Geometric Multiplication

 

Today I reviewed the concept of geometric multiplication with Bubs.  It is a simple multiplication problem, but the child draws it on graph paper and color codes it.  The problem he started with was 3,748 x 53.  

He first started with drawing the multiplicand of 3,748.  He started in the bottom right hand corner of the paper and made a dot.  Then he counted eight units to the left for the first number of his multiplicand.  He made another dot.  The length of that line represents eight units so he drew a line to connect the dots and wrote an "8" underneath the line.

He continued for the remaining categories of his multiplicand.

Here is the multiplicand graphed on paper.

Next he drew the multiplier.  He started with the same dot as the 8 for the units at the bottom right hand corner of the paper.  However, now he will move upwards counting vertically, instead of across the paper horizontally.  The unit of the multiplier is 3.  He counted up 3 lines and drew a dot.  Connect the lines and write a 3 to the right of the line.  This length represents the three units of the multiplier.  He connected all of the dots to make a rectangle.  He is multiplying so he will multiply the units by the units to get some amount.  How much is 8 x 3?  24.   This equation is written in the rectangle and then colored green for units.

He continues for the remaining categories and colors them according to their category: blue for tens, red for hundreds, and green for thousands.   You should be able to click on the picture to enlarge if the picture is too small.

Now, he moved to the next row vertically to multiply the 50 tens. He multiplied 50 x 8.  That gave him 400 units.  He marked the lines vertically and created another rectangle.  Then he colored it green for the units.  

He continued with the remaining categories in the second row.

The final step is to calculate his answer.  He looked at the products of each area of the diagram and added them together.  He recorded his answer as he added each category.

Global Cuisine - Venezuela

Here is our menu for our Venezuelan Cuisine.

Ok, so since I don't take pics of my kids faces (see why here), I had to figure out a creative way to get a picture of their costume.  I tried a profile pic here.  I only captured the boys for this meal because the girls were still showering and getting dressed and then our guests arrived.  For their costumes, we used kangas from Kenya, a sombrero from Mexico, and for some reason, my daughter chose to get T-Man an Australian outback hat.  I didn't say anything though because she tried! HA.

Ok, so before we delve too deep into this global cuisine tradition, I would like to throw out a disclaimer that we usually don't buy any clothes/accessories for our dinners.  We simply use what we have at home to try to recreate the outfits the best we can.  So, I hope we don't offend anyone that may be reading from a particular country!  That is not our intention.

The table is a great example of how we improvise.  A lady I used to work with is from Guatemala and gave me this table runner.  I decided to use it for Venezuela since it looked close enough!

 Our dinner started with Venezuelan Pan de Jamon as an appetizer.  My husband knows that I'm not a fan of olives, so he left those out of this.  He only put raisins and ham.  He also burned the palm sugar and opted to use maple syrup as a substitute.  The kids came running into the kitchen and told him enthusiastically that something was burning!  It was his palm sugar!!  He still pulled it off and it was a huge hit!

 

Our really good friends and our son, Bubs' Godparents, came over for dinner.  They brought the traditional Venezuelan rice drink called Chicha.  It was delicious.  She added ice, the drink, cinnamon, and a cinnamon stick for added flavor and for stirring.  Apparently, this drink was made by mothers and given to their kids after school to hold them over until dinnertime.  

Here is a picture of the rest of the meal.  It included Venezuelan Sweet Plantains, Pabellon Criollo (shredded skirt steak), Bollos Pelones (ground beef dumpling with leeks, olives, capers, and many other ingredients), Venezuelan beans and rice, and a cilantro mojo sauce to put on pretty much anything.

Dessert was a Chocolate Marquesa.  It is a layered cake with maria cookies and premium baking chocolate.  Let me just tell you that my darling husband makes great desserts, but the kitchen looked like a bomb went off after this.  My kitchen aid mixer was covered with cocoa powder, smeared butter residue, drippings of dried sweet condensed milk, and a dusting of powdered sugar!  I guess it was worth it in the end.  

I attempted to cut it nicely for a picture, but it sort of fell apart.  Not sure that it set for the 8 hr in the fridge.  It still tasted delicious.

The kids ran out of time to perform their song, but I did get books from the library and the older ones read about Venezuela.  Every week doesn't quite go as planned, but we always have a great time and love listening to the different music from each country.  The main point is that we are building a tradition of having dinner as a family on Sundays and exposing our children to different cultures.  

Stamp Game - Division

Today, I showed Bubs how to do long division using the stamp game.  He practiced writing it down on paper as well.  He tried to jump straight to paper and was struggling a bit, so we brought out the stamp game for reinforcements.  He has pretty much mastered racks and tubes and feels like the stamp game is "baby" work and actually started crying like a "baby" today when I told him to go get it off of the shelf!

