Archive for January, 2016

Eureka Math Module 4: Addition and Subtraction Within 200 with Word Problems to 100

Written by ValerieW. Posted in 2nd Grade

Dear Parents,

We are about to start yet another math module!
Grade 2 Module 4: 
Addition and Subtraction Within 200 with Word Problems to 100

In Module 4, students will learn place value strategies to  add and subtract within 100; they’ll do one- and two-step word problems of varying types within 100; and they will develop conceptual understanding of addition and subtraction of multi-digit numbers within 200.  Starting from concrete, then moving  to pictorial and lastly to a more abstract approach, students will use manipulatives and math drawings to help deepen their  understanding of the composition and decomposition of units.

They will not be taught the traditional algorithm (carrying and borrowing to add and subtract).

Many of us adults were taught the PROCEDURE of adding and subtracting using “carrying and borrowing.”  We were not taught the CONCEPT, the why of adding and subtracting, only how to do it, and a shortcut at that (carrying and borrowing is a shortcut!).

 We were taught, when we saw that there were too many units in the ones column,  how to “carry a ten” – – pass it over to the tens column.  We were also taught how to “borrow a ten” – – get numbers from the tens column to put in the ones column, in case there were not enough units in the ones column for use to carry out a subtraction problem.  It was if the number 35 could start having a conversation with itself, with one part asking the other to give it something!

Giving children the algorithm is like telling a person how to get somewhere:  go left, take the second right, go three streets, turn left again, etc. etc.  You need to memorize all the ins and outs in order to get to your destination.

Giving children strategies is like giving them the understanding of how to use a map to arrive at a destination:  they are given the big picture and guided to find and use multiple pathways to get to the destination.  Memorization is not required. 

In second grade we are striving to teach the students the CONCEPT of addition and subtraction.   What is really happening is that we are REGROUPING numbers by composing and decomposing them, that is, putting them together or breaking them up in different ways to make addition and subtraction easier to do.  In class, we also us the term exchange to emphasize the fact that they can trade 10 ones for a ten, 10 tens for a 100 – – an exchange of units of equal value. Here are two excellent videos to watch to help understand how to explain the process to second graders:

http://learnzillion.com/lessons/3118-explain-addition-using-place-value

 http://learnzillion.com/lessons/3119-explain-subtraction-using-place-value

Below are some simple drawings which we hope you will find useful to see the WHY and HOW of what we are doing in class.  When your child does the homework, he or she will need a pencil and a pen or marker in a contrasting color.  Below, we have used red to show contrast, but any color is fine.  We are DRAWING the numbers in base ten, in a way that simplifies the shape of base ten blocks:  

b10

48 will be 4 tens (6 lines) and 8 ones (8 circles or dots).

 

ADDITION:

48 + 24 = ________

DRAW the numbers in base 10 (meaning, lines for the tens, and circles or dots for the ones) on the place value chart.  Ask your child to organize the numbers;  tens like tally marks, ones like dots on a ten frame, as shown below).  The two numbers are placed  in middle part of mat, the first number above the second one. (The answer will be placed below the line.) We start out by adding up the ones.  Ooops!  Too many ones for the ones column (there are 12).  

addition 1

  1.  Take a red pen, and circle a group of 10 ones (you are  composing them into a group of ten).   addition 2
  2. With the red pen, draw an arrow over to the tens column, where you will be putting your group of ten.  Remember to cross off the circle of ones, so you don’t count it twice!  addition 3

 3Now add them all up, and DRAW the answer (the sum) at the bottom of the table in base ten (lines and circles).  Fill in the number sentence at the bottom.  You are finished!  addition 4

SUBTRACTION

WHAT’S THE DIFFERENCE?

 

When we subtract, we are actually looking at two quantities to see the difference between them, that is, we are trying to figure out how much more one group has than the other.

difference 1

  1.   We have two groups here.

 2. Before human beings had numerals with which to subtract  symbolically, they could figure out which  of two groups was bigger by taking away one from one group, one from the other, and so on, till one group disappeared and the larger group remained.  Here, we have taken away one from the group of  flowers , and one from the group of butterflies.  

difference 2

3.  We continue until the smaller group (butterflies) is entirely crossed off.  We see that the  group of  flowers still has 14 flowers. It is larger by 14.  The difference between the two groups is 14. 

difference 3

 

  1. When we subtract, we use the above rationale.  DRAW 35 and 19 in  base ten on the place value chart. We know that 35 is the larger of the two numbers, but we don’t know by how much.  We can see that there are only 5 ones in the top part of the table – – not enough to be able to successfully cross off all those 9 ones in the bottom number !  addition 1 
  2. We need to break 35 apart (decompose 35) in such a way that there will be enough ones in the top group to be able to successfully cross off all those 9 ones in the bottom group.  So,  with a red pen we’ll take a group of ten, cross it off (so we don’t accidentally count it later), draw an arrow to the ones column, and draw 10 ones in red in the ones column.  subtraction 2
  3. Now in red  we will cross off the 9 ones (from the 19), and also cross off 9 ones (from the 35).  (Remember the procedure from “what’s the difference?“)  subtraction 3
  4. Now we will cross off the 1 ten (from 19), and also the 1 ten (from 35). (Remember “what’s the difference?“) subtraction 4
  5. Finally we draw what is left in base ten:  (1 line and 6 circles), and we write that number in the number sentence: 35 – 19 = 16  subtraction 5

 

 If we teach our students the shortcut for doing addition and subtraction without previously giving them the rationale for their actions, learning the shortcut will be meaningless to them.

