**275On October 15, 2013, sixty-nine year old Joyce Howland was found dead in her home. After a seven-day trial, a Superior Court jury convicted the defendant of armed robbery and murder in the first degree in her death, on theories of extreme atrocity or cruelty and felony-murder. At trial, the Commonwealth **276argued that the defendant had robbed the victim of her jewelry, slit her throat, and sold the jewelry to obtain money for drugs. The jury heard testimony from the defendant's coworker, over the defendant's objection, that the defendant previously had said that if he were to break into a house that the two had seen, he would find it necessary to kill its occupants. During deliberation, the jury requested a magnifying glass, without stating the purpose for which they intended to use it.
On appeal, the defendant argues that the trial judge erred in providing the jury with a magnifying glass during deliberation, as a violation of the defendant's rights to due process and confrontation. The defendant argues also that the jury instruction on circumstantial evidence and inferences unconstitutionally "diminished the Commonwealth's burden of proof," and violated his due process rights. In addition, the defendant contends that his statements to his coworker should not have been admitted, and that the introduction of those statements requires a new trial. He also asks that we exercise our authority under G. L. c. 278, § 33E, to reduce the verdict of murder in the first degree or to order a new trial. For the reasons that follow, we affirm the convictions and decline to grant relief under G. L. c. 278, § 33E.
1. Facts. We recite facts that the jury could have found, viewed in the light most favorable to the Commonwealth. See Commonwealth v. Latimore, 378 Mass. 671, 677-678, 393 N.E.2d 370 (1979). We reserve some facts for later discussion.
The victim lived alone, and she suffered from lower back problems. At the time of her death in October 2013, she weighed under one hundred pounds. At some point in 2013, the victim contracted with a home maintenance and repair contractor to insulate her attic. In October 2013, that contractor hired a separate building and supply company to complete the job. The *1269defendant worked for the company that the victim hired to insulate her attic. He had been hired one to two weeks before the job was completed, after an acquaintance who worked for the company, Paulo Dias, introduced the defendant to the insulation department manager.
a. Events of Friday, October 11, 2013. On the morning of Friday, October 11, 2013, the defendant, Dias, and their supervisor arrived at the victim's house to begin the installation. The supervisor left soon thereafter, leaving Dias1 and the defendant alone with the victim, who was sitting on the couch. Dias and the **277defendant brought bags of insulation into the attic through a small opening in a closet located in the victim's bedroom.
Over the course of several hours, as the two men were working, Dias noticed several pieces of jewelry on a bureau in the victim's bedroom, including a herringbone chain necklace, another chain necklace, and some rings. The defendant and Dias discussed the jewelry and noted that it could be worth some money. They talked about possibly taking the jewelry, but decided against doing so, because they would be paid that day. The defendant explained nonetheless that if he were to attempt to take the jewelry, he would leave his tools behind and come back later; would knock on the door and be let in because he had forgotten his tools; and would hit the jewelry owner over the head and kill her.2
In addition to noticing the jewelry, Dias noted that the victim had prescription pills in her bathroom. Dias and the defendant determined that the pills were painkillers, and each consumed some. Neither Dias nor the defendant used any other drugs that day; Dias testified that the pills helped to ease his backache.
The two completed the installation at approximately noon. Dias did not have a driver's license, so the defendant drove him back to the building company where they worked, in a maroon company truck with white lettering.3 The defendant received his paycheck and cashed it that afternoon.
b. Events of Monday and Tuesday, October 14 and 15, 2013. On Monday, October 14, 2013, a holiday, Dias and the defendant worked on an insulation job for a different customer. When the supervisor drove the defendant to the worksite that morning, the defendant asked him for twenty dollars even though the supervisor had paid the defendant on Friday.