Once we moved past all of the tears, he set up his problem.  He divided 4,297 by 28.  The white strip is his division bar.  He lays out all of the tiles for the dividend and writes the divisor on a piece of paper.  (Sorry, the picture doesn't show the number on the white paper very well.)

He uses his button (the green circle above the division bar) to keep track of which category he is working on.  He then asks himself the question, "How many groups of 28 can I make with 4 thousands?"  His answer is zero.

He moves the button over the hundreds category.  The thousands and hundreds get pushed together.  Then he asks his question again.  "How many groups of 28 can I make with 42 hundreds?"  He now needs to exchange one of his thousand tiles for 10 red hundred tiles.

He exchanges his tile and then makes one group of 28.  His remaining tiles are 1 thousand tile and 4 hundred tiles.  

He records his answer on his paper.  He put a 1 above the 2 in his dividend.  He asks the question of how many did he use.  The answer is 28 of 42.  His remainder is 14.  This should match the amount of tiles he has left over.  Ideally, he writes his number on a blank ticket and places it in the correct category column above the division bar along with recording it on his paper.

The button is now moved over the ten category column.  At this point, thousands, hundreds, and tens need to be pushed together.  Remember, since the divisor has two digits, he can only have two different colors, or categories to work with.  He will need to exchange his green thousand tile for 10 hundred tiles.

"How many groups of 28 can I make with 140 tens?"  He starts sharing the tiles and comes up with 5 groups.  He has 9 tiles left over.  Bubs records his answer on his paper.

Now he brings down his final category of units to meet up with his tens that were remaining.  

He shares all of his tiles and is left with 13.

Records it on paper.

This is what the final problem should look like all laid out.  You can see how the categories end up at the bottom by the time you reach the units so the child can visualize that the number needs to be "brought down".  Oh my...just seeing those random pencils in the picture again.  Bubs!  He was obsessed with getting those in the pics.

Large Bead Frame - Multiplication

Today I presented multiplication on the large bead frame to Nito.  He was so excited to do this and actually said it was fun! Ha.  Go figure, math being fun.  He had the biggest grin on his face when he would check his answer and get it right.  The picture above is the large bead frame.  It has categories up to 1 million, unlike the small bead frame which only goes to 1, 000.

Unfortunately, I didn't have (or honestly can't find) the paper specifically for the large bead frame, so he had to use the small bead frame paper.  I just added the columns for tens and hundreds for him.  Ok, so here is his problem.  4,346 x 4.  He first starts with decomposing the number on the paper.  He starts with the units, which is 6.  Then he moves to the tens and records it as 40.  When he has completed decomposing, he makes brackets around the number and writes down what he is multiplying by, which is 4 for this problem.

Now it's time to move the beads on the frame.  The first number is units times the multiplier, which is 6 x 4, or 24.  He moves 4 unit beads to the right and then 2 ten beads to the right to form 24 on the frame.  

He moves to the tens.  4 x 4 which is 16.  He moves the ten beads until he reaches 10, then moves 1 hundred bead to the right, pushes the tens back to the left and keeps counting until he reaches 16.  

The next category is hundreds.   The same process is done, moving a thousand bead when needed.

He finishes up with the thousands and records his answer on his paper.

Here is his paper when he is finished.  He also did a few other problems since he thought it was so much fun and he got them all right.

Grammar Box - Adjective Command Cards

Nito and Bubs dabbled with some command cards from various grammar boxes today.  I wanted them to spend some time together working nicely while I had to step away and these usually work well since they have to stay active and move around the classroom.  

In this picture, they had to use pieces from the pink tower.  The adjectives were large, largest, small, and smallest.  Sorry, the pictures aren't the greatest.  Poor lighting!

Ok, so I was clearly not available to help them with some of these, but they improvised nicely.  They were supposed to use the circles in the plane insets.  However, they chose the globe, the clock stand, and a clay shaping piece.  The adjectives were large, small, and intermediate.

Oh my!  Here is another example of how they didn't read the card correctly, but they still made it work.  They were supposed to only use one color of tablets, but instead they chose white, yellow, brown, and black.  The adjectives were light, lightest, dark, and darkest.  

Ok, so these guys are hilarious!  At least they keep me smiling in the sometimes very stressful school day.  I would have chosen the smooth and rough boards for this work, but they chose a music staff board, a metal inset, a rough basket, and a rock.  The adjectives were smooth, smoother, rough, and roughest. 

Here we have light, lightest, heavy, and heaviest.  They actually whipped out the scale for this and somehow managed to put the candle and the thesaurus on it to see which one was heavier!  This makes me think that perhaps I should go and check on the status of our scale.  It could be broken at this point!

The brown stairs were used for this one.  The adjectives were thick, thickest, thin, and thinnest.

