Mystery Math A First Book of Algebra

I saw Mystery Math: A First Book of Algebraand was so hopeful it would live up to my expectations, I wasn't disappointed when I checked it out of the library. I've been arguing for years, that when you introduce math language to kids in a casual but consistent way early on, they won't necessarily understand it right away, but you plant seeds and with consistant useage the language and concepts take root. Kids aren't asked to learn a new language when presented with algebra. They've been introduced to this type of language since they've been working with math. The language gets more complex and the ideas more abstract, but the goal of using math language has been a consistant.

Algebra has long been a stumbling block in my family and it is frustrating because if taught differently most of the kids seem to understand it until forced back into the standard way of being taught it. This book starts by using humor and monsters to engage kids with the basic language of equations. The book begins by discussing see saws and balance, leading children towards the concept that equations must be balanced. Eventually the book introduces the idea that what happens to one side of an equation must always happen to the other in order for the balance to be maintained. This is done in a fun and humourous way with illustrations, but the language is math language and the equations are written correctly to introduce kids to equations as they are properely written.

Honestly, I wish I hadn't waited until Jr. High to start changing my way of thinking about equations. Algebra was a foreign language based on a language I thought I already knew and that was fruatrating to me and many of my classmates. We were learning new words for concepts we thought we already understood. What if someone had just casually without too much pressure started us off with the correct language for what we were learning so we didn't have to relearn everything at an arbritrary time people thought we were ready for algebra?

This book starts out solving simple addition and subtraction algebra problems and then moves on to mulitplication and division problems. The solutions are laid out quite well and with plenty of explanations for child and interested parents who might want examples that are clear to demonstrate the process to a child. The story is funny and cute to help keep the interest in pursuing the problems alive. The math is not overwhelming, but for a child only familiar with addition and subtraction, the multiplication and division sections might be more challenging.

I have been looking specifically for algebra related math materials and this is one of the more exciting basic books I've discovered. I'm continuing my quest for others, but this is one of the best I've seen at the introdcutory level to date.

Math at the Art Museum

I saw a listing for Math at the Art Museum and wanted to read it because I've always been interested in how art, music, and gym can help students who love those subjects, but are weak in others build skills in new ways.

This book begins that premise and actually would make for an interesting discussion about how more subject areas could work together with shared vocabulary, activities, and curriculum planning to help students recognize that math and science are accessible in areas they often never consider.

In this book two children are headed off with their parents to the Art Museum to visit a special exhibition titled, "Discover Math in Art." The family passes through the exhibits and the mathematical vocabulary is highlighted. The paintings through out the book are identified and the painter credited.

One of my favorites was Praying Mother and Son Rock Formation by Kim Jae-hong used to demonstrate symmetry, because this reminded me of my trip to see the art teacher when I needed help with this lesson plan. While the emphasis on symmetry was significant in the curriculum, the materials I had available to me, were rather limited for the age group I was teaching. It seemed this would be a logical choice for demonstrating a math concept in art class so we discussed my curriculum goals and the types of projects she would consider doing with the kids to meet those goals. As an artist, her appreciation for symmetry was far deeper than mine and she was able to find ways to explore it that I never would have considered. I can only say my students were blessed to have her additional instruction on the topic.

This book is very introductory, but it is an important one that I hope arrives at a few faculty meetings along with being used by parents and children to explore math and art. I do believe students do better when we help them build from strengths. For kids who love art, music, and gym being able to see math and science in those subjects makes science and math less intimidating. It doesn't mean we turn every lesson into a math lesson, but there are plenty of ways to embed vocabulary and concepts into a lesson without it losing it's original purpose.

It does require training and planning. Technical high schools in this area have already begun this transformation of working to embed more traditional learning curriculum into the student's shop periods. It takes training, but it is reflected in the students going from failing standardized tests to sometimes beating their classmates in traditional classrooms who spend more time focused solely on curriculum. Students are learning curriculum through trades and technical skills that interest them. In the same way students can and should learn skills they need in art, music, and gym. It doesn't take away from the time they spend in those classrooms, it just deepens the learning experience. Having teachers use math vocabulary when discussing art, music, and gym topics requires training, but it can lessen anxiety in kids who normally fear a math problem, but excel at figuring out the geometry required in a football play.