Over the course of that morning, when Dias and the defendant were standing outside the house where they were working, they saw the next door neighbors outside with a young child. Dias testified, over defense counsel's objection, that "the next-door neighbors were out there with their kid, little baby, about two, three years old that I could see, and it came up that if -- he was like, if I broke into this house, I'd have to kill everybody, and I was -- even the **278baby. And I was like, why would you have to kill the baby for? ... Why would you have to kill the baby if he couldn't even identify you, if you did something like that, you know?"4 *1270Dias and the defendant completed the insulation job around noon or 1 P.M. , and the supervisor brought them back to the office in the company truck. The supervisor asked the defendant if he would pick up insulation at a warehouse that afternoon. The defendant agreed that he would get the insulation and put it away, lock the truck and the shed, and telephone the supervisor when he was finished. The defendant took the maroon truck, and he dropped Dias off at home on his way to the warehouse. The supervisor received a telephone call from the defendant at 3:22 P.M. , during which the defendant told the supervisor that he had locked up around 2 P.M. Dias watched his children at home that afternoon until 4 or 5 P.M.
Sometime before 2 P.M. that day, the victim spoke with a longtime friend on the telephone; the victim said that she planned to join the friend at a trivia event that evening. The victim spoke with someone else by telephone at approximately 2 P.M. When the victim did not appear for the trivia event that evening, her friend telephoned but got no answer. The next morning, Tuesday, the friend drove to the victim's house. She found the front door unlocked, went inside, and discovered the victim lying on the floor of her bedroom. She ran outside and telephoned 911.
Paramedics arrived at approximately 11:15 A.M. One of the first responders saw a half-eaten meal on a coffee table. There was also a cigarette that looked like it had burned out. The victim was lying on her left side with a pool of blood surrounding her head. A paramedic determined that the victim had died prior to the first responders' arrival. When the victim was rolled over, a large incision was visible across the front of her neck. The victim's blood was found on a candle box in her bedroom and on multiple plates in the kitchen sink. A black knife in the sink tested positive for the presence of blood, but no confirmatory test determined whether the blood was human.5
An autopsy revealed that the cut across the victim's neck was seven and one-half inches long, on average one inch deep, and **279comprised at least two distinct cuts. The victim's veins and arteries were severed below the jaw. She also had numerous other cuts, scrapes, and bruises on her arms, face, neck, and torso. Blunt force trauma to one of her vertebrae was consistent with her head having been yanked backward, and superficial scrapes on her chin were consistent with defensive wounds. A forensic pathologist testified that from the beginning of the infliction of the major wound to her neck, the victim would have been conscious for ten seconds or more.
Surveillance video footage introduced at trial showed a maroon truck with white lettering, identified as the maroon company truck, traveling east on Route 6 on October 14, 2013, at approximately 2:16 P.M. The truck was carrying white bundles in the back that looked like insulation. What seemed to be the same truck appeared on surveillance video footage traveling in the opposite direction nineteen minutes later, at 2:35 P.M. In a recorded interview on Tuesday evening, October 15, 2013, the defendant told police that he had gone to the victim's house on Monday afternoon to retrieve a tape measure that he had left behind. He said that he was at the victim's house for a maximum of five minutes.6 Trial testimony established that if *1271someone were driving the maroon truck seen on the surveillance footage at 2:16 P.M. to the victim's house, and if the driver only stayed at the victim's house for a maximum of five minutes before returning, the truck should have been visible on the surveillance video no more than nine minutes after 2:16 P.M.
Surveillance video footage from a nearby restaurant showed an individual wearing light-colored pants appear to toss something into an alleyway at approximately 2:45 P.M. on October 14, 2013.7 A few days after this video footage was recorded, after hearing conversations among his staff about some type of incident in the area, the restaurant manager retrieved and watched the footage. He then went into the alley, found a prescription bottle label bearing the victim's name, and gave it to police.
