds and sixths.
IXL practice: 4th grade fractions-Q.7-Q.9
Tigers & Wolves:
This week 3rd graders worked to find and draw all the ways to make the equivalent of one yellow hexagon pattern block (we called these blocks “hexagon cookies” ) using blue diamonds (thirds), green triangles (sixths) and red trapezoids (halves). After drawing the patterns, students then wrote the fraction of the whole that each block represented. This week’s work focused on finding shapes to cover one whole, identifying fractional parts that add to one whole and writing fraction expressions. It is exciting to see the Tiger & Wolves so excited and comfortable with fractions. We are flying through this unit!
IXL practice: 3rd grade Fractions S.9 & S.10
Bears:
4th graders worked this week to divide a whole into a combination of halves, fourths and eights. First they experimented with geo-boards, then they made drafts on dot-paper squares, and finally copied a favorite one on to a large square. After finishing this large square, students wrote equations that reflect the relationship their designs illustrate. Their work focuses on exploring relationships among halves, fourths & eighths and writing equations that reflect pictures with halves, fourths and eighths. It is exciting to see the thoughtful and beautiful work the 4th graders are producing.
IXL practice: 4th grade Fractions Q.5, Q.6 & Q.7
Tigers & Wolves:
This week 3rd graders were busy investigating fair shares. The Tiger-Wolves worked to cut up paper rectangles as if they were brownies to share equally among a number of people. They demonstrated the various ways to share different amounts of brownies equally between 2-6 people. This work focused on understanding fractions as equal parts, partitioning area into equal parts and making a list of fraction facts.
IXL practice: 3rd grade Fractions S.1 Unit Fraction Review S.
Bears:
4th graders were working hard to investigate fractions and area with geo-boards this week. Using the square of the geo-board, students divided the area into halves, fourths and eights. Working together, the Bears then discussed their solutions and compared various shaped fourths to show that they were the same size. Their work focused on exploring the relationship among halves, fourths and eighths, understanding that equal parts of a whole do not need to be exactly equal in size and justifying their division of area into equal parts.
IXL practice: 4th grade Fractions Q.1 Equivalent Fractions
1 Unit fraction review
Our lessons directly related to our project during math this week! Jordan explained to us that if we wanted to be successful musicians, we needed to learn about reading music. We then spent a good part of the week learning what a “meter” was, identifying whole, half, quarter and sixteenth notes (along with being able to clap their rhythm), and we also learned to understand that one measure of music must contain enough fraction notes to add up to 1. Each day students were creating their own measures with different time signatures and finding various ways to combine (add fractions) to add up to 1. It was an exciting way to introduce our latest investigation into fractions!
We are brave multipliers and dividers and it is time to show all we have learned! On Monday the Tigers, Wolves and Bears will all take a summative assessment on multiplication and division. Below are the mathematical emphases the assessments will cover. On Tuesday we begin an investigation on fractions to help us with our song writing!
Tiger & Wolves (3rd grade):
Bears (4th grade):
This week the Tigers, Wolves and Bears all combined forces to work together on multiplication and division work. 3rd graders had opportunities to share proud, new knowledge and fourth graders were able to reinforce learned topics and push towards greater understanding by simply answering questions. Work this week revolved around understanding and solving multiplication and division stories propelling us toward using multiplication and division notation to write number sentences as well.
IXL: 3rd grade Division G.1 division facts to 5 & G.2 division facts to 10
IXL: 4th grade Division E.5 divide larger numbers by 1 digit, word problems
Tiger & Wolves:
Our array cards are completed! A brave accomplishment in our multiplication lives. Arrays help students not only know multiplication facts, but SEE and understand what these facts mean. After discussing strategies for working with our arrays, students worked independently to identify by shape the arrays with a total of 36 and then identify the factors of 36. Toward the end of the week we began examining the “language of multiplication of division”. Students discussed the actions suggested by multiplication and division word/story problems.