But by understanding the rationale behind addition and subtraction, these operations become meaningful, and easy to visualize and understand.

If you have any questions please don’t hesitate to ask us!

The Second Grade Team

The parts of our house

Written by Maria Guttierez. Posted in 2nd-3rd Grade Beginner SAL, SAL

For the past weeks, SAL students from 2nd and 3rd grade, have been working very hard on the parts of the house.

They have learned the name of the furniture we can find in each one of the rooms and have been using new grammar structures with the verbs “tener” and “haber”.

Through vocabulary contests, drawings and descriptions; SAL students have proved not only to have understood the contents of this topic but also to be able to use them in a meaningful way.

As a final project for this unit, students have been asked to create their own room by using recycled materials (due date is on February the 10th). Pupils will have to include all of the furniture we have been working on and will present it to the rest of their classmates.

The next unit we will be working on is related to food, we will keep you updated!

Joan Miró

Written by Maria Guttierez. Posted in 3rd Grade Spanish-Catalan Studies, Spanish-Catalan Studies

During the past weeks, 3rd graders from Spanish-Catalan Studies have been working on the figure and creations of one of the main important artists from Spain: Joan Miró.

We have learned a little bit about his life: where he was born, when he moved to Paris and why, which are his main paintings, sculptures and creations, how did his career as an artist developed, etc.

We have also made our own creations based on some of his masterpieces (you can see the results below!) and we have carried on a small project based on some of his sculptures.

On the following weeks we will be working on some of the main Spanish writers; we can’t wait to share with you everything that we will learn! We will keep you updated.

Our house

Written by Maria Guttierez. Posted in 1st Grade SAL, Kindergarten SAL, SAL

Our Kinder and 1st graders are learning about the parts of the house and some of the names of the objects you can find in it.

We have been practicing some previous vocabulary as well as we have learned many more. We have also introduced some new adjectives that help us to describe better each part of the house.

As a project for this unit we have “built” our own house! Students were arranged in groups of three/four and have been working on a specific area of the house by creating a beautiful drawing including the furniture you can find in each one of them.

Also, we have been singing and we do it very well! We will love to sing the song “Mi casita” to you and, maybe, you will like to learn it and dance with us too; so, here you can find the link in case you need it (https://www.youtube.com/watch?v=0O8W98KU-DE)  and the lyrics as well:

“YO TENGO UNA CASITA QUE ES ASÍ Y ASÍ;

QUE POR LA CHIMENEA SALE EL HUMO ASÍ Y ASÍ.

 QUE CUANDO QUIERO ENTRAR, YO GOLPEO ASÍ Y ASÍ.

ME LIMPIO LOS ZAPATOS ASÍ, ASÍ Y ASÍ.”

Descubriendo nuestro cuerpo

Written by Maria Guttierez. Posted in Castellano

Los alumnos de Castellano de Pre-K estamos trabajando las partes de nuestro cuerpo.

Para hacerlo empleamos distintos recursos tales como fichas,  el juego “Memory” para ampliar y reforzar el nuevo vocabulario o canciones que nos ayudan a aprender los contenidos de una forma más lúdica  (https://www.youtube.com/watch?v=NxQOHkjuybw).

Esta unidad nos está ayudando a comprender mejor y conocer más nuestro cuerpo. Os invitamos a que cantéis y bailéis con nosotros, que nos preguntéis por las distintas partes de nuestro cuerpo para que podamos compartir con vosotros todo lo que estamos aprendiendo.

¡Seguiremos actualizándoos!

Despertando los sentidos

Written by Maria Guttierez. Posted in Castellano

En clase de Castellano los niños y niñas de Nursery estamos trabajando con contenidos relacionado con los sentidos. Puesto que se trata de una unidad transversal, estamos incorporando vocabulario nuevo que nos permite expresar mejor qué sentimos cuando comemos alguna cosa, por ejemplo.

download

Hemos hecho algunas manualidades que nos han ayudado a descubrir el sentido del oído de forma distinta y hemos realizado algunas actividades online de discriminación auditiva que nos han gustado mucho.

Durante la semana que viene vamos a trabajar el sentido del tacto llevando a cabo algunas fichas que nos ayudarán a percibir texturas distintas.

¡Estamos muy contentos con todo lo que estamos aprendiendo!