**280Sometime on the afternoon of October 14, 2013, an individual known as "Mojo" contacted Jonathan Chicoine, and asked Chicoine to bring the defendant to a pawn shop because the defendant had something he "wanted to get rid of." Because Chicoine did not have government identification documents, and because such documents are necessary in order to sell something at a pawn shop, Chicoine enlisted the help of a female friend, who did have appropriate identification documents. Chicoine, this friend, and another female friend picked up the defendant at a restaurant using Mojo's automobile, a white four-door sedan. When the defendant got into the rear passenger seat, he was holding a small bag of jewelry, and he said that he wanted to pawn the jewelry for at least $ 400.8
The four drove to a pawn shop. The defendant handed a herringbone chain and another gold chain to the woman with the identification documents, who went into the pawn shop accompanied by the other woman. The defendant gave instructions not to use his name. The women returned with the jewelry a few minutes later, because the pawn shop would pay only $ 200; the group then drove to a second pawn shop. The women went inside, and Chicoine joined them after ten or fifteen minutes. The three returned to the vehicle with $ 380 from the sale. The defendant took the money.
Chicoine drove the group to a nearby gasoline station. The defendant got out of the vehicle and used his cellular telephone to call someone; he then walked to the side of a building, met with a man, and got back into the vehicle. A short while later, in the parking lot of a fast food restaurant, the others found out that the defendant was in possession of a clear plastic bag of heroin that he had not had earlier. He gave some to the women and put the rest in his pocket. He told one of the women that, regardless of how much she was questioned, she should say that she "got the jewelry from some black guy on the street for a couple pieces of crack." The group then drove to a drug store and a variety store, where they purchased needles and a glass pipe that could be used to *1272consume the heroin and smoke "crack" cocaine.
On the drive back, the defendant asked Chicoine if he had any clothes that the defendant could wear, because he was dirty from work. The defendant was wearing cream-colored or tan pants, **281which appeared to have blood on them. Chicoine gave the defendant a pair of jogging pants, and watched him put his dirty pants into a shopping bag that he put in a trash container in an alleyway.
Chicoine later retrieved the plastic bag and gave it to a State police trooper. The pants in the bag had a large, reddish-brown stain around the knee, which tested positive for human blood. A deoxyribonucleic acid (DNA) profile from the bloodstain matched the victim's DNA profile.9 The defendant's DNA profile matched a major profile drawn from the interior back portion of the waistband.10
When the defendant went to work on Tuesday, October 15, 2013, he asked his coworkers if he could borrow a knife because he did not know where his was.
2. Discussion. The defendant challenges the judge's decision, in response to jurors' request, to provide the jury a magnifying glass in the jury room. The defendant contends also that the jury instruction on circumstantial evidence and inferences improperly lowered the Commonwealth's burden of proof and violated his due process rights. In addition, the defendant challenges the judge's decision to allow the introduction of his statements regarding the neighbors that he and his coworker saw standing outside on Monday afternoon. The defendant also seeks relief under G. L. c. 278, § 33E.
a. Magnifying glass. In his closing argument, defense counsel conceded that surveillance video footage showed the defendant walking through the alleyway where the prescription bottle label was discovered; counsel also conceded that the defendant could be seen wearing the pants that were introduced in evidence. Counsel encouraged the jurors, however, to study the pants as depicted in the surveillance video recording closely, on the theory that the pants must have become badly bloodstained while being used by **282someone else.11 The Commonwealth argued that the *1273surveillance video recording might not be of sufficient quality to permit the kind of scrutiny that defense counsel had encouraged.12
During deliberation, the jury requested a magnifying glass, without explaining their reasons for the request. The judge surmised that they probably wanted the magnifying glass "to examine the [d]efendant's forceful argument about the discrepancy between the color or colors of the pants shown on [the restaurant surveillance] video and stills and the pants that [Chicoine] retrieved and presented to the police." The judge informed jurors that he wanted to defer answering their request for a magnifying class until he had conducted some research. After adjourning, the judge researched the science underlying digital image coloration. The parties also agreed to conduct research on issues related to the jury's request. That evening, the judge purchased a magnifying glass from an office supply store, so that he could review the materials himself using a magnifying glass.
The following day, the judge noted on the record that digital cameras produce color images by "only record[ing] the original **283color of a portion of the pixels in the image."13 Accordingly, he recognized that "[u]se of the magnifying glass may focus [jurors'] attention on a digital still that has potential distortions." The judge noted further that no one had testified about the accuracy of the depiction of colors in the photographs derived from the video recording. The judge explained that he had examined the still image that had been the focus of the defendant's closing argument, as well as the surveillance video footage, using a magnifying class. The judge determined that using the magnifying glass was "simply just a better way to look at" the images.
