Input - Output Machine Math Challenge Task Cards - Function Machine Problems

Rated 4.86 out of 5, based on 67 reviews

4.9 (67 ratings)

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The Teacher Studio

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Grade Levels

4th - 6th, Homeschool

Subjects

Math, Basic Operations, Other (Math)

Resource Type

GATE, Task Cards

Standards

CCSS4.OA.A.1

CCSS4.OA.A.3

CCSSMP1

CCSSMP2

CCSSMP7

Formats Included

PDF
Google Apps™

Pages

$4.00

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What educators are saying

These were amazing and all of my students loved them, they were fun, and really helped them get the hang of them!

— Misty R.

Rated 5 out of 5

Loved that this progressed in level of difficulty. I used this as a worksheet - just gave groups of students the cards as worksheets. The beginning was easy and the end gave a challenge to my top students which was great.

— Louann B.

Rated 5 out of 5

Description

Standards

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Reviews

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Description

This set of 24 input/output table task card math challenges are perfect to use as whole class warm-ups, small group instruction, math stations or centers, or even as intervention groups to work on problem solving and algebra thinking. Students love the function machines and the level of challenge varies for easy differentiaton.

Although designed to be used with fourth and fifth graders, these cards would also be perfect to use with older students needing additional review with algebra thinking. NOW INCLUDES DIGITAL SLIDE ACCESS!

The 24 problems included require students to use different operations (addition, subtraction, multiplication, and division) to solve a variety of input/output problems.

Students may be able to see the mathematical pattern (ex. “This is a

times 3, then subtract 4 pattern.”) or may end up using guess and check strategies to solve the problems. Students are not expected to use algebraic reasoning—but I DID pull some of my top students to show them how to write these “expressions” with variables. They LOVED it!

What do you get?

Answers are included as are three rubrics to use to help in scoring the Standards for Mathematical Practice!
Cards are included in both color and low-ink, black and white versions for ultimate flexibility.
There are blank recording sheets that can be used for students to track their work, or they can simply do their work in a notebook.
Answer key!

WHY DID I CREATE THESE?

Over the years I have noticed that students are often in search of an easy answer…a “fill in the blank”. The simple fact is, math is sometimes more complicated than that! In this set of task cards I want students to struggle…something many have never had to do!

In these input/output problems, students need to recognize that when you put a number in (left side of chart), “something” happens in the machine and a new number comes out. It could be something simple—like the machine could add 3 or double the number—or it could be more complex—like the machine multiplies the number times 3 and then takes away 1.

These more complex operations are not immediately obvious and require students to do some real algebraic thinking, guessing and checking, and reasoning.

When I first started, I heard lots of “I don’t get it!” and “It’s impossible!”, so I projected a card on the screen and talked through my guess and check strategies. Full color photos are even included with some teaching ideas!

WHAT IS THE CHALLENGE LEVEL?

Cards 1 - 12

These cards involve one step—for example, “add 12” or “double”. They are great to get started…and may be enough for some students! We did the first four as a class, and then students worked in partners to try the others.

Cards 13 – 24

These last 12 cards have TWO steps…making the pattern FAR more challenging to find. Cards may have patterns such as “multiply by 9, then subtract 2” or “multiply by 3 and then add 8”. All four operations are included. These are NOT easy! Students may get frustrated but encourage them to persevere, work together, and use their brains! These would also be perfect for an enrichment group or a station for fast finishers.

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Interested in a set of other algebra challenges?

CLICK HERE TO VIEW

This resource is also available as part of a "Teaching Tandem" product where you can get this resource AND a set of algebra thinking concept sorts combined at a reduced price. CLICK HERE TO VIEW

This is also available as a digital task card resource in my GOOGLE EDITION resources! CLICK HERE TO VIEW

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All rights reserved by ©The Teacher Studio. Purchase of this resource entitles the purchaser the right to reproduce the pages in limited quantities for single classroom use only. Duplication for an entire school, an entire school system, or commercial purposes is strictly forbidden without written permission from the author at fourthgradestudio@gmail.com. Additional licenses are available at a reduced price.

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Standards

to see state-specific standards (only available in the US).

CCSS4.OA.A.1

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

CCSS4.OA.A.3

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

CCSSMP1

Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

CCSSMP2

Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

CCSSMP7

Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression 𝑥² + 9𝑥 + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(𝑥 – 𝑦)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers 𝑥 and 𝑦.

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