Overall, I have to say that they did a decent job.  They are moving on to some of the other command cards in the next week or so.  I'll be sure to post their interpretations of the cards.

Global Cuisine

Puerto Rican Chocolate and Coffee Flancocho

I am finally getting around to posting (hopefully keeping it updated weekly) a page on the blog about the meals that my husband, DJ, cooks for our family every Sunday.  This tradition started almost a year ago when DJ cooked a meal for me for our anniversary.  Now, to give you some background information, my husband does NOT cook.  Well, at least he didn't a year ago.  His cooking consisted of oatmeal pancakes and anything on the gas grill outside.  That was the extent of it.  He decided to surprise me for our anniversary and cooked me all of my favorite foods.  Now, to be honest, I was a bit skeptical and a bit disappointed that we didn't go out for dinner.  With 6 kids, we don't get out much and an anniversary was a great excuse to get out of the house!

To make a long story short, his dinner was fabulous and he actually thought it was fun to cook for me for a change.  The following week he decided that he would try cooking for all of us on Sunday since he didn't have a lot going on.  He chose to cook something from Spain because we have been planning a trip there for awhile.  It was a huge success so he decided to make it a tradition.  I told a friend of mine about the idea and she took it a step further and suggested that I turn it into a homeschooling project and the kids would have to research the country that he was cooking for.  They would do a play, song, or give information on that country after dinner.

The kids have had a blast with this and my oldest daughter writes plays or musicals quite a bit.  They also dress up as close as they can to the traditional clothing from that country.  I will try to include pictures of their clothing, but it might prove to be a bit difficult since I do not include their faces.  I will also be posting pictures of the dishes he makes.  Music also makes an appearance at the dinner table and the kids love to learn new songs in different languages.  Their favorite is a Portuguese song called, Roda, Roda, Roda, (Caranguejo peixe e).  They did this song for Brazil.

DJ chose the first country, but then each week a different child chooses the country they want.  For the ones who can't read, we spin the globe and they point to a country.  We have ended up with some very, let's just say, interesting cuisines for our boring palates.  This has really helped to expand our children's tastes buds and try new things.  Ok, let's be honest, it has helped expand their mama's tastes buds as well!  I am quite the picky eater sometimes.

Here is a list of the countries that we have already done.  There were quite a few weeks when we had visitors or were away for some time so the meals did not happen every Sunday.

Spain, Italy, Angola, Canada, Mexico, Puerto Rico, Sudan, Brazil, Chile, Jamaica, Libya, Singapore (not a repeat), India, Belize, France, Guatemala, Japan, Lebanon, Turkey, Switzerland, Egypt, and Vietnam.

The picture above is from our last Sunday's meal from Puerto Rico.  The dessert was super yummy.  I was very impressed with my husband's ability to make a flan!  Next week: Venezuela!  Stay tuned.

Distributive Law for Multiplication

Nito was shown another presentation in the sequence for Distributive Law for Multiplication.  It seems that I have never posted anything for the Commutative Law, which is usually a prerequisite for this presentation.  I'll have to get on that!  However, I do show at the end of this presentation how to check your answer using the Commutative Law.

As I mentioned above, he has done the presentations on the Commutative Law, the exchanging of the multiplier with the multiplicand.  For this presentation, I chose a sum of two numbers for the multiplicand.  In the picture above, I chose 5 and 2. Since I am considering it a sum, he puts parentheses around the two bead bars. He will take this sum 3 times.  He uses a brown 3 card and places it on the outside of the parenthesis.  Ok, now ideally the child uses a gray card, but all I had on hand was brown construction paper when I made these materials.  I mean, who has time to drive 45m-1 hour round trip to Michael's with 6 kids just to get gray paper?!  Honestly, it doesn't matter the color paper, as long as it isn't white.

This is the box of bead bars that he uses.  It is a bit different from the checkerboard bead box because this one includes the ten bars.

What does taking this sum 3 times mean?  It means taking the 5 bar 3 times and the 2 bar 3 times.  The blue beads are the 5 bars and the green are the 2 bars.

Then the value is calculated and placed underneath the respective columns (15 and 6).

Then the beads are pushed together.

Now, the beads are exchanged to make a single number of 21.

Commutative Law Check

Since the child knows the commutative law, he can check his answer.  It says if you exchange the multiplier with the multiplicand, then you should get the same answer.  Nito laid out the problem after exchanging beads for tickets and tickets for beads.  In the picture above, the distributive law is on the left hand side and the commutative law is on the right hand side.  He laid out a 3 bead bar and now has a 5 and 2 brown card inside the parentheses. 

He begins by taking the 3 bead bar 5 times and then takes it 2 times.  He finds the answer and places the single number below.

This picture shows that the commutative law on the right hand side has an answer of 21 which matches his distributive law answer of 21.  His work checked out!