After hearing the parties' views on the subject, the judge decided, over the defendant's objection, to send the jury a magnifying glass. The judge provided jurors with a magnifying glass obtained from the registry of deeds, while also instructing the jury that "an exhibit that can include ... a still or video, is not ... assumed to be an accurate depiction." The judge continued, "It is for this jury to look at evidence about that particular still or that particular video, or a particular document, to find out about ... its creation, its review, and to also consider other evidence that is relevant to the question of whether a particular exhibit is reliable."
The defendant argues that the judge's provision of the magnifying glass to the jury introduced extraneous matters into the case, and, as a result, denied the defendant his rights to due process and confrontation under the Fifth, Sixth, and Fourteenth Amendments to the United States Constitution and art. 12 of the Massachusetts Declaration of Rights. The defendant maintains that the magnifying glass *1274"creat[ed] evidence that was not introduced at trial," and enabled the jury to "consider[ ] information not in evidence." We disagree.
"Extraneous matter is information, knowledge, or specific facts about one of the parties or the matter in litigation that did not come from the evidence at trial." Commonwealth v. Greineder, 458 Mass. 207, 246, 936 N.E.2d 372 (2010), vacated on other grounds, 567 U.S. 948, 133 S.Ct. 55, 183 L.Ed.2d 699 (2012), S.C., 464 Mass. 580, 984 N.E.2d 804 (2013). Information is not "extraneous" when it is cumulative of evidence introduced at trial. See Commonwealth v. Lally, 473 Mass. 693, 711, 46 N.E.3d 41 (2016) ; Greineder, supra at 247-248, 936 N.E.2d 372. We conclude that the defendant has not established by a preponderance of the evidence that delivering a **284magnifying glass to the jury introduced extraneous material into this case. See Commonwealth v. Miller, 475 Mass. 212, 221-222, 56 N.E.3d 168 (2016) (defendant bears burden of establishing by preponderance of evidence that there was introduction of extraneous material).
The jury's use of a magnifying glass did not introduce material beyond the scope of the trial evidence into the jury room. By contrast to other, potentially impermissible, means of manipulating evidence, a magnifying glass does not materially transform the evidence before the jury. See United States v. Miranda, 986 F.2d 1283, 1286 (9th Cir.), cert. denied, 508 U.S. 929, 113 S.Ct. 2393, 124 L.Ed.2d 295 (1993) (distinguishing jury's request for "blow-ups" of surveillance photographs introduced as exhibits from jurors' use of magnifying glass during deliberations, and deeming latter permissible). Indeed, the judge's own observation of the exhibits using a magnifying glass, coupled with his determination that the result was "simply just a better way to look at" the evidence, indicates that the magnifying glass did not impermissibly transform the evidence in such a way so as to go beyond "the scope of the evidence presented at trial." Greineder, 458 Mass. at 247, 936 N.E.2d 372. See State v. Griffin, 1993-NMSC-071, ¶ 30, 116 N.M. 689, 866 P.2d 1156 ("Enhancement of the jury's visual acuity through use of a magnifying glass is not [improper] experimentation [resulting in the introduction of extraneous information] unless there is some indication that the magnification produced additional evidence").
Further, in his closing argument, defense counsel encouraged jurors to "look closely" at the surveillance video recording and still images that counsel acknowledged depicted the defendant. There is no indication in the record that the jurors requested or used the magnifying glass to do anything other than look closely at the evidence, precisely as the defendant requested they do. See United States v. Young, 814 F.2d 392, 396 (7th Cir.), cert. denied, 484 U.S. 838, 108 S.Ct. 121, 98 L.Ed.2d 79 (1987) (not error to provide jury with magnifying glass where foreperson did not explain intended use and trial judge did not inquire as to intended use, but jury request was read in presence of both parties and there was "no evidence in the record, nor [did] the defendant contend, that the jury understood the magnifying glass to have any bearing as evidence in the case or that the jury would use it improperly"); State v. Everson, 166 Wash. 534, 536-537, 7 P.2d 603 (1932) ("if [an] experiment [during jury deliberations] involves merely a more critical examination of an exhibit than had been made of it in the court, there is no ground **285of objection.... [T]he jury merely more critically examined [evidence] by the aid of a magnifying glass. This did not put them in possession *1275of material facts which were not already in evidence").