IXL practice: Division G.3 division word problems-facts to 10
Bears:
This week the Bears were busy understanding and practicing division problems. They worked interpreting word problems to division notation, division notation to word problems and decided how to solve problems in which solutions do not come out evenly. We challenged our ideas about division by contrasting two kinds of division word problems (sharing and portioning) that can be written with the same division notation. Next week, double-digit multiplication here we come!
IXL practice: Division E.7 divide by 1-digit numbers: interpret remainder
Tigers & Wolves:
This week students were challenged to find different ways to arrange rows of chairs for an audience. Students first manipulated 12 cubes to see how many different rectangles they could make. They listed the dimensions of these rectangles and the factors of 12. Next, the Tigers & Wolves worked independently to determine the factors of other numbers by making arrays of each number. We learned the term “prime number” and were excited to share when we found new “prime numbers” as we worked on our arrays.
IXL practice: Multiplication Skill Builders F.4: multiply by 3 and F.5: multiply by 4
Bears:
Bears this week became comfortable with their array cards and started to find “small arrays” that make up “large arrays”. We were busy transcribing out these “small” and “large” array problems into number sentences such as “(8x4)=(2x8)+(2x8)”. Bears also started thinking about division this week! We began Friday introducing division notation through word problems that represent various types of division situations.
IXL practice: Division E.1: division facts and E.2 division fact word problems
There has been much buzz from students about wanting math homework. One of the best ways for students to practice at home is with IXL. IXL is a dynamic math practice website that allows students opportunities for reflection and tracking of progress. Any and all student activity is also reported to be on an individual basis that helps me further track progress. It also helps build computer skills that are growing every important in our ever-changing and exciting world. Enjoy the updates from the past week and checkout the corresponding IXL practices!
Tigers & Wolves:
This week students discussed number patterns in several of the charts and looked at some patterns across all the charts. They then used what they knew about multiples to play a game, “Cover 50”. This game focused on recognizing multiples of the same number, describing patterns in the 100s chart and becoming familiar with multiples.
IXL practice: third grade
Bears:
As students diligently continue working on labeling their array cards with dimensions and totals, we begin to get excited about new games we will play starting next week. These games will be encouraged to be played throughout winter break as a way to further build confidence with multiplication facts before we begin talking about division and double digit multiplication after break!
IXL practice: fourth grade
Tigers & Wolves:
This week 3rd graders completed their multiplies of 2-12 100s charts! This is a big accomplishment that is now an incredible resource for our continued multiplication and division exploration. Tigers & Wolves then had a chance to see the importance of their 100s chart during choice time this week. Students worked on four different activities; skip counting with a partner, making towers of multiplies, patterns across the charts and solving story problems. All these choices help the Tiger-Wolves to become more familiar with multiples and provide opportunities for students taking ownership of their work.
Bears:
Bears were busy this week completing their arrays of different numbers. Arrays are a model for multiplication that allows students a visual way to understand multiplication pairs. We continue to practice with arrays by making “array cards” that represent multiplication facts 2-12 and will begin playing games with these cards next week.
Early in the week the Tigers & Wolves were busy listening to problems presented in the book Each Orange Had 8 Slices by Paul Giganti & Donald Crews. Solving these problems involved two and three steps of multiplication thinking! On Thursday, students excitedly began using 100 charts to think about multiplication. Students explored 100 charts and highlighted multiples of 2s-5s by making a chart for each one. After break we will be busy investigating patterns that see within each 100s chart.
IXL math practice: Third Grade E.3 multiplication word problems
The Bears this week used cubes and graph paper to begin making all the possible arrays for a number. For each number they made a poster with all the possible arrays labeled with dimensions on it. After break, students will explore each other posters and begin making observations about factors of numbers and recognizing prime numbers.