Fractions in Disguise

Fractions in Disguise: A Math Adventure (Charlesbridge Math Adventures) is a math picture book that uses humor and a bit of robbery to engage students in reviewing the concepts of greatest common factors, lowest common denominators, and reducing fractions.

The story begins with fraction collectors gathered for an auction of a 5/9 fraction. During the auction, the lights go out and as in any good mystery the object disappears leaving the need to seek it out. George Cornelius Factor, GCF starts out on the journey to recover the 5/9 and in the process demonstrates the how and why fractions are reduced by finding the greatest common factor.

I love books that attempt to use humor, art, and fun to teach math concepts. I think this one might be a better review or post introductory book. I'm not sure I'd start my lessons on GCF and LCD with this book as it explains around the topic rather than directly defining. I think once kids had been introduced to the topics this would be a great, fun reinforcement of those concepts.

It also could just be used as a picture book that introduces the idea in passing without being too concerned with how much a child absorbs. The choice is really in the hands of the parent or teacher. The last page in the book does give a more formal explanation of how to reduce fractions. I did think this book might inspire some fraction art projects.

Sir Cumference and the Roundabout Battle

I've been a huge of Cindy Neuschwander's Sir Cumference series for quite some time. Sir Cumference and the Roundabout Battle does not disappoint. It provides a fun tale, while demonstrating an important math concept rounding.

In this episode we find Sir Cumference's steward, Edward Rounds working with his son, of the same name on the accounts. To avoid confusion the two are known as Rounds 1 and Rounds 2. While the younger, Rounds 2 enjoys counting, double digit adding is not his strength and he struggles with how to quickly add the columns of numbers to provide accurate counts that Sir Cumference and his men rely on in doing their daily tasks. His father emphasizes that while it is important to be an accurate counter to be steward, the ultimate purpose in counting is to supply an inventory that will be useful to those needing to use it in the castle. Accurate data from counting is essential for the inventory to be correct, but without finishing the final step in adding up the numbers the inventory is not very practical for those who come to ask for information.

Rounds 1 and 2 discuss how much easier it is to count with round numbers, but his father does emphasize the need for an accurate count. As the story continues, Rounds 2 stumbles upon an invasion force and now the inventory is more important than ever, for Sir Cumference needs to know how many bows and arrows he has available to fight off the incoming forces. Rounds 2 panics because he has not had the chance to finish adding all the columns. Rounds 2 lacks the time to add all the columns so he grabs a tape measure to help him figure the closest friendly 10 for each entry. Once he has his estimates, the columns are much easier to add. He is then able to present a rounded count just as the invasion force is arriving. It is looking scary for Sir Cumference's forces, but help arrives from an unexpected resource and all is resolved in favor of the heroes.

This was a great way to demonstrate a practical use for rounding. It also used larger numbers that demonstrated a need for rounding. One issue I struggled with as a child is we started rounding with problems I could answer without rounding. Why do the extra work of rounding when I know the "real" answer. This presents both Round 2 and the children with real practical reasons to round numbers.

Inchworm and a Half

I thought Inchworm and A Halfwas an interesting introduction to the English Measuring system. While the Metric system is based on ten, which is tied in to the counting we teach children in the early grades, the English system can be more challenging for children to understand.

Elinor J. Pinczes takes on the challenge by introducing the whole unit of an inch with an inchworm and then the fractional parts with the inchworm’s fellow worm friends. The inchworm starts out being thrilled with his ability to measure things that are whole inches because his body measures one whole inch. Then he hits a snag. A cucumber has a fractional piece left over and he is puzzled by the challenge of measuring it. It is then that he meets a half-inch worm and they head off to enjoy life, measuring things that are composed of whole and half inches.

Of course, they eventually have challenges that require a third and a quarter inch and as they do, they find worms who can help them meet those measuring challenges.

I have seen parents and teachers use yarn and paper to help children understand the various lengths in measurement, so worms seem like another creative way to engage children in thinking about the concept. This book would be a useful tool in engaging young readers in thinking about the English system of measurement.

Equal Shmequal

What do people mean when they say they want something to be equal? Equal Shmequalhelps children understand the mathematics involved in making a game of tug of war equal between a group of animals. The focus at first is on making things fair.