"Rather, by providing the jury with a magnifying glass, the [judge] permitted the jury to make a more critical examination of the exhibits introduced at trial." Young, 814 F.2d at 396, citing United States v. Beach, 296 F.2d 153, 158-159 (4th Cir. 1961). See United States v. Brewer, 783 F.2d 841, 843 (9th Cir.), cert. denied, 479 U.S. 831, 107 S.Ct. 118, 93 L.Ed.2d 64 (1986) ("We are unable to see how the use of the magnifying glass to view photographs differs from the use of corrective eyeglasses by jurors"); People v. Turner, 22 Cal. App. 3d 174, 183, 99 Cal.Rptr. 186 (1971) ("At most, the use of the magnifying glass involved an extension of the jury's sense of sight"); 2 McCormick on Evidence § 220 (K.S. Broun ed., 7th ed. 2016) (noting distinction between experiments constituting closer scrutiny of trial exhibit and experiments that go beyond evidence introduced in court).
The defendant's argument that "more than common knowledge was required" to analyze or compare video footage and still images is belied by the absence of any expert testimony about digital image coloration at trial, and counsel's own request that the jury closely scrutinize the surveillance video recording and still images. To the extent that digital image coloration processes may not comport with a lay viewer's understanding of what digital images depict, the judge accounted for this possibility and addressed it adequately by giving an instruction related to use of the magnifying glass at the time he gave the magnifying glass to the jury. The judge explained that no exhibit should be assumed to be an accurate depiction. Moreover, the jury in this case were not presented with images of fingerprints or handwriting samples, the comparison of which may be commonly understood to require scientific or technical knowledge.14 See People v. Moody, 195 A.D.2d 1016, 1016-1017, 600 N.Y.S.2d 581 (1993) (no error in granting jurors' request for magnifying glass during deliberations because magnifying glass enhances clarity of photographs similarly to reading glasses, and no fingerprint or handwriting comparisons were at **286issue). Compare United States v. George, 56 F.3d 1078, 1084 (9th Cir.), cert. denied, 516 U.S. 937, 116 S.Ct. 351, 133 L.Ed.2d 247 (1995) (concluding that "[n]o 'new evidence' resulted from the jurors' use of a magnifying glass to examine ... fingerprint cards and [a] gun"), with People v. Rhoden, 101 Ill. App. 3d 223, 226, 56 Ill.Dec. 746, 427 N.E.2d 1292 (1981) (noting that "the refusal to permit examination of fingerprint exhibits under magnification does not result in error," because "[t]he classification and method of comparison of fingerprints is a science requiring specialized study not common to most").
Additionally, the fact that the judge appears to have tested the magnifying glass he provided the jury refutes the argument that "there is nothing known about the power or quality of the magnifying glass" provided. As the judge explained:
"The Court, last night, purchased, personally, a ... 2M magnifying glass, thereby possibly removing the equipment deficiency. The Court then called someone at the Registry of Deeds, thinking that that system would have a magnifying glass. It did, and it has loaned us the magnifying glass, which appears to have somewhat similar resolution, *1276but easier to manipulate than the one that I purchased."
