Appendix of Word Problems
Place Value
1A. Escribe el número lo más grande de tres cifras que tienen seis centenas y cuatro decenas.
2A. Listan los cinco números impares que tienen un nueve en el lugar de millares, un ocho en la posición de centenas e un siete en el lugar de decenas.
Once children learn how to read the clues for the above type of problems, the teacher can make them up and continue to increase the place value positions, as above. It's important for students to differentiate between even numbers (números pares) and odd numbers (números impares). This is an important clue. My students come to really enjoy these problems and their increasing difficulty across the dimension of place value.
Take Away/Finding Difference
1A. Jorge pesaba 140 libras. Se pusó a régimen y perdió 15 libras. ¿Que pesa Jorge ahora?
2A.The little league baseball teams in Littleton have 102 more members than the basketball teams. If 45 members switch from baseball to basketball, then what will the difference be?
1B.An album can hold 400 stickers. Lily has 199 stickers. How many more stickers does she need to fill the album?
1C.A worker needs 3606 bricks to build a house. She has 2679 bricks now. How many more bricks must she get?
2C.The Declaration of Independence was signed in 1776. How many years was this before you were born? (note:This years crop of fourth graders was born in 1998.)
I have arranged these problems in order of increasing place value difficulty. As well the number of zeroes that need to be subtracted across increases in problem 1B. Problem 2C requires that children know the year in which they were born and know which number to use as the minuend and which to use as the subtrahend.
Subtracting Across Zeroes
1A.Luisa e Raúl teinen entre si $15.00. La parte de Luisa es $8.42. ¿Que parte de ese dinero es de Raúl?
2A.Luz se compró un bocadillo a $0.39 e un zumo de manzana a $0.55. Si pagó con unbillete de $1.00, ¿cúanto vuelto recibió?
1B.La senora Bazán tenía 46 en 2007. ¿Cuántos anos tenía en 1993?
1C.Las clases de la Escuela Azteca está recogiendo periódicos para la esfuerza de recogida de periódicos. La meta es recoger 10,000 periódicos. Recogimos 768 periódicos la primera semana, 3,456 la segunda semana, 2,987 periódicos la tercera semana. ¿Cuántos periódicos más necesitamos recojer?
I grouped problems one and two together because they both require subtraction across two zeroes. Problem 2A has the added dimension of being a multi-step problem that requires adding first and then subtracting. It also uses decimals.
1B is an interesting problem because the problem solver needs to first subtract years to find the number of years between 1993 and 2007. Then he needs to subtract that answer from 46 to find out how old Sra. Bazán is in 2007.
In problem 1C another dimension has been added—the place value has increased to 10,000. Like problem 1B, it is a multi-step problem requiring addition first and then subtracting the total from 10,000 to see how many newspapers still need to be collected to reach the goal.
Comparison
1A.Cesi tiene 42 cacahuates. Nestor tiene 22 cacahuates. ¿Cuántos cachuates tiene Nestor menos que Cesi?
2A.¿Por cuánto es más grande ciento cincuenta que veintitres?
3A.Se vendió Lupita 312 cajas de galletas. A Marta se vendió 228. ¿Cuántas cajas de galletas más se vendió Lupita que Marta?
1B. Juana, Marucha y Rita fueron a jugar á los bolos. ¿Cuántos puntos más que Juana marcó Marucha?
Jugador Total
Puntos de Juana 105
Puntos de Rita 129
Puntos de Marucha 181
1C. Tony pagó $920 por una moto y $245 por una bicicleta. (a) ¿ Cuánto pagó Tony para las dos? (b) ¿Que tanto más era la moto que la bicicleta?
Problems 1A, 2A and 3A are both simple comparison problems; however 2A requires a subtraction in the ones place and also requires that students read the numbers in script. 3A requires decomposing across three place value units. Another important feature of the Spanish word problems is that native speakers do not have to translate them back into their mother tongue in order to solve them, so they are able to go directly to the language of mathematics. I have found that this increases their mathematical learning curve. Then, when the students do reading problems in English, they are able to more easily understand the mathematical similarities in structure.
Problem 1B sets up a little chart where students need to choose the relevant data in order to solve the problem.
1C is a multi-step problem requiring first addition and then subtraction.