Tigers & Wolves:
This week students worked to make lists of things that come in groups of 2 to 12. With this list, the Tigers & Wolves worked in partner pairs to create multiplication problems based on the class lists, “if one car has 4 wheels, and there are 5 cars, how many wheels are there altogether?” Partners then traded problems for each other to solve. Throughout this work the Tigers & Wolves focused on recognizing multiplication situations, and posing and solving multiplication problems.
IXL practice: third grade E.1 "multliplication sentences"
Bears:
Bears this week were introduced to skip counting on the 100 chart. They created a set of highlighted 100 charts that show multiplication patterns of numbers. The Bears will use these charts throughout the unit to practice skip counting and playing games. Their work focused on practicing skip counting and looking for multiplication patterns of numbers 2-12.
IXL practice: fourth grade D.1 "multiplication facts up to 12"
Bears:
Bears spent the beginning of this week assessing multiplication facts from 2-12. Multiplication facts are important for math “fluency”. Just as we learn sight words in reading to read more fluently, we learn multiplication facts to be able to do more complicated and multi-step problems (double digit multiplication and division) with more ease. Yet, multiplication facts on their own do not teach us understanding. So while students will be given time to practice and learn multiplication facts, much of our learning during school will be on understanding “what is multiplication and division” and why and when do I use it.
IXL practice: fourth grade D.1 "multiplication facts up to 12"
Tigers-Wolves:
Multiplication is one of those things that third graders can’t wait to learn. They are ready to not just add and subtract but learn a new way to think about math. It is similar to the excitement of cursive instead of just print or the hope they have desks instead of tables (sorry I didn’t make that dream come true). And developmentally, third graders are ready for multiplication and division. But, it is important we keep that “excitement” in this new skill and that is why we start slow and deep in conceptual meaning. This week was spent thinking about “things in groups” and making visual representations of these groups. Next week, we begin to add number sentences to these groups and begin thinking about “how many in several groups”. Enjoy this exciting time in your third grader's mathematical life!
This week the Tigers, Wolves and Bears “celebrated learning” through a unit assessment! Before beginning, we talked about how assessments were a chance for students to show everything they learned, how it was a good opportunity for them to check-in on their learning and for me to see how successful my teaching was! Unit assessments will be sent home Monday. To celebrate Halloween we spent Thursday and Friday working on “pumpkin” math! Working in small groups, students were given a pumpkin and posed the question, “Which pumpkin has the most seeds?” Next, the difference between qualitative and quantitative observations were introduced. Then each group worked to complete qualitative data and quantitative data about their pumpkins. With their data in hand, we discuss which type of data is more useful in predicting the number of seeds in the pumpkins. Friday, we counted and analyzed our results! Monday we all move on to multiplication and division
Tigers & Wolves:
Bears:
Tigers & Wolves:
· The Tigers & Wolves we busy this week graphing and comparing data. Students worked in small groups creating two bar graphs, one representing last weeks data and one representing this weeks. Ask your student what data their group was working with and what they learned about their data. Next week, we will begin our final investigation exploring odd and even numbers.
IXL practice:Third Grade P.4 & P.5 create and interpert bar graphs
Bears:
· The Bears spent the week constructing pattern block and geoboard designs that have a line of symmetry. Later in the week the Bears investigated patter block designs that grew from a central hexagon to have rotational symmetry. On Friday the Bears when on a “symmetrical hunt” with Hilary walking around campus looking for symmetry in and around our school. Next week will bring a close to our mathematical thinking unit, and assessments before moving on to multiplication and division!
IXL practice:Fourth Grade P.24 rotational symmetry
Tigers & Wolves:
· The Tigers & Wolves began collecting and representing data this week. Students observed, classified, counted and recorded data about themselves. They played a game called “Guess my Rule” as a way of collecting information to begin thinking about how the data could be collected in different ways. Next week, we will graph our data and begin our final investigation exploring odd and even numbers. We’ll end our unit on Mathematical Thinking and dive right into multiplication and division after we complete that investigation!