Overall, we conclude that the judge did not abuse his discretion in allowing the jurors' request for a magnifying glass, following consultation with the parties; in conducting independent investigation of the use and effects of a magnifying glass on specific trial exhibits; or in providing instructions to the jury designed to account for the possibility that digital images might contain distortions. See Evans v. United States, 883 A.2d 146, 151 (D.C. 2005), cert. denied, 549 U.S. 870, 127 S.Ct. 357, 166 L.Ed.2d 121 (2006), quoting Boland v. Dolan, 140 N.J. 174, 182, 657 A.2d 1189 (1995) ("where, as here, the jury make[ ] a formal request for a magnification device, which the trial court grants, 'the use of a magnifying glass by jurors for exhibits properly introduced at trial is within the trial court's discretion' "). See also Dixon v. A.J. Cunningham Co., 257 Mass. 63, 71, 153 N.E. 257 (1926) ; Commonwealth v. Pixley, 42 Mass. App. Ct. 927, 928, 677 N.E.2d 273 (1997).
b. Instruction on circumstantial evidence. The defendant contends that the judge's instructions on circumstantial evidence impermissibly lessened the burden of proof and violated his due process rights. Of course, the Commonwealth bears the burden of proving a defendant's guilt beyond a reasonable doubt. See Commonwealth v. Pinckney, 419 Mass. 341, 342, 644 N.E.2d 973 (1995), citing In re Winship, 397 U.S. 358, 364, 90 S.Ct. 1068, 25 L.Ed.2d 368 (1970). The judge properly instructed **287the jury in language that hewed very closely, indeed was nearly verbatim, to the instruction on reasonable doubt that we presented as authoritative in Commonwealth v. Russell, 470 Mass. 464, 477-478, 23 N.E.3d 867 (2015). Separately, the judge instructed on circumstantial evidence and inferences that could be drawn therefrom; he noted that circumstantial evidence was particularly important in this case because there was "no direct evidence of who committed the killing and how it occurred."
The judge illustrated the concepts of circumstantial evidence and inferences using the example of a firefighter who responds to a burning building, makes several observations, and comes to a reasoned inference that the owner of the building intentionally set the fire. In the example, a firefighter who responds to a fire sees the owner of a burning building lurking in the vicinity of the building as it burns; determines after professional investigation that the fire was caused by flammable material consistent with material that the owner recently purchased; determines that the fire was intentionally set; learns that the building was in tax foreclosure; learns that the owner had an insurance policy in case of fire; and infers that the fire was intentionally set by the building's owner.
The defendant argues that the judge's use of the arson example to explain circumstantial evidence and inferences "trivialized the [Commonwealth's] burden of proof by demonstrating that a chain of inferences satisfied the burden and therefore diminished it below the constitutional standard of due process secured by the Fifth and Fourteenth Amendments ... and [art.] 12." The defendant contends that the arson example "went improperly far beyond the simple example" presented in Instruction 3.100 of the Criminal Model Jury Instructions for Use in the District Court (2009), which provides an example of a mailbox owner who does not observe a mail carrier deliver mail, but is able to infer that a mail carrier arrived from the fact that the mailbox was empty in the morning but filled with mail at night. Overall, the defendant maintains, the judge in this case "gave the jury the impression *1277that a chain of inferences from circumstantial evidence was sufficient, leaving the jury with a diminished burden of proof."
Because the defendant did not object, we review to determine whether the instructions created a substantial likelihood of a miscarriage of justice. See **288Commonwealth v. Vizcarrondo, 427 Mass. 392, 392 n.1, 693 N.E.2d 677 (1998), S.C., 431 Mass. 360, 727 N.E.2d 821 (2000).15 We conclude that there was no error in the instructions, and therefore no substantial likelihood of a miscarriage of justice.16
"In considering whether a [jury] charge lowers the criminal standard of proof, we consider the charge, taken as a whole, and assess the possible impact of [an] alleged error on the deliberations of a reasonable juror, i.e., whether a reasonable juror could have used the instruction incorrectly."17 Commonwealth v. Rosa, 422 Mass. 18, 27, 661 N.E.2d 56 (1996). This inquiry is not purely speculative but, rather, must be supported by some evidence in the record. See Commonwealth v. O'Brian, 445 Mass. 720, 732, 840 N.E.2d 500, cert. denied, 549 U.S. 898, 127 S.Ct. 213, 166 L.Ed.2d 171 (2006) (in assessing reasonable doubt instruction, finding "no evidence that the jury did not understand the high degree of certainty required to find the defendant guilty"); Rosa, supra at 29, 661 N.E.2d 56 ("The jury in this case were quite discerning.... [T]hey ... distinguished between theories ... of murder. It is at best purely speculative to think that the jury were misled as to their responsibility to find proof beyond a reasonable doubt").