Decimals
1A. Fred's time in a race was 14.5 seconds. Jordan's time was 15.3 seconds. Who ran faster and how much faster?
1B. Betty earned $16.00 selling lemonade at a lemonade stand. Marvin earned $13.50. How much more lemonade money did Betty earn than Marvin?
2A. Nathan's weight was 82.5 pounds three years ago. Now he weighs 76 pounds. How much weight did he lose?
3A. Betty and Marvin want to buy a C.D. that costs $19.95. Betty earned $16.00 selling lemonade and Marvin earned $13.50. If they put their money together, will they be able to purchase the C.D.? Will they have any money left over?
Problems 1A and 1B are straight subtraction with decimals except that B has two decimal places and also subtracting across zeroes. Problem 2A, however, is introducing a new dimension of subtraction requiring the problem solver to add a decimal point and a zero to hold the tenths place. This problem may require some modeling, but I will first see if students can come up with a conjecture in their groups. 3A is a multi-step problem combining addition and subtraction.
Fractions
1A. 4/5 de los jovenes en un coro son muchachas. ¿Que fracción de los jovenes son muchachos?
1B. Minghua spent 3/7 of his money on a book and the rest on a tennis racket. What fraction of his money was spent on a racket?
2A. Elena tiene 3/4 de un litro de jugo de naranja. Tomé 1/2 litro del jugo. ¿Cuánto jugo resta?
3A. A container can hold 3 cups of liquid. It contains 1 3/4 cups of water. How much more water is needed to fill the container?
Problems 1A and 1B require subtracting the given fraction from the whole fraction which is not given. The challenge for the students, therefore, is to come up with the unnamed fraction. 2A requires finding a common denominator. After students meet in group to make their conjectures, we will probably come together whole-class in order to solve the problem. 3A combines adds the dimension of decomposing a whole number into a fraction. It will be interesting to see how much of the process children can figure out in their groups.
Multi-Step Problems
The following problems are arranged, as much as possible, to increase in technical difficulty, and/or number of steps needed to solve the problems.
1. En la mesa hay 10 manzanas. Navier se comió tres, Laura se comió dos y Raquel se comió cuatro. ¿Cuántas manzanas quedaron?
2. There are 260 members in a chess club. 136 of them are boys. (a) How many girls are there in the chess club? (b) How many more boys than girls are there in the club?
3 .Ms. Montoya has 13 boys and 15 girls in her class. On Friday, 7 students were absent. Four of the absent students were girls. How many boys were in class on Friday?
4. Eusenia tiene $20.53 que ahorré de cuidar ninos. Quiere comprar una blusa que cuesta $15.99. (a) Cuánto dinero restará? (b) Tiene suficiente dinero a comprar un pedazo de torta que cuesta $3.25?
5. Martín participó en dos de estas actividades. Pagó con un billete de $10.00. Recibió de vuelto $3.75. ¿ En qué dos actividades participó Martín?
Actividad Costo
Cine $3.50
Minigolf $3.00
Patinaje $2.00
Cochecitos $2.75
6. La clase se propusó como meta 1,250 latas de aluminio para su proyecto de recoger latas. Hasta ahora han recogido 735 latas. ¿Cuántas latas más necesitan para alcanzar su meta?
7. Cuando tres muchachas se subieron a una báscula esta marcó 166 libras como su peso total. Uno do los muchachos bajó y la báscula marcó 106 libras. Otra muchacha bajó y la báscula marcó 57 libras. ¿Cuánto pesaba cada muchacho? (Sugerencia: Utilizando los hechos dados, comienaz con 166 libras y resuélvelo al revés.)
8. A painter mixed 1.46 liters of black paint with 0.8 liters of white paint to get gray paint. Then he used 0.96 liters of the gray paint. How much gray paint did he have left?
9. One football stadium, built in 1982 has 64,035 seats. Another stadium, built in 1987, has 74,916 seats. How many more seats does the newer stadium have?
10. Ms. Wasser is ordering supplies for her class for the next school year. She has three tally sheets. The first tally sheet totals $28.46, the second totals $17.83 and the third totals $30.00. She has $100.00 to spend. How much money has she spent altogether? How much money does she have left?
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