As the animals work through the math involved they realize that to make things fair they have to understand the math involved with the game. Numbers alone do not make for a balanced game of tug of war. One large creature can beat a much larger group of smaller creatures if he is stronger. As the animals continue to work on the problem, they also learn that balance is not alone enough to make an equal contest. Effort is another factor that plays into the contest.

I thought the strongest part of the book was watching the animals use the seesaw to try to balance out weight as a factor in creating balanced teams. The premise was a bit unrealistic. Children will find that teams and life are rarely completely fair and balanced as the theme of this book pushes. However, I did think using animals was an interesting way to introduce children to the idea that there is a difference between having numerical balance, the same number of animals, and weight balance. From the pictures, children can see that there is balance in the numbers, but clearly not balance in the outcome until the weights are balanced. Even then, when the bear does not try, the outcome is not as expected.

The Great Divide

Dayle Ann Dodds introduces children to division in The Great Divide: A Mathematical Marathon as racers encounter hazards that leave them divided into groups. Each hazard leaves the group divided in half until there is only one racer remaining to win the race.

I thought Full House: An Invitation to Fractions did a better job in providing children with visual demonstrations of the math concepts and how the math would be represented in numerical form. This is a cute math story, but not nearly as strong as many of the other math picture books I have been reviewing.

A Very Improbable Story

A Very Improbable Storyis a picture book designed to introduce children to the idea of probability.

Ethan awakes one morning to find a cat on his head, only it is not his cat. The cat refuses to leave until Ethan wins a game of Odds. The cat proceeds to beat Ethan and he is left wondering if he will be wearing a cat hat to his final soccer match.

As he keeps playing the game, Ethan realizes that the high probabilities make his chances of winning unlikely. At breakfast, he discovers a low probability option that finally gets the cat off his head. He uses his new knowledge of probability to work on improving his shot choice and hopes it will result in a win for his team.

This will not help children master probability, but it will introduce them to the concept and some general idea of where probabilities occur in the real world. It is again a great way to introduce a concept that can be challenging to learners early as a way of easing anxiety later.

Full House an Invitation to Fractions

Full House: An Invitation to Fractionsinvites young readers to see fractions in action in an age appropriate manner.

In an author statement Ms. Dodds states, "Fractions were always a bit difficult for me to understand." In this book, she sets out to demonstrate that even young children can start to see fractions as parts of wholes and recognize their number format. She takes the fear out of fractions by introducing them at a young age, helping parents and teachers to demonstrate there is no boogey man fraction monster. It is just another part of math in our environment.

The story she weaves to help teach fractions is about Miss Bloom who runs the Strawberry Inn with six rooms including her own. She is hopeful of filling the Inn and as each guest arrives the readers are shown the fraction of rooms that are now filled. When the final guest arrives, the reader is shown how 6/6 is equal to one whole because the whole Inn is full. A final fraction story emerges regarding Miss Bloom's cake when the guests get hungry in the middle of the night and only leave her 1/6 the of the cake for herself.

I think this is another great book for introducing math concepts early in an age appropriate manner. I do not expect children to grasp fractions after reading this or any other children's picture book. However, it does plant a seed. With additional exposure, children do start to build math concepts. Thus, fractions and other math topics are no longer great mysteries to be tackled in later years.

The Greedy Triangle

The Greedy Triangle (Scholastic Bookshelf)is a creative way to teach children the language of geometrical shapes and about the importance of being satisfied with yourself.

The Greedy Triangle is happy being a triangle fitting itself under a person's arm when they put a hand on a hip, along with many other wonderful tasks. However, one day when it is bored, it asks a magical shapeshifter for another angle and another side and our trip through shape geometry begins. As with most picture books, children can predict that the triangle will never be happy with its new shape and always returns to the shapeshifter for one more side and one more angle.

The story introduces children to looking at shapes as formation of sides and angles that increase and can be seen as building up from other shapes. At the end, the triangle has lost his friends and cannot remember why he was so dissatisfied at being a triangle and requests that the shapeshifter make him a triangle again.

I am always looking for fun math stories that introduce concepts and vocabulary to children. This book would be most appropriate for young children. Unlike some of the other books I reviewed, I do not see this one appealing to an older audience of children.