A review of the record in this case reveals no evidence that the jury could have failed to understand the "awesome duty of the jury to determine whether the defendant's guilt was proved beyond a reasonable doubt." Commonwealth v. Ferreira, 373 Mass. 116, 129, 364 N.E.2d 1264 (1977). First, the fact that this jury did not convict the defendant on a theory of deliberate premeditation indicates that they understood the high degree of certainty required to find the defendant guilty. See O'Brian, 445 Mass. at 732, 840 N.E.2d 500 (that "the jury did not convict the defendant of murder in the first degree on a theory of deliberate premeditation" illustrated jury's understanding of burden of proof). See also Rosa, 422 Mass. at 29, 661 N.E.2d 56.
Second, this case differs from Commonwealth v. Pomerleau, 10 Mass. App. Ct. 208, 406 N.E.2d 430 (1980), on which the defendant relies. In **289Pomerleau, supra at 213, 406 N.E.2d 430, the judge "attempted to convert [an] example [explaining circumstantial evidence and inferences] to one illustrating how doubt might be formed in the minds of the jurors," thereby leading to likely confusion over the relationship between successive inferences *1278and reasonable doubt. See id. at 214, 406 N.E.2d 430. Here, in contrast, the judge provided jurors with an unambiguous and adequate instruction on reasonable doubt, see Russell, 470 Mass. at 477-478, 23 N.E.3d 867, as well as separate and distinct instructions on circumstantial evidence and inferences to be drawn therefrom.
Third, the record makes clear that the jurors "were not left free to premise their verdict[s] on speculative inferences." Commonwealth v. Dostie, 425 Mass. 372, 377, 681 N.E.2d 282 (1997). The instructions on circumstantial evidence, of which the arson example formed one part, underscored that the practice of drawing inferences was "not guesswork." Moreover, the judge appropriately clarified that several "rules" constrain the practice of inference making. He explained that inferences must be drawn from the evidence, that each inference must be reasonable and not a guess, and that any inference constituting an element of an offense must be established beyond a reasonable doubt."18 The judge also properly emphasized that the drawing of inferences could favor the defendant. Finally, the judge instructed the jurors to consider evidence favoring an inference in conjunction with evidence standing against it, including the lack of evidence, in determining whether that evidence satisfied the standard of beyond a reasonable doubt.
To be sure, as we have explained in assessing questions of evidentiary insufficiency, "[t]here must be more than slight evidence to support each essential element [of a criminal conviction;] a conviction may not rest upon the piling of inference upon inference or conjecture and speculation" (quotation and citations omitted). Commonwealth v. Reaves, 434 Mass. 383, 390, 750 N.E.2d 464 (2001). Our review of the judge's instructions, however, persuades us that **290the instructions would not have suggested to a reasonable juror that the act of making successive inferences itself might erase reasonable doubt. Contrast Pomerleau, 10 Mass. App. Ct. at 213-214, 406 N.E.2d 430. Indeed, "we have permitted ... a jury to make an inference based on an inference to come to a conclusion of guilt or innocence ... [b]ut we require that each inference must be a reasonable and logical conclusion from the prior inference; we have made clear that a jury may not use conjecture or guesswork to choose between alternative inferences." Dostie, 425 Mass. at 376, 681 N.E.2d 282.