IXL practice: P.9 Create Pictographs
Bears:
· Bears spend the early part of the week entering numbers and observing patterns on a partially filled 300 chart . They then used their charts to compute differences and play a bingo game that involved adding and subtracting multiplies of 10 in numbers 101 to 200. Next week the Bears will investigate geometry concepts at the 4th grade level before ending our unit on Mathematical Thinking and moving on to multiplication and division!
Choice is a powerful thing for children. It creates ownership of work and helps build confidence in understanding. “Academic Choice” is a factor in our classroom, particularly with math. This week both groups had many opportunities to “choose” their work. Students document their choices and are held accountable for completing each activity in full.
Tigers & Wolves:
Throughout the week strategies for addition problems, exploring which numbers can be divided in half evenly, learning new addition combinations and finding the values of coins were emphasized and practiced through a series of games and activities of the student’s choice.
Bears:
· Through “academic choice” the Bears practiced configuring numbers whose sums are close to 100, adding coins to make dollars, grouping coins for more efficient counting and using decimals points to represent coin values. Each concept was reinforced through games that required cooperation and understanding within a group. The students often practiced using mathematical language and logic to “prove” their answers to their partners.
This week in math all groups continued to grow as mathematical thinkers! Enjoy the updates.
Tigers & Wolves: The Tiger & Wolves math group had an opportunity to explore building symmetrical patterns. Using, geo shapes and mirrors they learned how to construct a design with mirror symmetry while developing strategies for numerical patterns. "If side A has 3 shapes, how many shapes will your design have if it has mirror symmetry?" Tiger-Wolves used known addition combinations to figure more complex ones as well.
Bears: The Bears practiced finding number pairs that equal 100, using place value and finding differences through playing "Close to 100". Later in the week, the Bears began working with money. They practiced recognizing US coin values while organizing and keeping track of counting money. In partners, the Bears worked together sharing strategies of how to find amounts in coins of up to 50 dollars.
After assessments last week, students broke up into mathematical groups the Tigers, Wolves and Bears. All students this week dove in our first unit, “Mathematical Thinking”. Ask your student which group they are in and enjoy reading the updates from below!
· Bears: The Bears worked independently, in partners and our small group to explore materials that are used as problem solving tools and practiced grouping things for more efficient counting. We estimated how many hundreds are in the total group of three-digit things. Throughout our investigations we practiced communicating with mathematical thinking, written ,and spoken language.
o IXL practice: place value at the 3rd grade. As a reminder, skills and practice at students’ grade level are what students are expected to know by the end of the year and we will use the previous grade year as review to begin.
· Tigers & Wolves: This week we practiced counting and grouping quantities to make 100. We then looked at another way to represent 100: the 100 chart. We became familiar with number patterns on the 100 chart and added it as a tool to our math journals and learned a game to play on it “Plus, Minus, Stay the Same”. We also practiced communicating with mathematical thinking, thought, and written and spoken language.
o IXL practice: place value at the 2nd grade. As a reminder, skills and practice at students grade level are what students are expected to know by the end of the year and we will use the previous grade year as review to begin.
Math is a living, breathing thing in our classroom. It is full of inquiry and excitement and an everyday part of our life. This past week we practiced “mathematical thinking” with manipulative investigation, math games and independent individualized math assessments. We also established routines and behaviors for both collaborative and independent math work. Next week we begin our math curriculum, Investigations, with our first unit appropriately titled, “Mathematical Thinking at 3rd and 4th grade”.
Another exciting part of our math curriculum this year includes a dynamic and expansive math practice website named IXL. Each student has an individual account that can be accessed both at school and at home. An email will be sent to each family this weekend regarding student access. As we get rolling with our math curriculum, I will highlight areas in IXL that students are encouraged to practice. For now, students are welcome to explore their mathematical grade level. As it is the beginning of the year, students may feel some frustration regarding mathematical topics that they have not been introduced to, if this is happening to your child, encourage them to review their previous grade for a refresher.
Come back here next week to get a detailed run down of what we did in math.