Taken as a whole, the judge's instructions on circumstantial evidence and inferences "correctly stated the relevant principles and essentially cautioned the jury to be sure of the strength and logic of any inferences they drew." See Commonwealth v. Schand, 420 Mass. 783, 795, 653 N.E.2d 566 (1995). The jury are presumed to follow all instructions they are given. Rosa, 422 Mass. at 29, 661 N.E.2d 56, citing Commonwealth v. Albert, 391 Mass. 853, 859, 466 N.E.2d 78 (1984). Accordingly, we do not agree with the defendant's contention that, "[i]n light of [the judge's] instructions, the jury [were] likely to believe that merely because circumstantial evidence built up, any doubt that they had *1279was unreasonable." We underscore that, moving forward, while in general "[t]he use of an illustration to explain an inference in connection with the concept of circumstantial evidence is permissible," Commonwealth v. Shea, 398 Mass. 264, 271, 496 N.E.2d 631 (1986), it is better practice to avoid examples in which hypothetical individuals commit crimes.
c. Defendant's statement to his coworker. The defendant argues that the judge erred in permitting Dias to testify to the defendant's statement on Monday, October 14, 2013, that, if he were to break into the neighbors' house, he would kill the neighbors, including their young child. The defendant asserts that any potential probative value in this statement was outweighed by the potential for prejudice, and that, as a result, the decision to allow the statement to be introduced denied the defendant his right to due process rights under the Federal and State Constitutions. Because the defendant objected at trial, we review for prejudicial error. See Commonwealth v. Montez, 450 Mass. 736, 744, 881 N.E.2d 753 (2008).
We conclude that the judge did not abuse his discretion in allowing Dias to testify about the defendant's prior statement, particularly in light of the limiting instruction that the judge provided immediately before Dias's testimony, and the clarifying instruction he provided immediately afterward. Accordingly, the admission of the statement did not violate the defendant's constitutional rights.
**291Before Dias testified about the defendant's statement, the judge instructed that the statement's "only purpose, I emphasize, is to, if it does, shed any light on any intent [the defendant] may have had with respect to [the victim] insofar as anything occurring on [the] date of [the killing]." The judge also instructed the jurors that they should ask themselves a threshold question, "[D]id the [d]efendant say that? ... If you don't believe he made [the statement], you don't pay any regard to it." Immediately after Dias testified about the defendant's out-of-court statement, the judge reminded jurors that they were to be "concerned [only] with [the defendant's] words, not with [Dias's] words, unless they give meaning to what the [d]efendant said. That's the limited purpose of his words."
"The trial judge is afforded substantial discretion in deciding whether, and for what purposes, evidence is relevant, and a trial judge's rulings on these questions are reversible only for an abuse of discretion" (citation omitted). Commonwealth v. McCowen, 458 Mass. 461, 485, 939 N.E.2d 735 (2010). Evidence that may be inadmissible for the purpose of demonstrating a defendant's character or propensity to commit the charged crime "may be admissible, if relevant, for other purposes, including proof of motive," Commonwealth v. Mendes, 441 Mass. 459, 464, 806 N.E.2d 393 (2004), or intent. See Mass. G. Evid. § 404(b) (2019).
Here, we cannot say that the judge abused his discretion in determining that the defendant's statement shed further light on his intent, i.e., to rob and to kill in connection with a robbery; nor can we say that the judge abused his discretion in determining that the probative value of the statement outweighed any risk of unfair prejudice. That Dias already had testified about the defendant's separate statement regarding killing and robbing the victim does not, as the defendant suggests, make his statement about the neighbors irrelevant to proving his intent. The statement at issue was made on the day the victim was killed, days after the defendant's earlier statement about the victim; it reasonably may have tended to show that the defendant had been serious in his stated intent to rob and kill in connection with a *1280robbery, and that he was not, as Dias assumed, merely "messing around" when he said it. The potential for undue prejudice was mitigated in some part by Dias's testimony about the defendant's earlier statement concerning robbing and killing the victim. In addition, the limiting instructions alleviated the risk that the jury would rely on the statement for an improper purpose. See Rosa, 422 Mass. at 29, 661 N.E.2d 56 **292(jury are presumed to follow judge's instructions).
d. Relief pursuant to G. L. c. 278, § 33E. We have reviewed the record, in accordance with our statutory duty under G. L. c. 278, § 33E, and identify no basis upon which to order a new trial or to reduce the degree of guilt.
Judgments affirmed.